Question 1

Evaluate.
-$$\cos \left( \frac { 2,222,013 \pi } { 2 } \right)$$

Accepted Answer

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

Question 2

Match the function with its graph.
-1) $y = - \csc x$
2) $y = - \sec x$
3) $y = - \tan x$
4) $y = - \cot x$

a.
 
b.
 
c.
 
d.

Accepted Answer

A)  1C, 2A, 3B, 4D 
B)  1B, 2D, 3C, 4A 
C)  1A, 2D, 3C, 4B 
D)  1A, 2B, 3C, 4D 
A)  1C, 2A, 3B, 4D 
B)  1B, 2D, 3C, 4A 
C)  1A, 2D, 3C, 4B 
D)  1A, 2B, 3C, 4D

Question 3

Find the specified quantity.
-Find the vertical translation of $y = 4 + 2 \sin \left( 5 x + \frac { \pi } { 3 } \right)$.

Accepted Answer

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

Question 4

Use a calculator to find the function value to four decimal places.
-$\sin 17 ^ { \circ } 10 ^ { \prime }$

Accepted Answer

A)  $0.2952$ 
B)  $0.9555$ 
C)  $0.3089$ 
D)  $0.9614$ 
A)  $0.2952$ 
B)  $0.9555$ 
C)  $0.3089$ 
D)  $0.9614$

Question 5

Find the zeros of the function in the interval $ [-2 \pi, 2 \pi] $.
-$$f ( x ) = - \frac { 1 } { 6 } \sin \frac { x } { 2 }$$

Accepted Answer

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

Question 6

Find the exact solution to the equation without a calculator.
-$$\tan ^ { - 1 } ( \tan x ) = - \frac { \pi } { 6 }$$

Accepted Answer

A)  $- \frac { \pi } { 12 }$ 
B)  0 
C)  $\frac { \pi } { 6 }$ 
D)  $- \frac { \pi } { 6 }$ 
A)  $- \frac { \pi } { 12 }$ 
B)  0 
C)  $\frac { \pi } { 6 }$ 
D)  $- \frac { \pi } { 6 }$

Question 7

Use a calculator to solve for x in the given interval
-$\sec \theta = - 4.0545,0 \leq \theta \leq 2 \pi$

Accepted Answer

A)  $2.90$ or $3.38$ 
B)  $4.46$ or $4.96$ 
C)  $1.82$ or $4.96$ 
D)  $1.82$ or $4.46$ 
A)  $2.90$ or $3.38$ 
B)  $4.46$ or $4.96$ 
C)  $1.82$ or $4.96$ 
D)  $1.82$ or $4.46$

Question 8

Identify the maximum and minimum values of the function in the interval $ [-2 \pi, 2 \pi] $. Use your understanding of transformations, not your graphing calculator.
-$y = - 9 \sin x$

Accepted Answer

A)  Maximum value $= 18$; minimum value $= - 18$ 
B)  Maximum value $= 9$; minimum value $= 0$ 
C)  Maximum value $= 9$; minimum value $= - 9$ 
D)  Maximum value $= 18$; minimum value $= 0$ 
A)  Maximum value $= 18$; minimum value $= - 18$ 
B)  Maximum value $= 9$; minimum value $= 0$ 
C)  Maximum value $= 9$; minimum value $= - 9$ 
D)  Maximum value $= 18$; minimum value $= 0$

Question 9

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$183.08 ^ { \circ }$

Accepted Answer

A)  $183 ^ { \circ } 2 ^ { \prime } 8 ^ { \prime \prime }$ 
B)  $183 ^ { \circ } 4 ^ { \prime } 8 ^ { \prime \prime }$ 
C)  $183 ^ { \circ } 5 ^ { \prime } 48 ^ { \prime \prime }$ 
D)  $183 ^ { \circ } 4 ^ { \prime } 48 ^ { \prime \prime }$ 
A)  $183 ^ { \circ } 2 ^ { \prime } 8 ^ { \prime \prime }$ 
B)  $183 ^ { \circ } 4 ^ { \prime } 8 ^ { \prime \prime }$ 
C)  $183 ^ { \circ } 5 ^ { \prime } 48 ^ { \prime \prime }$ 
D)  $183 ^ { \circ } 4 ^ { \prime } 48 ^ { \prime \prime }$

Question 10

Use a calculator to find the function value to four decimal places.
-$\cot 14.3 ^ { \circ }$

Accepted Answer

A)  $0.2470$ 
B)  $3.9232$ 
C)  $0.2549$ 
D)  $6.0869$ 
A)  $0.2470$ 
B)  $3.9232$ 
C)  $0.2549$ 
D)  $6.0869$

Question 11

Solve the problem.
-The maximum monthly average temperature in Smithville is $89 ^ { \circ }$ in July, and the minimum is $33 ^ { \circ }$ in January. Determine $f ( x ) = a \cos ( b ( x - c ) ) + d$ so that $f ( x )$ models the monthly average temperature in Smithville, where $x$ is the month and $x = 1$ corresponds to January.

Accepted Answer

A)  $H ( x ) = 28 \cos \left( \frac { \pi } { 12 } ( x - 7 ) \right) + 61$ 
B)  $f ( x ) = 61 \cos \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 28$ 
C)  $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 61$ 
D)  $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 4 ) \right\} + 61$ 
A)  $H ( x ) = 28 \cos \left( \frac { \pi } { 12 } ( x - 7 ) \right) + 61$ 
B)  $f ( x ) = 61 \cos \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 28$ 
C)  $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 7 ) \right) + 61$ 
D)  $f ( x ) = 28 \cos \left( \frac { \pi } { 6 } ( x - 4 ) \right\} + 61$

Question 12

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary.
-$$f ( x ) = 4 \sin 3 x - 2 \cos 3 x$$

Accepted Answer

A)  $\mathrm { a } = 6.00 , \mathrm {~b} = 2 , \mathrm {~h} = 0.63$ 
B)  $\mathrm { a } = 4.47 , \mathrm {~b} = 6 , \mathrm {~h} = 0.15$ 
C)  $\mathrm { a } = 0.15 , \mathrm {~b} = 3 , \mathrm {~h} = 4.47$ 
D)  $\mathrm { a } = 4.47 , \mathrm {~b} = 3 , \mathrm {~h} = 0.15$ 
A)  $\mathrm { a } = 6.00 , \mathrm {~b} = 2 , \mathrm {~h} = 0.63$ 
B)  $\mathrm { a } = 4.47 , \mathrm {~b} = 6 , \mathrm {~h} = 0.15$ 
C)  $\mathrm { a } = 0.15 , \mathrm {~b} = 3 , \mathrm {~h} = 4.47$ 
D)  $\mathrm { a } = 4.47 , \mathrm {~b} = 3 , \mathrm {~h} = 0.15$

Question 13

Use the arc length formula and the given information to find the indicated quantity.
-$\mathrm { r } = 2 \mathrm { ft } , \theta = 36 ^ { \circ }$; find $\mathrm { s }$

Accepted Answer

A)  $\frac { 1 } { 5 } \pi \mathrm { ft }$ 
B)  $\frac { 2 } { 5 } \pi \mathrm { ft }$ 
C)  $72 \mathrm { ft }$ 
D)  $144 \mathrm { ft }$ 
A)  $\frac { 1 } { 5 } \pi \mathrm { ft }$ 
B)  $\frac { 2 } { 5 } \pi \mathrm { ft }$ 
C)  $72 \mathrm { ft }$ 
D)  $144 \mathrm { ft }$

Question 14

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$60.57 ^ { \circ }$

Accepted Answer

A)  $1.0571$ 
B)  $0.5286$ 
C)  $0.7048$ 
D)  $0.3365$ 
A)  $1.0571$ 
B)  $0.5286$ 
C)  $0.7048$ 
D)  $0.3365$

Question 15

Find the domain and range of the function.
-$$f ( x ) = 3 \sin ^ { 2 } x$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $[ 0,3 ]$ 
B)  Domain: $[ 0,3 ]$; range: $( - \infty , \infty )$ 
C)  Domain: $[ 0 , \infty )$; range: $[ - 3,3 ]$ 
D)  Domain: $( - \infty , \infty )$; range $[ - 3,3 ]$ 
A)  Domain: $( - \infty , \infty )$; range: $[ 0,3 ]$ 
B)  Domain: $[ 0,3 ]$; range: $( - \infty , \infty )$ 
C)  Domain: $[ 0 , \infty )$; range: $[ - 3,3 ]$ 
D)  Domain: $( - \infty , \infty )$; range $[ - 3,3 ]$

Question 16

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$$\cos \theta = \frac { 10 } { 11 } ; \sec \theta$$

Accepted Answer

A)  $\frac { \sqrt { 21 } } { 10 }$ 
B)  $\frac { \sqrt { 21 } } { 11 }$ 
C)  $\frac { 10 } { \sqrt { 21 } }$ 
D)  $\frac { 11 } { 10 }$ 
A)  $\frac { \sqrt { 21 } } { 10 }$ 
B)  $\frac { \sqrt { 21 } } { 11 }$ 
C)  $\frac { 10 } { \sqrt { 21 } }$ 
D)  $\frac { 11 } { 10 }$

Question 17

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph.
-$$y = \sec \frac { 1 } { 6 } x$$

Accepted Answer

A)  Horizontal shrink by a factor of $\frac { 1 } { 6 }$ 
B)  Vertical translation up 6 units 
C)  Horizontal stretch by a factor of 6 
D)  Vertical shrink by a factor of $\frac { 1 } { 6 }$ 
A)  Horizontal shrink by a factor of $\frac { 1 } { 6 }$ 
B)  Vertical translation up 6 units 
C)  Horizontal stretch by a factor of 6 
D)  Vertical shrink by a factor of $\frac { 1 } { 6 }$

Question 18

Convert from degrees to radians. Use the value of &pi; found on a calculator and round answers to four decimal places, as needed.
-$36 ^ { \circ }$

Accepted Answer

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

Question 19

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\csc \theta = \frac { 9 } { 2 } ; \cot \theta$

Accepted Answer

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

Question 20

Graph the function.
-$y=\frac{1}{2} \cos \frac{3}{4} x$

Accepted Answer

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

Evaluate. - $\cos \left( \frac { 2,222,013 \pi } { 2 } \right)$

Find the specified quantity. -Find the vertical translation of $y = 4 + 2 \sin \left( 5 x + \frac { \pi } { 3 } \right)$ .

Use a calculator to find the function value to four decimal places. - $\sin 17 ^ { \circ } 10 ^ { \prime }$

Find the zeros of the function in the interval $[-2 \pi, 2 \pi]$ . - $f ( x ) = - \frac { 1 } { 6 } \sin \frac { x } { 2 }$

Find the exact solution to the equation without a calculator. - $\tan ^ { - 1 } ( \tan x ) = - \frac { \pi } { 6 }$

Use a calculator to solve for x in the given interval - $\sec \theta = - 4.0545,0 \leq \theta \leq 2 \pi$

Identify the maximum and minimum values of the function in the interval $[-2 \pi, 2 \pi]$ . Use your understanding of transformations, not your graphing calculator. - $y = - 9 \sin x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $183.08 ^ { \circ }$

Use a calculator to find the function value to four decimal places. - $\cot 14.3 ^ { \circ }$

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - $f ( x ) = 4 \sin 3 x - 2 \cos 3 x$

Use the arc length formula and the given information to find the indicated quantity. - $\mathrm { r } = 2 \mathrm { ft } , \theta = 36 ^ { \circ }$ ; find $\mathrm { s }$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $60.57 ^ { \circ }$

Find the domain and range of the function. - $f ( x ) = 3 \sin ^ { 2 } x$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\cos \theta = \frac { 10 } { 11 } ; \sec \theta$

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. - $y = \sec \frac { 1 } { 6 } x$

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - $36 ^ { \circ }$

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\csc \theta = \frac { 9 } { 2 } ; \cot \theta$

Graph the function. - $y=\frac{1}{2} \cos \frac{3}{4} x$ $Graph the function. - y=\frac{1}{2} \cos \frac{3}{4} x$

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. - cos⁡(2,222,013π2)\cos \left( \frac { 2,222,013 \pi } { 2 } \right)cos(22,222,013π​)

Match the function with its graph. -1) y=−csc⁡xy = - \csc xy=−cscx 2) y=−sec⁡xy = - \sec xy=−secx 3) y=−tan⁡xy = - \tan xy=−tanx 4) y=−cot⁡xy = - \cot xy=−cotx a. b. c. d.

Find the specified quantity. -Find the vertical translation of y=4+2sin⁡(5x+π3)y = 4 + 2 \sin \left( 5 x + \frac { \pi } { 3 } \right)y=4+2sin(5x+3π​) .

Use a calculator to find the function value to four decimal places. - sin⁡17∘10′\sin 17 ^ { \circ } 10 ^ { \prime }sin17∘10′

Find the zeros of the function in the interval [−2π,2π] [-2 \pi, 2 \pi] [−2π,2π] . - f(x)=−16sin⁡x2f ( x ) = - \frac { 1 } { 6 } \sin \frac { x } { 2 }f(x)=−61​sin2x​

Find the exact solution to the equation without a calculator. - tan⁡−1(tan⁡x)=−π6\tan ^ { - 1 } ( \tan x ) = - \frac { \pi } { 6 }tan−1(tanx)=−6π​

Use a calculator to solve for x in the given interval - sec⁡θ=−4.0545,0≤θ≤2π\sec \theta = - 4.0545,0 \leq \theta \leq 2 \pisecθ=−4.0545,0≤θ≤2π

Identify the maximum and minimum values of the function in the interval [−2π,2π] [-2 \pi, 2 \pi] [−2π,2π] . Use your understanding of transformations, not your graphing calculator. - y=−9sin⁡xy = - 9 \sin xy=−9sinx

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 183.08∘183.08 ^ { \circ }183.08∘

Use a calculator to find the function value to four decimal places. - cot⁡14.3∘\cot 14.3 ^ { \circ }cot14.3∘

Find a, b, and h so that f(x) a sin (b(x - h)). Round to two decimal places if necessary. - f(x)=4sin⁡3x−2cos⁡3xf ( x ) = 4 \sin 3 x - 2 \cos 3 xf(x)=4sin3x−2cos3x

Use the arc length formula and the given information to find the indicated quantity. - r=2ft,θ=36∘\mathrm { r } = 2 \mathrm { ft } , \theta = 36 ^ { \circ }r=2ft,θ=36∘ ; find s\mathrm { s }s

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 60.57∘60.57 ^ { \circ }60.57∘

Find the domain and range of the function. - f(x)=3sin⁡2xf ( x ) = 3 \sin ^ { 2 } xf(x)=3sin2x

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - cos⁡θ=1011;sec⁡θ\cos \theta = \frac { 10 } { 11 } ; \sec \thetacosθ=1110​;secθ

Describe the transformation required to obtain the graph of the given function from the basic trigonometric graph. - y=sec⁡16xy = \sec \frac { 1 } { 6 } xy=sec61​x

Convert from degrees to radians. Use the value of π found on a calculator and round answers to four decimal places, as needed. - 36∘36 ^ { \circ }36∘

Assume that θ \theta θ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - csc⁡θ=92;cot⁡θ\csc \theta = \frac { 9 } { 2 } ; \cot \thetacscθ=29​;cotθ

Graph the function. - y=12cos⁡34xy=\frac{1}{2} \cos \frac{3}{4} xy=21​cos43​x