Question 1

Write the equation of a sine function that has the given characteristics.
-Amplitude: 4
Period: $3 \pi$

Accepted Answer

A)  $y = 6 \sin \left( \frac { 2 } { 5 } x \right)$ 
B)  $y = 5 \sin \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = 5 \sin ( 6 x )$ 
D)  $y = \sin ( 6 x ) + 5$ 
A)  $y = 6 \sin \left( \frac { 2 } { 5 } x \right)$ 
B)  $y = 5 \sin \left( \frac { 1 } { 3 } x \right)$ 
C)  $y = 5 \sin ( 6 x )$ 
D)  $y = \sin ( 6 x ) + 5$

Question 2

Find the phase shift of the function.
-$$y = 3 \cos \left( - 3 x - \frac { \pi } { 2 } \right)$$

Accepted Answer

A)  $\frac { \pi } { 2 }$ units to the left 
B)  $\frac { \pi } { 2 }$ units to the right 
C)  $\frac { \pi } { 6 }$ units to the right 
D)  $\frac { \pi } { 6 }$ units to the left 
A)  $\frac { \pi } { 2 }$ units to the left 
B)  $\frac { \pi } { 2 }$ units to the right 
C)  $\frac { \pi } { 6 }$ units to the right 
D)  $\frac { \pi } { 6 }$ units to the left

Question 3

Find the exact value of the expression if θ = 30°. Do not use a calculator.
-$f ( \theta ) = \cos \theta \quad$ Find $[ f ( \theta ) ] ^ { 2 }$.

Accepted Answer

A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  $\sqrt { 3 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { \sqrt { 3 } } { 2 }$ 
B)  $\sqrt { 3 }$ 
C)  $\frac { 3 } { 4 }$ 
D)  $\frac { 1 } { 4 }$

Question 4

Choose the one alternative that best completes the statement or answers the question.
-A carousel has a radius of 15 feet and takes 28 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? If necessary, round the answer to two decimal places.

Accepted Answer

A)  94.25 ft/sec 
B)  0.54 ft/sec 
C)  3.37 ft/sec 
D)  11.73 ft/sec 
A)  94.25 ft/sec 
B)  0.54 ft/sec 
C)  3.37 ft/sec 
D)  11.73 ft/sec

Question 5

Find the exact value. Do not use a calculator.
-$\cos \frac { 3 \pi } { 2 }$

Accepted Answer

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

Question 6

Find the exact value of the expression if θ = 30°. Do not use a calculator.
-$f ( \theta ) = \tan \theta \quad$ Find $f ( \theta )$

Accepted Answer

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

Question 7

Use a calculator to find the approximate value of the expression rounded to two decimal places.
-$\cot 0.1811$

Accepted Answer

A)  0.98 
B)  5.46 
C)  1.02 
D)  0.18 
A)  0.98 
B)  5.46 
C)  1.02 
D)  0.18

Question 8

Choose the one alternative that best completes the statement or answers the question.
Use transformations to graph the function.
-$y=4 \sin x$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 9

Convert the angle in radians to degrees.
-$\frac{11 \pi}{12}$

Accepted Answer

A) 
$150^{\circ}$ 
B) 
$210^{\circ}$ 
C) 
$160^{\circ}$ 
D) 
$165^{\circ}$ 
A) 
$150^{\circ}$ 
B) 
$210^{\circ}$ 
C) 
$160^{\circ}$ 
D) 
$165^{\circ}$

Question 10

Choose the one alternative that best completes the statement or answers the question.
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$\cos \left( - 60 ^ { \circ } \right)$

Accepted Answer

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

Question 11

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator.
-$\tan 930 ^ { \circ }$

Accepted Answer

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

Question 12

Find the exact value of the indicated trigonometric function of θ.
-$\sec \theta = \frac { 9 } { 2 } , \quad \theta$ in quadrant $\mathrm { IV } \quad$ Find $\tan \theta$

Accepted Answer

A)  $- \frac { \sqrt { 77 } } { 9 }$ 
B)  $- \frac { \sqrt { 77 } } { 2 }$ 
C)  $- \sqrt { 77 }$ 
D)  $- \frac { 9 } { 2 }$ 
A)  $- \frac { \sqrt { 77 } } { 9 }$ 
B)  $- \frac { \sqrt { 77 } } { 2 }$ 
C)  $- \sqrt { 77 }$ 
D)  $- \frac { 9 } { 2 }$

Question 13

Find the exact value. Do not use a calculator.
-$\sin 0$

Accepted Answer

A)  1 
B)  0 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  undefined 
A)  1 
B)  0 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  undefined

Question 14

Convert the angle to D° M' S'' form. Round the answer to the nearest second.
-$310.04 ^ { \circ }$

Accepted Answer

A)  $310 ^ { \circ } 2 ^ { \prime } 24 ^ { \prime \prime }$ 
B)  $310 ^ { \circ } 23 ^ { \prime } 4 ^ { \prime \prime }$ 
C)  $310 ^ { \circ } 3 ^ { \prime } 23 ^ { \prime \prime }$ 
D)  $310 ^ { \circ } 2 ^ { \prime } 4 { } ^ { \prime \prime }$ 
A)  $310 ^ { \circ } 2 ^ { \prime } 24 ^ { \prime \prime }$ 
B)  $310 ^ { \circ } 23 ^ { \prime } 4 ^ { \prime \prime }$ 
C)  $310 ^ { \circ } 3 ^ { \prime } 23 ^ { \prime \prime }$ 
D)  $310 ^ { \circ } 2 ^ { \prime } 4 { } ^ { \prime \prime }$

Question 15

Choose the one alternative that best completes the statement or answers the question.
Use the even-odd properties to find the exact value of the expression. Do not use a calculator.
-$$\csc \left( - \frac { \pi } { 3 } \right)$$

Accepted Answer

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

Question 16

Find the exact value. Do not use a calculator.
-$\sin \pi$

Accepted Answer

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

Question 17

Graph the sinusoidal function.
-$y=4 \sin (\pi x)$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 18

Find the exact value of the indicated trigonometric function of θ.
-$\tan \theta = - \frac { 21 } { 20 } , \quad 270 ^ { \circ } < \theta < 360 ^ { \circ } \quad$ Find $\cos \theta$

Accepted Answer

A)  $- \frac { 15 } { 17 }$ 
B)  $\frac { - 21 \sqrt { 41 } } { 41 }$ 
C)  $- 15$ 
D)  $\frac { 20 \sqrt { 41 } } { 41 }$ 
A)  $- \frac { 15 } { 17 }$ 
B)  $\frac { - 21 \sqrt { 41 } } { 41 }$ 
C)  $- 15$ 
D)  $\frac { 20 \sqrt { 41 } } { 41 }$

Question 19

Without graphing the function, determine its amplitude or period as requested.
-$y = 5 \sin \frac { 1 } { 4 } x \quad$ Find the amplitude.

Accepted Answer

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

Question 20

Without graphing the function, determine its amplitude or period as requested.
-$y = - 4 \cos \frac { 1 } { 3 } x \quad$ Find the amplitude.

Accepted Answer

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

Write the equation of a sine function that has the given characteristics. -Amplitude: 4 Period: $3 \pi$

Find the phase shift of the function. - $y = 3 \cos \left( - 3 x - \frac { \pi } { 2 } \right)$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \cos \theta \quad$ Find $[ f ( \theta ) ] ^ { 2 }$ .

Choose the one alternative that best completes the statement or answers the question. -A carousel has a radius of 15 feet and takes 28 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? If necessary, round the answer to two decimal places.

Find the exact value. Do not use a calculator. - $\cos \frac { 3 \pi } { 2 }$

Find the exact value of the expression if θ = 30°. Do not use a calculator. - $f ( \theta ) = \tan \theta \quad$ Find $f ( \theta )$

Use a calculator to find the approximate value of the expression rounded to two decimal places. - $\cot 0.1811$

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - $y=4 \sin x$ $Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=4 \sin x$

Convert the angle in radians to degrees. - $\frac{11 \pi}{12}$

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\cos \left( - 60 ^ { \circ } \right)$

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - $\tan 930 ^ { \circ }$

Find the exact value of the indicated trigonometric function of θ. - $\sec \theta = \frac { 9 } { 2 } , \quad \theta$ in quadrant $\mathrm { IV } \quad$ Find $\tan \theta$

Find the exact value. Do not use a calculator. - $\sin 0$

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - $310.04 ^ { \circ }$

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - $\csc \left( - \frac { \pi } { 3 } \right)$

Find the exact value. Do not use a calculator. - $\sin \pi$

Graph the sinusoidal function. - $y=4 \sin (\pi x)$ $Graph the sinusoidal function. - y=4 \sin (\pi x)$

Find the exact value of the indicated trigonometric function of θ. - $\tan \theta = - \frac { 21 } { 20 } , \quad 270 ^ { \circ } < \theta < 360 ^ { \circ } \quad$ Find $\cos \theta$

Without graphing the function, determine its amplitude or period as requested. - $y = 5 \sin \frac { 1 } { 4 } x \quad$ Find the amplitude.

Without graphing the function, determine its amplitude or period as requested. - $y = - 4 \cos \frac { 1 } { 3 } x \quad$ Find the amplitude.

Functions and Their Graphs

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Foundations: a Prelude to Functions

Graphing Utilities

Filters

Exam 5: Trigonometric Functions

Write the equation of a sine function that has the given characteristics. -Amplitude: 4 Period: 3π3 \pi3π

Find the phase shift of the function. - y=3cos⁡(−3x−π2)y = 3 \cos \left( - 3 x - \frac { \pi } { 2 } \right)y=3cos(−3x−2π​)

Find the exact value of the expression if θ = 30°. Do not use a calculator. - f(θ)=cos⁡θf ( \theta ) = \cos \theta \quadf(θ)=cosθ Find [f(θ)]2[ f ( \theta ) ] ^ { 2 }[f(θ)]2 .

Choose the one alternative that best completes the statement or answers the question. -A carousel has a radius of 15 feet and takes 28 seconds to make one complete revolution. What is the linear speed of the carousel at its outside edge? If necessary, round the answer to two decimal places.

Find the exact value. Do not use a calculator. - cos⁡3π2\cos \frac { 3 \pi } { 2 }cos23π​

Find the exact value of the expression if θ = 30°. Do not use a calculator. - f(θ)=tan⁡θf ( \theta ) = \tan \theta \quadf(θ)=tanθ Find f(θ)f ( \theta )f(θ)

Use a calculator to find the approximate value of the expression rounded to two decimal places. - cot⁡0.1811\cot 0.1811cot0.1811

Choose the one alternative that best completes the statement or answers the question. Use transformations to graph the function. - y=4sin⁡xy=4 \sin xy=4sinx

Convert the angle in radians to degrees. - 11π12\frac{11 \pi}{12}1211π​

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - cos⁡(−60∘)\cos \left( - 60 ^ { \circ } \right)cos(−60∘)

Use the fact that the trigonometric functions are periodic to find the exact value of the expression. Do not use a calculator. - tan⁡930∘\tan 930 ^ { \circ }tan930∘

Find the exact value of the indicated trigonometric function of θ. - sec⁡θ=92,θ\sec \theta = \frac { 9 } { 2 } , \quad \thetasecθ=29​,θ in quadrant IV\mathrm { IV } \quadIV Find tan⁡θ\tan \thetatanθ

Find the exact value. Do not use a calculator. - sin⁡0\sin 0sin0

Convert the angle to D° M' S'' form. Round the answer to the nearest second. - 310.04∘310.04 ^ { \circ }310.04∘

Choose the one alternative that best completes the statement or answers the question. Use the even-odd properties to find the exact value of the expression. Do not use a calculator. - csc⁡(−π3)\csc \left( - \frac { \pi } { 3 } \right)csc(−3π​)

Find the exact value. Do not use a calculator. - sin⁡π\sin \pisinπ

Graph the sinusoidal function. - y=4sin⁡(πx)y=4 \sin (\pi x)y=4sin(πx)

Find the exact value of the indicated trigonometric function of θ. - tan⁡θ=−2120,270∘<θ<360∘\tan \theta = - \frac { 21 } { 20 } , \quad 270 ^ { \circ } < \theta < 360 ^ { \circ } \quadtanθ=−2021​,270∘<θ<360∘ Find cos⁡θ\cos \thetacosθ

Without graphing the function, determine its amplitude or period as requested. - y=5sin⁡14xy = 5 \sin \frac { 1 } { 4 } x \quady=5sin41​x Find the amplitude.

Without graphing the function, determine its amplitude or period as requested. - y=−4cos⁡13xy = - 4 \cos \frac { 1 } { 3 } x \quady=−4cos31​x Find the amplitude.