1MA 01. TRIGONOMETRIA/1MA.01.3 Relació entre raons 1MA.01.3.10DT RELACIÓ FONAMENTAL

Relació fonamental

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/math»

Se'n dedueix que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»cos§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#177;«/mo»«msqrt mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mrow»«/mstyle»«/math»

Calculadora: si cosα = 0,5 cal escriure: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt/»«mfenced»«mrow»«mn»1«/mn»«mo»-«/mo»«mn»0«/mn»«mo».«/mo»«msup»«mn»5«/mn»«mn»2«/mn»«/msup»«/mrow»«/mfenced»«/math»

Es recorda que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»tg§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»sin§#945;«/mi»«mi mathvariant=¨bold¨»cos§#945;«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1MA.01.3.11Q cos → sin El cosinus d'un angle del quadrant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calculeu el seu sinus sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 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="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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>q</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>q1</mi><mo>*</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mfrac><mn>7</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</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"><mfrac><msqrt><mn>51</mn></msqrt><mn>10</mn></mfrac></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="check_simplified"/><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">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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal emprar l'expressió: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#177;«/mo»«msqrt mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mrow»«/mstyle»«/math» i pensar que el signe depèn del quadrant.

]]> 1MA.01.3.12Q cos → tg El cosinus d'un angle del quadrant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula la seva tangent sense calcular l'angle

Format de la resposta: fracció o arrel simplificades.

]]> 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="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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>q</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s11</mi><mo>=</mo><mi>q1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>s11</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mfrac><mn>9</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>19</mn></msqrt><mn>10</mn></mfrac></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"><mo>-</mo><mfrac><msqrt><mn>19</mn></msqrt><mn>9</mn></mfrac></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="check_simplified"/><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">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> Primer es calcula el sinus amb l'expressió:«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#177;«/mo»«msqrt mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mrow»«/mstyle»«/math» i pensar que el signe depèn del quadrant; després es calcula tg = sin/cos

]]> 1MA.01.3.25Q sin → tg El sinus d'un angle del quadrant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«/mrow»«/mstyle»«/math» és«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mstyle»«/math».
Calculeu la seva tangent sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 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="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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>q</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mfrac><mi>c_1</mi><mn>10</mn></mfrac></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s11</mi><mo>=</mo><mi>q1</mi><mo>*</mo><mi>s1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>c</mi><mi>s11</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>3</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>91</mn></msqrt><mn>10</mn></mfrac></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"><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>91</mn></msqrt></mrow><mn>91</mn></mfrac></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="check_simplified"/><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">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> Cal emprar l'expressió: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cosa«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#177;«/mo»«msqrt mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«/msqrt»«/mrow»«/mstyle»«/math»
i pensar que el signe depèn del quadrant.

Un cop trobat el cosinus, es recorda que tgx = sinx/cosx

]]> 1MA.01.3.31Q tg → sin La tangent d'un angle del quadrant «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/mi»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula el seu sinus sense calcular l'angle.

Format de la resposta: fracció o arrel simplificada i racionalitzada

]]> 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="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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>q</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mi>c_10</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msqrt><mfrac><msup><mi>c</mi><mn>2</mn></msup><mrow><mn>1</mn><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfrac></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>q1</mi><mo>*</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>74</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>74</mn><mo>*</mo><msqrt><mn>5477</mn></msqrt></mrow><mn>5477</mn></mfrac></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"><mfrac><mrow><mn>74</mn><mo>*</mo><msqrt><mn>5477</mn></msqrt></mrow><mn>5477</mn></mfrac></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="check_simplified"/><assertion name="check_rationalized"/><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">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> Cal resoldre el sistema següent:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mspace linebreak=¨newline¨/»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi mathvariant=¨bold¨»sinx«/mi»«mi mathvariant=¨bold¨»cosx«/mi»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»tga«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mrow»«/mstyle»«/math»

Si es divideix la 1a equació per sin²x:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sinx«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#177;«/mo»«msqrt mathcolor=¨#00007F¨»«mfrac»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/msqrt»«/mrow»«/mstyle»«/math»

]]> 1MA.01.3.32Q tg → cos La tangent d'un angle del quadrant #q és #c.
Calcula el seu cosinus sense calcular l'angle

Format de la resposta: fracció o arrel simplificada i racionalitzada

]]> 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="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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>q</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>q</mi><mo>=</mo><mn>3</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mtd></mtr></mtable><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mo>-</mo><mi>c_1</mi></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><msqrt><mfrac><mn>1</mn><mrow><mn>1</mn><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></mfrac></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>q1</mi><mo>*</mo><mi>s1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>485</mn></msqrt><mn>485</mn></mfrac></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"><mo>-</mo><mfrac><msqrt><mn>485</mn></msqrt><mn>485</mn></mfrac></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="check_simplified"/><assertion name="check_rationalized"/><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">8</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> Cal resoldre el sistema següent:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mspace linebreak=¨newline¨/»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi mathvariant=¨bold¨»sinx«/mi»«mi mathvariant=¨bold¨»cosx«/mi»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»tga«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«/mstyle»«/math»

si es substitueix sinx per tga·cosa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#00007F¨»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«msup»«mi mathvariant=¨bold¨»tg«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1MA.01.3.50DT RAONS DE L'ANGLE COMPLEMENTARI Raons de l'angle complementari

sin (90º-a) = cos a

cos(90º - a) = sin a

tg (90º - a) = 1/tg a

]]> 0.0000000 0.0000000 0 1MA.01.3.51Q sin(90-a) El sinus d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula el sinus del seu complementari sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.52Q cos(90-a) El cosinus d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula el cosinus del seu complementari sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.53Q tg(90-a) La tangent d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula la tangent del seu complementari sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 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="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>(</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac><mo>,</mo><mn>1</mn><mo>,</mo><msqrt><mn>3</mn></msqrt><mo>)</mo></mtd></mtr></mtable></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>c</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mrow><mrow><mi>sol</mi><mo>=</mo><msqrt><mn>3</mn></msqrt></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><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"><mi>q</mi><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></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"><mfrac><mn>1</mn><mn>2</mn></mfrac></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="check_simplified"/><assertion name="check_rationalized"/><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">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¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tg«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»90«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»tga«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1MA.01.3.61Q sin(π/2-a) Si sina és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math» quant val «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»sin«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mfrac»«mi mathvariant=¨bold¨»§#960;«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»§#945;«/mi»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.62Q cos(π/2-a) Si el cosinus d'un angle a és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math», quin és el cosinus de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#003300¨»«mrow»«mfrac»«mi mathvariant=¨bold¨ mathsize=¨12px¨»§#960;«/mi»«mn mathvariant=¨bold¨ mathsize=¨12px¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mi mathvariant=¨bold¨ mathsize=¨12px¨»a«/mi»«/mrow»«/mfenced»«/math»

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.63Q tg(π/2-a) Si la tangent d'un angle a és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math», quina és la tangent de l'angle «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨»«mrow»«mfrac»«mi mathvariant=¨bold¨»§#960;«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.70DT RAONS ANGLE SUPPLEMENTARI Raons de l'angle suplementari

sin (180º-a) = sin a

cos(180º - a) = - cos a

tg (180º - a) = - tg a

]]> 0.0000000 0.0000000 0 1MA.01.3.71Q sin(180-a) El sinus d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula el sinus del seu suplementari sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.72Q cos(180-a) El cosinus d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula el cosinus del seu suplementari sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.73Q tg(180-a) La tangent d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math».
Calcula la tangent del seu suplementari sense calcular l'angle.

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.81Q sin(π-a) El sinus d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math». Quin és el sinus de π - a

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.82Q cos(π-a) El cosinus d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math». Quin és el cosinus de π - a

Format de la resposta: fracció o arrel simplificades.

]]> 1MA.01.3.83Q tg(π-a) La tangent d'un angle és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«/mrow»«/mstyle»«/math». Quina és la tangent de π - a

Format de la resposta: fracció o arrel simplificades.

]]>