Question 1

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three
decimal places.
-$\cos ^ { - 1 } ( 0.2493 )$

Accepted Answer

A)  $1.319$ 
B)  $4.964$ 
C)  $0.252$ 
D)  $4.460$ 
A)  $1.319$ 
B)  $4.964$ 
C)  $0.252$ 
D)  $4.460$

Question 2

Choose the point on the terminal side of .
-$$\theta = - 225 ^ { \circ }$$

Accepted Answer

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

Question 3

Select the functions that have identical graphs.
-(i) $y = \sin x$
(ii) $y = \cos \left( x + \frac { 3 \pi } { 2 } \right)$
(iii) $y = \cos x$

Accepted Answer

A)  $i$ and iii 
B)  ii and iii 
C)  $i$, ii and iii 
D)  $\mathrm { i }$ and ii 
A)  $i$ and iii 
B)  ii and iii 
C)  $i$, ii and iii 
D)  $\mathrm { i }$ and ii

Question 4

Solve the problem.
-A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 7 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Accepted Answer

A)  $y = - 5 \cos 7 \pi t$ 
B)  $y = - 5 \cos 14 \pi t$ 
C)  $y = 5 \cos 14 \pi t$ 
D)  $y = 5 \cos \frac { 1 } { 7 } t$ 
A)  $y = - 5 \cos 7 \pi t$ 
B)  $y = - 5 \cos 14 \pi t$ 
C)  $y = 5 \cos 14 \pi t$ 
D)  $y = 5 \cos \frac { 1 } { 7 } t$

Question 5

Find the exact solution to the equation without a calculator.
-$\sin \left( \sin ^ { - 1 } x \right) = - 0.8$

Accepted Answer

A)  0 
B)  $- 1.6$ 
C)  $- 0.8$ 
D)  $- 0.4$ 
A)  0 
B)  $- 1.6$ 
C)  $- 0.8$ 
D)  $- 0.4$

Question 6

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two
decimal places.
-$- 2.8632$

Accepted Answer

A)  $- 163.55 ^ { \circ }$ 
B)  $- 163.05 ^ { \circ }$ 
C)  $- 164.05 ^ { \circ }$ 
D)  $- 164.75 ^ { \circ }$ 
A)  $- 163.55 ^ { \circ }$ 
B)  $- 163.05 ^ { \circ }$ 
C)  $- 164.05 ^ { \circ }$ 
D)  $- 164.75 ^ { \circ }$

Question 7

Use a calculator to graph the function.
-$y=-\sin ^{3} x$

Accepted Answer

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

Question 8

Determine whether the graph of f(x) is a sinusoid.
-$$f ( x ) = 9 \cos 2 x - \cot x$$

Accepted Answer

A) True 
 B)False

Question 9

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

Accepted Answer

A)  $\sec \theta = \frac { \sqrt { 85 } } { 7 }$ 
B)  $\sec \theta = \frac { 7 \sqrt { 85 } } { 85 }$ 
C)  $\sec \theta = \frac { 6 } { 7 }$ 
D)  $\sec \theta = \frac { 7 } { 6 }$ 
A)  $\sec \theta = \frac { \sqrt { 85 } } { 7 }$ 
B)  $\sec \theta = \frac { 7 \sqrt { 85 } } { 85 }$ 
C)  $\sec \theta = \frac { 6 } { 7 }$ 
D)  $\sec \theta = \frac { 7 } { 6 }$

Question 10

Determine whether the given function is positive or negative for values of t in the specified quadrant.
-Quadrant II, cot $t$

Accepted Answer

A)  Positive 
B)  Negative 
A)  Positive 
B)  Negative

Question 11

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined."
-$\mathrm { P } ( 21,28 )$; find $\sin \theta$.

Accepted Answer

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

Question 12

Graph the function.
-$y=3 \sin 2 x-2 \cos x$

Accepted Answer

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

Question 13

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-tan 0.1345

Accepted Answer

A)  0.1341 
B)  0.1353 
C)  1.009 
D)  0.9910 
A)  0.1341 
B)  0.1353 
C)  1.009 
D)  0.9910

Question 14

Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\tan \theta = \frac { 1 } { 8 } ; \sin \theta$

Accepted Answer

A)  $\sqrt { 65 }$ 
B)  $\frac { \sqrt { 65 } } { 8 }$ 
C)  $\frac { 8 \sqrt { 65 } } { 65 }$ 
D)  $\frac { \sqrt { 65 } } { 65 }$ 
A)  $\sqrt { 65 }$ 
B)  $\frac { \sqrt { 65 } } { 8 }$ 
C)  $\frac { 8 \sqrt { 65 } } { 65 }$ 
D)  $\frac { \sqrt { 65 } } { 65 }$

Question 15

Solve for x in the given interval.
-$$\csc x = - 1,3 \pi \leq x \leq 4 \pi$$

Accepted Answer

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

Question 16

Solve the problem.
-At an altitude of $3800 \mathrm { ft }$, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 5 miles away by land? (Round your answer to the nearest tenth of a degree.)

Accepted Answer

A)  $89.9 ^ { \circ }$ 
B)  $88.9 ^ { \circ }$ 
C)  $8.2 ^ { \circ }$ 
D)  $9.2 ^ { \circ }$ 
A)  $89.9 ^ { \circ }$ 
B)  $88.9 ^ { \circ }$ 
C)  $8.2 ^ { \circ }$ 
D)  $9.2 ^ { \circ }$

Question 17

Use a calculator to evaluate the function. Round your answer to 4 decimal places.
-$\tan \left( \frac { \pi } { 10 } \right)$

Accepted Answer

A)  $0.3640$ 
B)  $0.2679$ 
C)  $0.0055$ 
D)  $0.3249$ 
A)  $0.3640$ 
B)  $0.2679$ 
C)  $0.0055$ 
D)  $0.3249$

Question 18

Choose the graph which matches the function.
-$$f ( x ) = 5 x \sin 2 x$$

Accepted Answer

A)  Damping factor $= 2$, damping occurs as $x \rightarrow 0$ 
B)  Damping factor $= 5 x$, damping occurs as $x \rightarrow \infty$ 
C)  No damping 
D)  Damping factor $= 5 x$, damping occurs as $x \rightarrow 0$ 
A)  Damping factor $= 2$, damping occurs as $x \rightarrow 0$ 
B)  Damping factor $= 5 x$, damping occurs as $x \rightarrow \infty$ 
C)  No damping 
D)  Damping factor $= 5 x$, damping occurs as $x \rightarrow 0$

Question 19

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places.
-$\arccos 0.55$

Accepted Answer

A)  $56.63 ^ { \circ }$ 
B)  $66.73 ^ { \circ }$ 
C)  $28.81 ^ { \circ }$ 
D)  $33.37 ^ { \circ }$ 
A)  $56.63 ^ { \circ }$ 
B)  $66.73 ^ { \circ }$ 
C)  $28.81 ^ { \circ }$ 
D)  $33.37 ^ { \circ }$

Question 20

Solve the problem.
-Consider the formula $T = 591 - 76 \cos 2 \theta$, where $\theta$ is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of $\theta$ for which the value of $\mathrm { T }$ will be 559 ?

Accepted Answer

A)  $68.10 ^ { \circ }$ 
B)  $29.55 ^ { \circ }$ 
C)  $32.55 ^ { \circ }$ 
D)  $65.10 ^ { \circ }$ 
A)  $68.10 ^ { \circ }$ 
B)  $29.55 ^ { \circ }$ 
C)  $32.55 ^ { \circ }$ 
D)  $65.10 ^ { \circ }$

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - $\cos ^ { - 1 } ( 0.2493 )$

Choose the point on the terminal side of . - $\theta = - 225 ^ { \circ }$

Select the functions that have identical graphs. -(i) $y = \sin x$ (ii) $y = \cos \left( x + \frac { 3 \pi } { 2 } \right)$ (iii) $y = \cos x$

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is $\frac { 1 } { 7 }$ second, determine a trigonometric model that gives the position of the weight at time $t$ seconds.

Find the exact solution to the equation without a calculator. - $\sin \left( \sin ^ { - 1 } x \right) = - 0.8$

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - $- 2.8632$

Use a calculator to graph the function. - $y=-\sin ^{3} x$ $Use a calculator to graph the function. - y=-\sin ^{3} x$

Determine whether the graph of f(x) is a sinusoid. - $f ( x ) = 9 \cos 2 x - \cot x$

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

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, cot $t$

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - $\mathrm { P } ( 21,28 )$ ; find $\sin \theta$ .

Graph the function. - $y=3 \sin 2 x-2 \cos x$ $Graph the function. - y=3 \sin 2 x-2 \cos x$

Use a calculator to evaluate the function. Round your answer to 4 decimal places. -tan 0.1345

Assume that $\theta$ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric function. - $\tan \theta = \frac { 1 } { 8 } ; \sin \theta$

Solve for x in the given interval. - $\csc x = - 1,3 \pi \leq x \leq 4 \pi$

Solve the problem. -At an altitude of $3800 \mathrm { ft }$ , the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 5 miles away by land? (Round your answer to the nearest tenth of a degree.)

Use a calculator to evaluate the function. Round your answer to 4 decimal places. - $\tan \left( \frac { \pi } { 10 } \right)$

Choose the graph which matches the function. - $f ( x ) = 5 x \sin 2 x$

Use a calculator to find the approximate value. Express your answer in degrees rounded to two decimal places. - $\arccos 0.55$

Solve the problem. -Consider the formula $T = 591 - 76 \cos 2 \theta$ , where $\theta$ is measured in degrees. To the nearest hundredth of a degree, what is the smallest positive value of $\theta$ for which the value of $\mathrm { T }$ will be 559 ?

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

Filters

Exam 4: Trigonometric Functions

Use a calculator to find the approximate value of the expression. Express your answer in radians and round to three decimal places. - cos⁡−1(0.2493)\cos ^ { - 1 } ( 0.2493 )cos−1(0.2493)

Choose the point on the terminal side of . - θ=−225∘\theta = - 225 ^ { \circ }θ=−225∘

Select the functions that have identical graphs. -(i) y=sin⁡xy = \sin xy=sinx (ii) y=cos⁡(x+3π2)y = \cos \left( x + \frac { 3 \pi } { 2 } \right)y=cos(x+23π​) (iii) y=cos⁡xy = \cos xy=cosx

Solve the problem. -A weight attached to a spring is pulled down 5 inches below the equilibrium position. Assuming that the period of the system is 17\frac { 1 } { 7 }71​ second, determine a trigonometric model that gives the position of the weight at time ttt seconds.

Find the exact solution to the equation without a calculator. - sin⁡(sin⁡−1x)=−0.8\sin \left( \sin ^ { - 1 } x \right) = - 0.8sin(sin−1x)=−0.8

Convert the radian measure to degree measure. Use the value of found on a calculator and round answers to two decimal places. - −2.8632- 2.8632−2.8632

Use a calculator to graph the function. - y=−sin⁡3xy=-\sin ^{3} xy=−sin3x

Determine whether the graph of f(x) is a sinusoid. - f(x)=9cos⁡2x−cot⁡xf ( x ) = 9 \cos 2 x - \cot xf(x)=9cos2x−cotx

Find the trigonometric function value for the angle shown. - sec⁡θ\sec \thetasecθ

Determine whether the given function is positive or negative for values of t in the specified quadrant. -Quadrant II, cot ttt

Point P is on the terminal side of θ . Evaluate the six trigonometric functions for θ. If the function is undefined, write "undefined." - P(21,28)\mathrm { P } ( 21,28 )P(21,28) ; find sin⁡θ\sin \thetasinθ .

Graph the function. - y=3sin⁡2x−2cos⁡xy=3 \sin 2 x-2 \cos xy=3sin2x−2cosx