Question 1

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined."
-$\cos 9 \pi$

Accepted Answer

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

Question 2

Determine whether the graph of f(x) is a sinusoid.
-$$f ( x ) = 12 \cos x + \tan x$$

Accepted Answer

A) True 
 B)False

Question 3

Find the exact solution to the equation without a calculator.
-$6 \arcsin x = \pi$

Accepted Answer

A)  $x = - 5 + 3 \sqrt { 2 }$ 
B)  $x = \pm \frac { 3 } { 4 }$ 
C)  $x = 2$ 
D)  $x = \frac { 1 } { 2 }$ 
A)  $x = - 5 + 3 \sqrt { 2 }$ 
B)  $x = \pm \frac { 3 } { 4 }$ 
C)  $x = 2$ 
D)  $x = \frac { 1 } { 2 }$

Question 4

Solve the problem.
-The output voltage for an a.c. generator is approximated by $\mathrm { v } = 156 \cos \left( 120 \pi \mathrm { t } - \frac { \pi } { 3 } \right)$. Find the smallest positive value of $t$ for which the output is 68 volts. (Use $3.1416$ as an approximation for $\pi$.)

Accepted Answer

A)  $t = 0.0124$ 
B)  $t = 0.0114$ 
C)  $\mathrm { t } = 0.0047$ 
D)  $t = 0.0057$ 
A)  $t = 0.0124$ 
B)  $t = 0.0114$ 
C)  $\mathrm { t } = 0.0047$ 
D)  $t = 0.0057$

Question 5

Find the exact value of the composition.
-$\tan \left( 2 \tan ^ { - 1 } ( 2 ) \right)$

Accepted Answer

A)  $- \frac { 4 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $- \frac { 2 } { 3 }$ 
D)  $\frac { 4 } { 3 }$ 
A)  $- \frac { 4 } { 3 }$ 
B)  $\frac { 2 } { 3 }$ 
C)  $- \frac { 2 } { 3 }$ 
D)  $\frac { 4 } { 3 }$

Question 6

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$263 ^ { \circ } 19 ^ { \prime } 58 ^ { \prime \prime }$

Accepted Answer

A)  $263.34 ^ { \circ }$ 
B)  $263.33 ^ { \circ }$ 
C)  $263.29 ^ { \circ }$ 
D)  $263.39 ^ { \circ }$ 
A)  $263.34 ^ { \circ }$ 
B)  $263.33 ^ { \circ }$ 
C)  $263.29 ^ { \circ }$ 
D)  $263.39 ^ { \circ }$

Question 7

Solve the right triangle for all missing sides and angles to the nearest tenth.
- 
$\begin{array}{l}
c=10 \
B=26.3^{\circ}
\end{array}$

Accepted Answer

A)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~b} = 4.9$ 
B)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~b} = 4.4$ 
C)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 4.9 , \mathrm {~b} = 4.4$ 
D)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 4.4 , \mathrm {~b} = 9$ 
A)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~b} = 4.9$ 
B)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 9 , \mathrm {~b} = 4.4$ 
C)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 4.9 , \mathrm {~b} = 4.4$ 
D)  $\mathrm { A } = 63.7 ^ { \circ } , \mathrm { a } = 4.4 , \mathrm {~b} = 9$

Question 8

Use a calculator to find the function value to four decimal places.
-$\tan 61.67 ^ { \circ }$

Accepted Answer

A)  $1.8549$ 
B)  $0.6169$ 
C)  $34.3007$ 
D)  $0.4745$ 
A)  $1.8549$ 
B)  $0.6169$ 
C)  $34.3007$ 
D)  $0.4745$

Question 9

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
-$\pi / 6$

Accepted Answer

A)  $30 ^ { \circ }$ 
B)  $0.523 ^ { \circ }$ 
C)  $30 \pi ^ { \circ }$ 
D)  $( \pi / 6 ) ^ { \circ }$ 
A)  $30 ^ { \circ }$ 
B)  $0.523 ^ { \circ }$ 
C)  $30 \pi ^ { \circ }$ 
D)  $( \pi / 6 ) ^ { \circ }$

Question 10

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$- 630 ^ { \circ }$

Accepted Answer

A)  $- 7 \pi$ 
B)  $\frac { 7 \pi } { 2 }$ 
C)  $- \frac { 7 \pi } { 4 }$ 
D)  $= \frac { 7 \pi } { 2 }$ 
A)  $- 7 \pi$ 
B)  $\frac { 7 \pi } { 2 }$ 
C)  $- \frac { 7 \pi } { 4 }$ 
D)  $= \frac { 7 \pi } { 2 }$

Question 11

Solve the problem.
-Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is $9.2$ centimeters and the radius of the larger wheel is $13.1$ centimeters. Through how many degrees will the larger wheel rotate if the smaller one rotates $211 ^ { \circ }$ ?

Accepted Answer

A)  $148.08 ^ { \circ }$ 
B)  $149.18 ^ { \circ }$ 
C)  $150.18 ^ { \circ }$ 
D)  $148.18 ^ { \circ }$ 
A)  $148.08 ^ { \circ }$ 
B)  $149.18 ^ { \circ }$ 
C)  $150.18 ^ { \circ }$ 
D)  $148.18 ^ { \circ }$

Question 12

Solve the problem.
-A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 22 feet and the height from the ground to the front doors is 7 feet, how long is the ramp?
(Round to the nearest tenth.)

Accepted Answer

A)  5.4 ft 
B)  20.9 ft 
C)  23.1 ft 
D)  9.9 ft 
A)  5.4 ft 
B)  20.9 ft 
C)  23.1 ft 
D)  9.9 ft

Question 13

Find the exact value of the composition.
-$\arccos \left( \cos \frac { \pi } { 2 } \right)$

Accepted Answer

A)  $\frac { \pi } { 2 }$ 
B)  $\pi$ 
C)  0 
D)  $\frac { \pi } { 3 }$ 
A)  $\frac { \pi } { 2 }$ 
B)  $\pi$ 
C)  0 
D)  $\frac { \pi } { 3 }$

Question 14

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric
graph.
-$f ( x ) = 7 \tan ^ { - 1 } \left( \frac { x } { 6 } \right)$

Accepted Answer

A)  Vertical stretch by a factor of 6 and horizontal stretch by a factor of 7 
B)  Vertical stretch by a factor of 7 and horizontal stretch by a factor of 6 
C)  Vertical stretch by a factor of 7 and horizontal shrink by a factor of $\frac { 1 } { 6 }$ 
D)  Vertical translation up 7 units and horizontal translation to the right 6 units 
A)  Vertical stretch by a factor of 6 and horizontal stretch by a factor of 7 
B)  Vertical stretch by a factor of 7 and horizontal stretch by a factor of 6 
C)  Vertical stretch by a factor of 7 and horizontal shrink by a factor of $\frac { 1 } { 6 }$ 
D)  Vertical translation up 7 units and horizontal translation to the right 6 units

Question 15

Solve the problem.
-A generator produces an alternating current according to the equation $\mathrm { I } = 64 \sin 137 \pi \mathrm { t }$, where $t$ is time in seconds and I is the current in amperes. What is the smallest time $t$ such that $I = 32$ ?

Accepted Answer

A)  $\frac { 1 } { 548 } \mathrm { sec }$ 
B)  $\frac { 1 } { 274 } \mathrm { sec }$ 
C)  $\frac { 1 } { 822 } \mathrm { sec }$ 
D)  $\frac { 1 } { 411 } \sec$ 
A)  $\frac { 1 } { 548 } \mathrm { sec }$ 
B)  $\frac { 1 } { 274 } \mathrm { sec }$ 
C)  $\frac { 1 } { 822 } \mathrm { sec }$ 
D)  $\frac { 1 } { 411 } \sec$

Question 16

Find the value of the unique real number between 0 and 2 that satisfies the given conditions.
-$\cos \theta = - \frac { 1 } { 2 }$ and $\sin \theta < 0$

Accepted Answer

A)  $\frac { 5 \pi } { 6 }$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { 7 \pi } { 6 }$ 
D)  $\frac { 2 \pi } { 3 }$ 
A)  $\frac { 5 \pi } { 6 }$ 
B)  $\frac { 4 \pi } { 3 }$ 
C)  $\frac { 7 \pi } { 6 }$ 
D)  $\frac { 2 \pi } { 3 }$

Question 17

Solve the problem.
-Suppose that the average monthly low temperatures for a small town are shown in the table.

Model this data using $f ( x ) = a \sin ( b ( x - c ) ) + d$.

Accepted Answer

A)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 42$ 
B)  $f ( x ) = 23 \sin \left( \frac { \pi } { 12 } ( x - 4 ) \right) + 42$ 
C)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$ 
D)  $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$ 
A)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 42$ 
B)  $f ( x ) = 23 \sin \left( \frac { \pi } { 12 } ( x - 4 ) \right) + 42$ 
C)  $f ( x ) = 23 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 42$ 
D)  $f ( x ) = 42 \sin \left( \frac { \pi } { 6 } ( x - 4 ) \right) + 23$

Question 18

Determine whether the function is periodic. If it is periodic, find the period.
-$$f ( x ) = 8 \cos ( 2 x + 1 ) - \sin ( 3 x - 1 )$$

Accepted Answer

A)  $2 \pi$ 
B)  Not periodic 
C)  $\pi$ 
D)  $4 \pi$ 
A)  $2 \pi$ 
B)  Not periodic 
C)  $\pi$ 
D)  $4 \pi$

Question 19

Choose the point on the terminal side of .
-$$\theta = \frac { - 3 \pi } { 4 }$$

Accepted Answer

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

Question 20

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\tan \mathrm { A }$ and $\cot \mathrm { A }$.

Accepted Answer

A)  $\tan \mathrm { A } = \frac { 12 } { 5 } ; \cot \mathrm { A } = \frac { 5 } { 12 }$ 
B)  $\tan \mathrm { A } = \frac { 13 } { 5 } ; \cot \mathrm { A } = \frac { 13 } { 12 }$ 
C)  $\tan \mathrm { A } = \frac { 5 } { 13 } ; \cot \mathrm { A } = \frac { 12 } { 13 }$ 
D)  $\tan \mathrm { A } = \frac { 5 } { 12 } ; \cot \mathrm { A } = \frac { 12 } { 5 }$ 
A)  $\tan \mathrm { A } = \frac { 12 } { 5 } ; \cot \mathrm { A } = \frac { 5 } { 12 }$ 
B)  $\tan \mathrm { A } = \frac { 13 } { 5 } ; \cot \mathrm { A } = \frac { 13 } { 12 }$ 
C)  $\tan \mathrm { A } = \frac { 5 } { 13 } ; \cot \mathrm { A } = \frac { 12 } { 13 }$ 
D)  $\tan \mathrm { A } = \frac { 5 } { 12 } ; \cot \mathrm { A } = \frac { 12 } { 5 }$

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - $\cos 9 \pi$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 12 \cos x + \tan x$

Find the exact solution to the equation without a calculator. - $6 \arcsin x = \pi$

Solve the problem. -The output voltage for an a.c. generator is approximated by $\mathrm { v } = 156 \cos \left( 120 \pi \mathrm { t } - \frac { \pi } { 3 } \right)$ . Find the smallest positive value of $t$ for which the output is 68 volts. (Use $3.1416$ as an approximation for $\pi$ .)

Find the exact value of the composition. - $\tan \left( 2 \tan ^ { - 1 } ( 2 ) \right)$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $263 ^ { \circ } 19 ^ { \prime } 58 ^ { \prime \prime }$

Solve the right triangle for all missing sides and angles to the nearest tenth. - $Solve the right triangle for all missing sides and angles to the nearest tenth. - \begin{array}{l} c=10 \\ B=26.3^{\circ} \end{array}$ c=10 B=26.

Use a calculator to find the function value to four decimal places. - $\tan 61.67 ^ { \circ }$

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - $\pi / 6$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $- 630 ^ { \circ }$

Solve the problem. -A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ramp is 22 feet and the height from the ground to the front doors is 7 feet, how long is the ramp? (Round to the nearest tenth.)

Find the exact value of the composition. - $\arccos \left( \cos \frac { \pi } { 2 } \right)$

Describe the transformation required to obtain the graph of the given function from the basic inverse trigonometric graph. - $f ( x ) = 7 \tan ^ { - 1 } \left( \frac { x } { 6 } \right)$

Solve the problem. -A generator produces an alternating current according to the equation $\mathrm { I } = 64 \sin 137 \pi \mathrm { t }$ , where $t$ is time in seconds and I is the current in amperes. What is the smallest time $t$ such that $I = 32$ ?

Find the value of the unique real number between 0 and 2 that satisfies the given conditions. - $\cos \theta = - \frac { 1 } { 2 }$ and $\sin \theta < 0$

Determine whether the function is periodic. If it is periodic, find the period. - $f ( x ) = 8 \cos ( 2 x + 1 ) - \sin ( 3 x - 1 )$

Choose the point on the terminal side of . - $\theta = \frac { - 3 \pi } { 4 }$

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

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

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Exam 4: Trigonometric Functions

Evaluate the trigonometric function of the given quadrantal angle. If the value is undefined, write "undefined." - cos⁡9π\cos 9 \picos9π

Determine whether the graph of f(x) is a sinusoid. - f(x)=12cos⁡x+tan⁡xf ( x ) = 12 \cos x + \tan xf(x)=12cosx+tanx

Find the exact solution to the equation without a calculator. - 6arcsin⁡x=π6 \arcsin x = \pi6arcsinx=π

Find the exact value of the composition. - tan⁡(2tan⁡−1(2))\tan \left( 2 \tan ^ { - 1 } ( 2 ) \right)tan(2tan−1(2))

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 263∘19′58′′263 ^ { \circ } 19 ^ { \prime } 58 ^ { \prime \prime }263∘19′58′′

Solve the right triangle for all missing sides and angles to the nearest tenth. - c=10 B=26.

Use a calculator to find the function value to four decimal places. - tan⁡61.67∘\tan 61.67 ^ { \circ }tan61.67∘

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - π/6\pi / 6π/6

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - −630∘- 630 ^ { \circ }−630∘