Trigonometry
SP.X.v.trig.0017.1D
a = #a, #tD]]>
1.0000000
0.3333333
0
0
#sD
<question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>{</mo><pi/><mo>/</mo><mn>3</mn><mo>,</mo><pi/><mo>/</mo><mn>4</mn><mo>,</mo><pi/><mo>/</mo><mn>6</mn><mo>,</mo><mo>-</mo><pi/><mo>/</mo><mn>3</mn><mo>,</mo><mo>-</mo><pi/><mo>/</mo><mn>4</mn><mo>,</mo><mo>-</mo><pi/><mo>/</mo><mn>6</mn><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mi>random</mi><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>*</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msub><mi>A</mi><mi>i</mi></msub><mo>+</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1</mi><mo>=</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi><mo>=</mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi><mo>=</mo><mi>tan</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi><mo>=</mo><mi>cotan</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>"</mo><mo> </mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo> </mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>"</mo><mo> </mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mo>"</mo><mo> </mo><mi>tg</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mo> </mo><mo>"</mo><mi>ctg</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tA</mi><mo>=</mo><mo>"</mo><mi>arcsin</mi><mo>(</mo><mo>(</mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo> </mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tB</mi><mo>=</mo><mo>"</mo><mi>arccos</mi><mo>(</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tC</mi><mo>=</mo><mo>"</mo><mo> </mo><mi>arctg</mi><mo>(</mo><mi>ctg</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tD</mi><mo>=</mo><mo>"</mo><mi>arcctg</mi><mo>(</mo><mi>tg</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo> </mo><mo> </mo><mo> </mo><mo>.</mo><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sA</mi><mo>=</mo><mi>asin</mi><mo>(</mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sB</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sC</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>cotan</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sD</mi><mo>=</mo><mi>acotan</mi><mo>(</mo><mi>tan</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mn>13</mn><mo>*</mo><pi/></mrow><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><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>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo></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>tan</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cotan</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>asin</mi><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.5236</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sA</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><pi/><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sB</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><pi/><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sC</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><pi/><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sD</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><pi/><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sE</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sE</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sF</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sF</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s1a</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2b</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3c</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4d</mi></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>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sD</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</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"></data></localData></question>