1MA 01. TRIGONOMETRIA/1MA.01.5 EqTrigonomètriques 1MA.01.5.00DT EQUACIONS TRIGONOMÈTRIQUES Equacions trigonomètriques

Es resolen fàcilment,

emprant la taula de les raons trigonomètriques dels angles de 0,30º,45º,60º,90º)
fent servir les funcions inverses de la calculadora (shift+sin, shift+cos, shift+tan)

Propietats aplicables

sina = sin(180º-a) = sin(π -a)

cosa = cos (-a)

tga = tg(180º+a) = tg(π+a)

]]> 0.0000000 0.0000000 0 1MA.01.5.10DT RAONS DE 0,30,... a sina cosa tga a sina cosa tga 0 0 1 0 210º=7π/6 -1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/mstyle»«/math» 30º=π/6 1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/mstyle»«/math» 225º=5π/4 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» 1 45º=π/4 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» 1 240º=4π/3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math»
-1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mstyle»«/math» 60º=π/3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» 1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mstyle»«/math» 270º=3π/2 -1 0 ∞ 90º=π/2 1 0 ∞ 300º=5π/3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» 1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mstyle»«/math» 120º=2π/3 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» -1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mstyle»«/math» 315º=7π/4 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» -1 135º=3π/4 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» -1 330º=11π/6 -1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/mrow»«/mstyle»«/math» 150º=5π/6 1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/mrow»«/mstyle»«/math» 360º=2π 0 1 0 180º=π 0 -1 0 ]]> 0.0000000 0.0000000 0 1MA.01.5.11Q EquacióSinRadiants Resol: sin x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: en radiants: π i fraccions de π «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»{«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»4«/mn»«/mfrac»«mo»+«/mo»«mn»2«/mn»«mi»k§#960;«/mi»«mo»}«/mo»«/mrow»«/mstyle»«/math»

L'altre angle és π menys el que hem deduït de la taula.

]]> 1MA.01.5.12Q EquacióCosRadiants Resol: cos x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»

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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo»§#160;«/mo»«/mstyle»«/math» és el cosinus de 2 angles de la primera volta:

Per tant, les dues solucions són:

Es transformen a positives si cal.

]]> 1MA.01.5.13Q EquacióTgRadiants Resol: tg x = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«/mrow»«/mstyle»«/math»

L'altre angle és π+α

]]> 1MA.01.5.21Q EquacióSinus(ax+b)Radiants Resol l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

Format del resultat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»+«/mo»«mfrac»«mi»k§#960;«/mi»«mn»3«/mn»«/mfrac»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»k«/mi»«mi»§#960;«/mi»«/mrow»«mn»3«/mn»«/mfrac»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»g«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»p«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>11</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><pi/><mo>)</mo><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>asin</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w1</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>w11</mi><mo>=</mo><mi>w1</mi></mrow><mrow><mi>w11</mi><mo>=</mo><mi>w1</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><pi/><mo>-</mo><mi>w1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w2</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>w21</mi><mo>=</mo><mi>w2</mi></mrow><mrow><mi>w21</mi><mo>=</mo><mi>w2</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x11</mi><mo>=</mo><mfrac><mrow><mi>w11</mi><mo>-</mo><mi>b</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x11</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>x1</mi><mo>=</mo><mi>x11</mi></mrow><mrow><mi>x1</mi><mo>=</mo><mi>x11</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x21</mi><mo>=</mo><mfrac><mrow><mi>w21</mi><mo>-</mo><mi>b</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x21</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>x2</mi><mo>=</mo><mi>x21</mi></mrow><mrow><mi>x2</mi><mo>=</mo><mi>x21</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>k</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>k</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>b</mi><mo>*</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>w11</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>w21</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>arc</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>w11</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>circumferència</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>segment</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>circumferència</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>segment</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mrow><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></mrow></mfenced><mo>=</mo><mo>-</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>,</mo><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><pi/><mn>4</mn></mfrac><mo>,</mo><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w11</mi><mo>,</mo><mi>w21</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>7</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac><mo>,</mo><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>x2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><pi/><mn>10</mn></mfrac><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><pi/></mrow><mn>5</mn></mfrac><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><pi/><mn>10</mn></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><pi/></mrow><mn>5</mn></mfrac><mo>*</mo><mi>k</mi></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>,</mo><mi>G2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi><mo>,</mo><mi>tauler2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">6</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math» és el sinus de 2 angles de la primera volta:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»11«/mn»«/mstyle»«/math» : #G1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»21«/mn»«/mstyle»«/math»: #G2

Per tant, cal resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> Per resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Es transformen els angles a positius si cal.

]]> 1MA.01.5.22Q EquacióCos(ax+b)Radiants Resol l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

Format del resultat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»+«/mo»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mo»-«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mi»k«/mi»«mi»§#960;«/mi»«/mrow»«/mfenced»«/math»

i que #w1 i #w2 (=-#w1)tenen el mateix cosinus,

cal resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold-italic¨»k«/mi»«mi mathvariant=¨bold-italic¨»§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1MA.01.5.23Q Equació tg(ax+b) radiants Resol l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

Format del resultat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mrow»«mi»x«/mi»«mo»=«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»+«/mo»«mi»k§#960;«/mi»«mo»,«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«mo»+«/mo»«mi»k«/mi»«mi»§#960;«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»n«/mi»«mi mathvariant=¨bold-italic¨»g«/mi»«mi mathvariant=¨bold-italic¨»l«/mi»«mi mathvariant=¨bold-italic¨»e«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»p«/mi»«mi mathvariant=¨bold-italic¨»o«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»t«/mi»«mi mathvariant=¨bold-italic¨»i«/mi»«mi mathvariant=¨bold-italic¨»u«/mi»«mi mathvariant=¨bold-italic¨»s«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>11</mn><mn>6</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mn>3</mn><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac><mo>,</mo><mn>1</mn><mo>,</mo><msqrt><mn>3</mn></msqrt></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mfenced><mrow><mi>tan</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><pi/><mo>)</mo><mo>=</mo><mi>c</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo>=</mo><pi/><mo>+</mo><mi>z1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>z1</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>w11</mi><mo>=</mo><mi>z1</mi></mrow><mrow><mi>w11</mi><mo>=</mo><mi>z1</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>z2</mi><mo>⩾</mo><mn>2</mn><mo>*</mo><pi/></mrow><mrow><mi>w21</mi><mo>=</mo><mi>z2</mi><mo>-</mo><mn>2</mn><mo>*</mo><pi/></mrow><mrow><mi>w21</mi><mo>=</mo><mi>z2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>min</mi><mo>(</mo><mi>w11</mi><mo>,</mo><mi>w21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>max</mi><mo>(</mo><mi>w11</mi><mo>,</mo><mi>w21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x11</mi><mo>=</mo><mfrac><mrow><mi>w1</mi><mo>-</mo><mi>b</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x11</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>x1</mi><mo>=</mo><mi>x11</mi></mrow><mrow><mi>x1</mi><mo>=</mo><mi>x11</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x21</mi><mo>=</mo><mfrac><mrow><mi>w2</mi><mo>-</mo><mi>b</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>x21</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>x2</mi><mo>=</mo><mi>x21</mi></mrow><mrow><mi>x2</mi><mo>=</mo><mi>x21</mi><mo>+</mo><mn>2</mn><mo>*</mo><pi/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>x1</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>k</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mi>x2</mi><mo>+</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>k</mi><mo>*</mo><pi/></mrow><mi>a</mi></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>b</mi><mo>*</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>w1</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>w2</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>arc</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>w1</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>circumferència</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>segment</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>arc</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>w2</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>circumferència</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>segment</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mfenced><mrow><mi>x</mi><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></mrow></mfenced><mo>=</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><pi/></mrow><mn>2</mn></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><pi/><mn>2</mn></mfrac></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z1</mi><mo>,</mo><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><pi/><mn>4</mn></mfrac><mo>,</mo><mfrac><pi/><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>z2</mi><mo>,</mo><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac><mo>,</mo><mfrac><mrow><mn>5</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>,</mo><mi>G2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi><mo>,</mo><mi>tauler2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">6</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo»§#160;«/mo»«/mrow»«/mstyle»«/math» és la tangent de 2 angles de la primera volta:

Per tant, cal resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> Per resoldre cada una de les equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mfenced open=¨{¨ close=¨}¨»«mtable mathcolor=¨#00007F¨ columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mi mathvariant=¨bold¨»k§#960;«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfrac»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1MA.01.5.31Q Equació sin(ax+b) graus Resol l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

Format del resultat: {x=31+90k,x=320+90k} graus arrodonits sense unitats i positius (suma 360º, si cal)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>35</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>111</mn><mo>,</mo><mn>999</mn></mrow></mfenced></mrow><mn>1000</mn></mfrac><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>b</mi><mo>*</mo><mfrac><pi/><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>sin</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>)</mo><mo>=</mo><mi>c</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><msub><mi>R</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s1</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>t1</mi><mo>=</mo><mn>360</mn><mo>+</mo><mi>s1</mi></mrow><mrow><mi>t1</mi><mo>=</mo><mi>s1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>s2</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>t2</mi><mo>=</mo><mn>360</mn><mo>+</mo><mi>s2</mi></mrow><mrow><mi>t2</mi><mo>=</mo><mi>s2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>t1</mi><mo>+</mo><mfrac><mrow><mi>k</mi><mo>*</mo><mn>360</mn></mrow><mi>a</mi></mfrac><mo>,</mo><mi>x</mi><mo>=</mo><mi>t2</mi><mo>+</mo><mfrac><mrow><mi>k</mi><mo>*</mo><mn>360</mn></mrow><mi>a</mi></mfrac></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mrow><mi>asin</mi><mo>(</mo><mi>c</mi><mo>)</mo><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>w1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>asin</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>⩾</mo><mn>0</mn></mrow><mrow><mi>t11</mi><mo>=</mo><mi>t1</mi></mrow><mrow><mi>t11</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>+</mo><mi>t1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><pi/><mo>-</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>arc</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>t11</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>circumferència</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>segment</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>arc</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>t2</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>circumferència</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mn>1</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>segment</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>c</mi></mrow></mfenced><mo>,</mo><mi>punt</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mi>c</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mfenced><mrow><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>110</mn></mrow></mfenced><mo>=</mo><mn>0.258</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>0.41473</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>0.24019</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>90</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>336</mn><mo>,</mo><mi>x</mi><mo>=</mo><mn>90</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>14</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>,</mo><mi>t11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>0.26095</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>,</mo><mi>t2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>165</mn><mo>,</mo><mn>2.8806</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>,</mo><mi>G2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi><mo>,</mo><mi>tauler2</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">6</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«/mrow»«/mstyle»«/math» (en verd) és el sinus de dos angles:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math»º : #G1 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#176;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»180«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«/mstyle»«/math»: #G2

Cal resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«mo mathvariant=¨bold¨»§#186;«/mo»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«mo mathvariant=¨bold¨»§#186;«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1MA.01.5.32Q Equació cos(ax+b) graus Resol l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

Fes servir cos a = cos (-a)

Format del resultat: {x=31+90k,x=320+90k} graus arrodonits sense unitats i positius (sumeu 360º, si cal)

i que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»w«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/math» tenen el mateix cosinus,

cal resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 1MA.01.5.33Q Equació tg(ax+b) graus Resol l'equació: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math»

Format del resultat: {x=30+90k,x=320+90k} graus arrodonits sense unitats i positius (sumeu 360º, si cal)

cal resoldre les dues equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»w«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»360«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

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