Pre-Calc/Trig Unit 2: Circular Functions/3.3 Unit Circle
Angle for exact value (Cos-3rd quadrant)
Find the exact value of θ in the given interval that has the given circular function value.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»,«/mo»«mfrac»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«/math»; cos θ = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math»
]]>
1.0000000
0.3333333
0
0
#answer]]>
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Angle for exact value (Sin-2nd quadrant) *issue w/decimals
Find the exact value of θ in the given interval that has the given circular function value.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mfrac»«mi mathvariant=¨normal¨»§#960;«/mi»«mn»2«/mn»«/mfrac»«mo»,«/mo»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«/mfenced»«/math»; sin θ = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math»
]]>
1.0000000
0.3333333
0
0
#answer]]>
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Angle for exact value (Tan-3rd quadrant)
Find the exact value of θ in the given interval that has the given circular function value.
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨normal¨»§#960;«/mi»«mo»,«/mo»«mfrac»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»§#960;«/mi»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mfenced»«/math»; tan θ = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«/math»
]]>
1.0000000
0.3333333
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0
#answer]]>
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Evaluate sin w/calculator
Use a calculator to evaluate the function. Round to 4 decimal places.
sin #a
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1.0000000
0.3333333
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Exact value-radians (Cos)
Find the exact circular function value. Give answer as a properly simplified fraction.
cos #a
]]>
1.0000000
0.3333333
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#answer]]>
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Exact value-radians (Sin)
Find the exact circular function value. Give answer as a properly simplified fraction.
Sin #a
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0.3333333
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#answer]]>
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Exact value-radians (Tan)
Find the exact circular function value. Give answer as a properly simplified fraction.
Tan #a
]]>
1.0000000
0.3333333
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#answer]]>
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Find the exact value of s in the given interval that has the given circular ...
Find the exact value of s in the given interval that has the given circular function value.
; tan s = 1]]>
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1.0000000
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true
true
abc
]]>
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
Correct
]]>
/9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAAmAA8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9EfGXx38KeBPEX9h6lH4iutS2o2zRvCuqaogLKzKpktbaRA+1GbZu3ADJGMGuh8BePNH+Jfhi18QaC17Jpd0W8mS/065sJHAOCfKuI0fHoduD1BNM1nwlNrPivT9UbU5ILOzsLu1W0hQq5mmMWJ/M3cFEjdQNp/1pOeBWb8GvBGtfDX4c6N4W1vX7fxLJpFvHY2uoQaebJmto0VIhKhlkDSAL8zqVDdkXu0lbX+tX/wAB/wDB0B9Lf1/X9dzyr4zfBr4F/CD4aeIPFbfAnwNrU2m2c1zDptv4asEe5aONpCu4wkIoVGZmwdqqxwSAD6t8Mfhp4H8A6Y154N8FeH/Bv9rQwy3aaFpkFn52FJQSGJF37fMfGem5sYya4b9qb4NeLvi54JvbTwZ4km0jV59Ou9K+xzXNrb2MsVymyR5Xk0+7lyAANsXlkgsN6k5r0j4aaVreheANA07xJcJda7aWccN3PHcLOryKMEiRYIA2cdRDH/u1ScHT/vX/AAHKy5UvP9Lfr/VjpqKKKgR//9k=
Incorrect
]]>
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
Incorrect
]]>
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Incorrect
Find the exact value of s in the given interval that has the given circular ...
Find the exact value of s in the given interval that has the given circular function value.
; sin s = 
]]>
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1.0000000
0.3333333
0
true
true
abc
]]>
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Correct
]]>
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Incorrect
]]>
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Incorrect
]]>
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Incorrect
Inverse sec (decimal) ***Wrong
Find the value of t in the interval [0, π/2] that makes the statement true. Round to the thousandths place.
sec t = #a
]]>
1.0000000
0.3333333
0
0
#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>2</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>9</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><mrow><mo>(</mo><mi>arccos</mi><mo> </mo><mi>a</mi><mo>)</mo></mrow></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>
Inverse tan (decimal)
Find the value of s in the interval [0, π/2] that makes the statement true. Round to the thousandths place.
tan s = #a
]]>
1.0000000
0.3333333
0
0
#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>4</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>6</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><mi>arctan</mi><mo> </mo><mi>a</mi></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></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>
Solve the problem.The maximum afternoon temperature in Granderson is modeled ...
Solve the problem.
The maximum afternoon temperature in Granderson is modeled by 
where t represents the maximum afternoon temperature in degrees Fahrenheit in month x, with 
representing January, 
representing February, and so on. Find the maximum afternoon temperature in May.]]>
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
1.0000000
0.3333333
0
true
true
abc
77°F
Correct
88°F
Incorrect
47°F
Incorrect
82°F
Incorrect