Pre-Calc/Trig Unit 1: Trig Functions/1.4 Using Trig FunctionsCos function given ordered pairSuppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ.
(#a , #b ); Find cos θ
Give answer as a simplified fraction
]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mi>a</mi><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Identify the quadrant for the angle θ satisfying the following conditions....Identify the quadrant for the angle θ satisfying the following conditions.
sin θ > 0 and cos θ < 0]]>1.00000000.33333330truetrueabcQuadrant IICorrectQuadrant IIncorrectQuadrant IIIIncorrectQuadrant IVIncorrectSin function given ordered pairSuppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ.
(#a , #b ); Find sin θ
Give answer as a simplified fraction
]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mi>b</mi><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Tan function given ordered pairSuppose that θ is in standard position and the given point is on the terminal side of θ. Give the exact value of the indicated trig function for θ.
(#a , #b ); Find tan θ
Give answer as a simplified fraction
]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Trig Values given quadrant IIFind tan θ, given that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»=«/mo»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math» and θ is in quadrant II. Enter answer as a simplified fraction.]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo> </mo><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mo>-</mo><mfrac><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt><mi>a</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Trig Values given quadrant IIIFind cos θ, given that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»tan«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math» and θ is in quadrant II. Enter answer as a simplified fraction.]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo> </mo><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mo>-</mo><mfrac><mi>b</mi><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Trig Values given quadrant IVFind sin θ, given that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»cos«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math» and θ is in quadrant IV. Enter answer as a simplified fraction.]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo> </mo><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mo>-</mo><mfrac><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt><mi>b</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Trig Values given sign of cofunctionFind cos θ, given that «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»tan«/mi»«mo»§#160;«/mo»«mi»§#952;«/mi»«mo»=«/mo»«mo»-«/mo»«mfrac»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/mfrac»«/math» and sin θ > 0. Enter answer as a simplified fraction.]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo> </mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mo>-</mo><mfrac><mi>b</mi><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">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">null</data></localData></question> Use Reciprocal Identities (Fractions)Use the appropriate identity to find the indicated function value. Simplify the fraction.
cos θ, given that sec θ = #a
]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mn>1</mn><mi>a</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></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">null</data></localData></question> Use Reciprocal Identity (Decimal)Use the appropriate identity to find the indicated function value. If the given value is a decimal, round your answer to three decimal places.
cot θ, given that tan θ = #a]]>1.00000000.333333300#answer]]>
<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>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>0004</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mn>1</mn><mi>a</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</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">null</data></localData></question>