1MA 01. TRIGONOMETRIA/1MA.01.5 EqTrigonomètriques 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>&lt;</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 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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 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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»

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