Question 1

Evaluate.
-$$\cos \left( \frac { \pi } { 6 } + 2918 \pi \right)$$

Accepted Answer

A)  $\sqrt { 3 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ 
A)  $\sqrt { 3 }$ 
B)  $- \frac { 1 } { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  $\frac { 1 } { 2 }$ C

Question 2

Use a calculator to solve for x in the given interval
-$\sin \theta = 0.7231,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Accepted Answer

A)  $- 46.31 ^ { \circ }$ 
B)  $46.31 ^ { \circ }$ 
C)  $136.31 ^ { \circ }$ 
D)  $35.87 ^ { \circ }$ 
A)  $- 46.31 ^ { \circ }$ 
B)  $46.31 ^ { \circ }$ 
C)  $136.31 ^ { \circ }$ 
D)  $35.87 ^ { \circ }$ B

Question 3

Find the exact solution to the equation without a calculator.
-$$\cos ^ { - 1 } ( \cos x ) = \frac { 1 } { 4 }$$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  4 
D)  0 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 8 }$ 
C)  4 
D)  0 A

Question 4

Find the exact value of the composition.
-$$\cos ^ { - 1 } \left( \cos \left( - \frac { \pi } { 6 } \right) \right)$$

Accepted Answer

A)  $\frac { 5 \pi } { 6 }$ 
B)  $\frac { 7 \pi } { 6 }$ 
C)  $- \frac { \pi } { 6 }$ 
D)  $\frac { \pi } { 6 }$ 
A)  $\frac { 5 \pi } { 6 }$ 
B)  $\frac { 7 \pi } { 6 }$ 
C)  $- \frac { \pi } { 6 }$ 
D)  $\frac { \pi } { 6 }$

Question 5

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined."
-$\tan \left( 1350 ^ { \circ } \right)$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  0 
D)  undefined 
A)  1 
B)  $- 1$ 
C)  0 
D)  undefined

Question 6

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle.
-$20 ^ { \circ }$

Accepted Answer

A)  $110 ^ { \circ } : - 70 ^ { \circ }$ 
B)  $200 ^ { \circ } - 160 ^ { \circ }$ 
C)  $ 380^{\circ} ;-160^{\circ} $ 
D)  $380 ^ { \circ } \cdot - 3400 ^ { \circ }$ 
A)  $110 ^ { \circ } : - 70 ^ { \circ }$ 
B)  $200 ^ { \circ } - 160 ^ { \circ }$ 
C)  $ 380^{\circ} ;-160^{\circ} $ 
D)  $380 ^ { \circ } \cdot - 3400 ^ { \circ }$

Question 7

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\csc \theta = \frac { 5 } { 2 } ; \cos \theta$

Accepted Answer

A)  $\frac { \sqrt { 21 } } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  $\frac { 2 } { \sqrt { 21 } }$ 
D)  $\frac { \sqrt { 21 } } { 2 }$ 
A)  $\frac { \sqrt { 21 } } { 5 }$ 
B)  $\frac { 2 } { 5 }$ 
C)  $\frac { 2 } { \sqrt { 21 } }$ 
D)  $\frac { \sqrt { 21 } } { 2 }$

Question 8

Find the zeros of the function in the interval $ [-2 \pi, 2 \pi] $.
-$$f ( x ) = \frac { 1 } { 2 } \cos 2 x$$

Accepted Answer

A)  $\pm \frac { \pi } { 2 } , \pm \frac { 3 \pi } { 2 }$ 
B)  $\pm \pi , \pm 3 \pi$ 
C)  $0 , \pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 }$ 
D)  $\pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 } , \pm \frac { 5 \pi } { 4 } , \pm \frac { 7 \pi } { 4 }$ 
A)  $\pm \frac { \pi } { 2 } , \pm \frac { 3 \pi } { 2 }$ 
B)  $\pm \pi , \pm 3 \pi$ 
C)  $0 , \pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 }$ 
D)  $\pm \frac { \pi } { 4 } , \pm \frac { 3 \pi } { 4 } , \pm \frac { 5 \pi } { 4 } , \pm \frac { 7 \pi } { 4 }$

Question 9

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined."
-$\tan 720 ^ { \circ }$

Accepted Answer

A)  undefined 
B)  0 
C)  $- 1$ 
D)  1 
A)  undefined 
B)  0 
C)  $- 1$ 
D)  1

Question 10

Evaluate without using a calculator by using ratios in a reference triangle.
-$\cot \frac { 3 \pi } { 4 }$

Accepted Answer

A)  $- \sqrt { 2 }$ 
B)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
C)  $- \frac { \sqrt { 3 } } { 2 }$ 
D)  $- 1$ 
A)  $- \sqrt { 2 }$ 
B)  $- \frac { 2 \sqrt { 3 } } { 3 }$ 
C)  $- \frac { \sqrt { 3 } } { 2 }$ 
D)  $- 1$

Question 11

Choose the point on the terminal side of .
-$$\theta = \frac { 11 \pi } { 6 }$$

Accepted Answer

A)  $( 1 , - \sqrt { 3 } )$ 
B)  $( 1 , - 1 )$ 
C)  $( - \sqrt { 3 } , 1 )$ 
D)  $( \sqrt { 3 } , - 1 )$ 
A)  $( 1 , - \sqrt { 3 } )$ 
B)  $( 1 , - 1 )$ 
C)  $( - \sqrt { 3 } , 1 )$ 
D)  $( \sqrt { 3 } , - 1 )$

Question 12

Write the word or phrase that best completes each statement or answers the question.
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior.
-f(x) = sec 2x

Accepted Answer

Domain: All reals except odd multiples o

Question 13

Choose the point on the terminal side of .
-$$\theta = - 45 ^ { \circ }$$

Accepted Answer

A)  $( 4 , - 4 )$ 
B)  $( 5,5 )$ 
C)  $( - 2,2 )$ 
D)  $( - 3 , - 3 )$ 
A)  $( 4 , - 4 )$ 
B)  $( 5,5 )$ 
C)  $( - 2,2 )$ 
D)  $( - 3 , - 3 )$

Question 14

Find the exact value of the real number y.
-$$y = \cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$$

Accepted Answer

A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $\frac { 11 \pi } { 6 }$ 
D)  $\frac { \pi } { 4 }$ 
A)  $\frac { 7 \pi } { 4 }$ 
B)  $\frac { \pi } { 6 }$ 
C)  $\frac { 11 \pi } { 6 }$ 
D)  $\frac { \pi } { 4 }$

Question 15

Solve for x in the given interval.
-$$\csc x = 2,0 \leq x \leq \frac { \pi } { 2 }$$

Accepted Answer

A)  $\frac { \pi } { 6 }$ 
B)  $\frac { 5 \pi } { 6 }$ 
C)  $\frac { \pi } { 3 }$ 
D)  $\frac { \pi } { 4 }$ 
A)  $\frac { \pi } { 6 }$ 
B)  $\frac { 5 \pi } { 6 }$ 
C)  $\frac { \pi } { 3 }$ 
D)  $\frac { \pi } { 4 }$

Question 16

Solve the problem.
-A fire is sighted due west of lookout A. The bearing of the fire from lookout $\mathrm { B } , 9.5$ miles due south of $\mathrm { A }$, is $\mathrm { N }$ $57.50 ^ { \circ } \mathrm { W }$. How far is the fire from B (to the nearest tenth of a mile)?

Accepted Answer

A)  $19.7 \mathrm { mi }$ 
B)  $20.7 \mathrm { mi }$ 
C)  $17.7 \mathrm { mi }$ 
D)  $18.7 \mathrm { mi }$ 
A)  $19.7 \mathrm { mi }$ 
B)  $20.7 \mathrm { mi }$ 
C)  $17.7 \mathrm { mi }$ 
D)  $18.7 \mathrm { mi }$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior.
-f(x) = - tan x

Accepted Answer

Domain: All reals except odd multiples o

Question 18

Find the trigonometric function value for the angle shown.
-$$\tan \theta$$

Accepted Answer

A)  $\tan \theta = \frac { 2 \sqrt { 2 } } { 3 }$ 
B)  $\tan \theta = \frac { 3 \sqrt { 2 } } { 4 }$ 
C)  $\tan \theta = - \frac { 4 } { 34 }$ 
D)  $\tan \theta = - \frac { 3 \sqrt { 2 } } { 34 }$ 
A)  $\tan \theta = \frac { 2 \sqrt { 2 } } { 3 }$ 
B)  $\tan \theta = \frac { 3 \sqrt { 2 } } { 4 }$ 
C)  $\tan \theta = - \frac { 4 } { 34 }$ 
D)  $\tan \theta = - \frac { 3 \sqrt { 2 } } { 34 }$

Question 19

Find approximate solutions for the equation in the interval $ -\pi<\mathbf{X}<\pi $. Round to three decimal places.
-$3 \cos x = \sec x$

Accepted Answer

A)  $- 2.186,2.186$ 
B)  $- 1.955 , - 0.862,0.862,1.955$ 
C)  $- 2.186 , - 0.955,0.955,2.186$ 
D)  $- 0.955,0.955$ 
A)  $- 2.186,2.186$ 
B)  $- 1.955 , - 0.862,0.862,1.955$ 
C)  $- 2.186 , - 0.955,0.955,2.186$ 
D)  $- 0.955,0.955$

Question 20

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$$\tan ^ { - 1 } ( - 16.8 )$$

Accepted Answer

A)  $43.3 ^ { \circ }$ 
B)  $86.59 ^ { \circ }$ 
C)  $- 86.59 ^ { \circ }$ 
D)  $64.95 ^ { \circ }$ 
A)  $43.3 ^ { \circ }$ 
B)  $86.59 ^ { \circ }$ 
C)  $- 86.59 ^ { \circ }$ 
D)  $64.95 ^ { \circ }$

Evaluate. - $\cos \left( \frac { \pi } { 6 } + 2918 \pi \right)$

Use a calculator to solve for x in the given interval - $\sin \theta = 0.7231,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }$

Find the exact solution to the equation without a calculator. - $\cos ^ { - 1 } ( \cos x ) = \frac { 1 } { 4 }$

Find the exact value of the composition. - $\cos ^ { - 1 } \left( \cos \left( - \frac { \pi } { 6 } \right) \right)$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\tan \left( 1350 ^ { \circ } \right)$

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - $20 ^ { \circ }$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\csc \theta = \frac { 5 } { 2 } ; \cos \theta$

Find the zeros of the function in the interval $[-2 \pi, 2 \pi]$ . - $f ( x ) = \frac { 1 } { 2 } \cos 2 x$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\tan 720 ^ { \circ }$

Evaluate without using a calculator by using ratios in a reference triangle. - $\cot \frac { 3 \pi } { 4 }$

Choose the point on the terminal side of . - $\theta = \frac { 11 \pi } { 6 }$

Write the word or phrase that best completes each statement or answers the question. Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = sec 2x

Choose the point on the terminal side of . - $\theta = - 45 ^ { \circ }$

Find the exact value of the real number y. - $y = \cos ^ { - 1 } \left( \frac { \sqrt { 2 } } { 2 } \right)$

Solve for x in the given interval. - $\csc x = 2,0 \leq x \leq \frac { \pi } { 2 }$

Solve the problem. -A fire is sighted due west of lookout A. The bearing of the fire from lookout $\mathrm { B } , 9.5$ miles due south of $\mathrm { A }$ , is $\mathrm { N }$ $57.50 ^ { \circ } \mathrm { W }$ . How far is the fire from B (to the nearest tenth of a mile)?

Write the word or phrase that best completes each statement or answers the question. Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, asymptotes, and end behavior. -f(x) = - tan x

Find the trigonometric function value for the angle shown. - $\tan \theta$ $Find the trigonometric function value for the angle shown. - \tan \theta$

Find approximate solutions for the equation in the interval $-\pi<\mathbf{X}<\pi$ . Round to three decimal places. - $3 \cos x = \sec x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\tan ^ { - 1 } ( - 16.8 )$

Functions and Graphs

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 4: Trigonometric Functions

Evaluate. - cos⁡(π6+2918π)\cos \left( \frac { \pi } { 6 } + 2918 \pi \right)cos(6π​+2918π)

Use a calculator to solve for x in the given interval - sin⁡θ=0.7231,0∘≤θ≤90∘\sin \theta = 0.7231,0 ^ { \circ } \leq \theta \leq 90 ^ { \circ }sinθ=0.7231,0∘≤θ≤90∘

Find the exact solution to the equation without a calculator. - cos⁡−1(cos⁡x)=14\cos ^ { - 1 } ( \cos x ) = \frac { 1 } { 4 }cos−1(cosx)=41​

Find the exact value of the composition. - cos⁡−1(cos⁡(−π6))\cos ^ { - 1 } \left( \cos \left( - \frac { \pi } { 6 } \right) \right)cos−1(cos(−6π​))

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - tan⁡(1350∘)\tan \left( 1350 ^ { \circ } \right)tan(1350∘)

Find the measures of two angles, one positive and one negative, that are coterminal with the given angle. - 20∘20 ^ { \circ }20∘

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - csc⁡θ=52;cos⁡θ\csc \theta = \frac { 5 } { 2 } ; \cos \thetacscθ=25​;cosθ

Find the zeros of the function in the interval [−2π,2π] [-2 \pi, 2 \pi] [−2π,2π] . - f(x)=12cos⁡2xf ( x ) = \frac { 1 } { 2 } \cos 2 xf(x)=21​cos2x

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - tan⁡720∘\tan 720 ^ { \circ }tan720∘

Evaluate without using a calculator by using ratios in a reference triangle. - cot⁡3π4\cot \frac { 3 \pi } { 4 }cot43π​

Choose the point on the terminal side of . - θ=11π6\theta = \frac { 11 \pi } { 6 }θ=611π​