1MA 01. TRIGONOMETRIA/1MA.01.3 Relació entre raons 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»

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