Question 1

Determine the quadrant in which the angle $- 170.8 ^ { \circ }$ lies.

Accepted Answer

A)  Quadrant IV 
B)  Quadrant III 
C)  Quadrant I 
D)  Quadrant II 
A)  Quadrant IV 
B)  Quadrant III 
C)  Quadrant I 
D)  Quadrant II

Question 2

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$.
radius: $r = 10$ inches arc length: $s = 47$ inches

Accepted Answer

A)  $\frac { 10 } { 47 }$ 
B)  $\frac { 10 \pi } { 47 }$ 
C)  $\frac { 47 \pi } { 10 }$ 
D)  $\frac { 47 } { 20 }$ 
E)  $\frac { 47 } { 10 }$ 
A)  $\frac { 10 } { 47 }$ 
B)  $\frac { 10 \pi } { 47 }$ 
C)  $\frac { 47 \pi } { 10 }$ 
D)  $\frac { 47 } { 20 }$ 
E)  $\frac { 47 } { 10 }$

Question 3

Find the indicated trigonometric value in the specified quadrant.
Function Quadrant Trigonometric Value
$$\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \theta$$

Accepted Answer

A)  $\frac { 2 } { 3 \sqrt { 13 } }$ 
B)  $\frac { 3 \sqrt { 13 } } { 11 }$ 
C)  $\frac { 11 } { 3 \sqrt { 13 } }$ 
D)  $\frac { 2 } { 11 }$ 
E)  Undefined 
A)  $\frac { 2 } { 3 \sqrt { 13 } }$ 
B)  $\frac { 3 \sqrt { 13 } } { 11 }$ 
C)  $\frac { 11 } { 3 \sqrt { 13 } }$ 
D)  $\frac { 2 } { 11 }$ 
E)  Undefined

Question 4

Determine the graph of $y = \cos \left( \frac { 5 x } { 3 } \right)$.

Accepted Answer

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

Question 5

Determine the period and amplitude of $y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)$.

Accepted Answer

A)  period: $\frac { 2 \pi } { 13 }$; amplitude: 5 
B)  period: $26 \pi$; amplitude: 5 
C)  period: $13 \pi$; amplitude: 10 
D)  period: $\frac { \pi } { 13 }$; amplitude: 5 
E)  period: $- \frac { 2 \pi } { 13 }$; amplitude: $- 5$ 
A)  period: $\frac { 2 \pi } { 13 }$; amplitude: 5 
B)  period: $26 \pi$; amplitude: 5 
C)  period: $13 \pi$; amplitude: 10 
D)  period: $\frac { \pi } { 13 }$; amplitude: 5 
E)  period: $- \frac { 2 \pi } { 13 }$; amplitude: $- 5$

Question 6

Use a calculator to evaluate $\tan 4.8$. Round your answer to four decimal places.

Accepted Answer

A)  $- 3.5723$ 
B)  $- 12.1349$ 
C)  $- 11.3849$ 
D)  $0.0840$ 
E)  $0.5840$ 
A)  $- 3.5723$ 
B)  $- 12.1349$ 
C)  $- 11.3849$ 
D)  $0.0840$ 
E)  $0.5840$

Question 7

Rewrite the given angle in radian measure as a multiple of $\pi$. (Do not use a calculator.)
$- 110 ^ { \circ }$

Accepted Answer

A)  $- \frac { 7 \pi } { 18 }$ 
B)  $- \pi$ 
C)  $- \frac { 11 \pi } { 36 }$ 
D)  $- \frac { 11 \pi } { 18 }$ 
E)  $- \frac { 5 \pi } { 9 }$ 
A)  $- \frac { 7 \pi } { 18 }$ 
B)  $- \pi$ 
C)  $- \frac { 11 \pi } { 36 }$ 
D)  $- \frac { 11 \pi } { 18 }$ 
E)  $- \frac { 5 \pi } { 9 }$

Question 8

Find the reference angle for the angle $6.1$ radians. Round your answer to one decimal place.

Accepted Answer

A)  $- 3.0$ 
B)  $- 0.2$ 
C)  $3.0$ 
D)  $0.2$ 
E)  $- 12.4$ 
A)  $- 3.0$ 
B)  $- 0.2$ 
C)  $3.0$ 
D)  $0.2$ 
E)  $- 12.4$

Question 9

Find (if possible) the complement and supplement of the given angle. $1.2$

Accepted Answer

A)  complement: $1.2$; supplement: $\pi - 1.2 \approx 1.9$ 
B)  complement: $\frac { \pi } { 2 } - 2.5 \approx 0.4$; no supplement 
C)  complement: $\frac { \pi } { 2 } - 1.2 \approx 0.4$; supplement: $\pi - 1.2 \approx 1.9$ 
D)  no complement; supplement: $\pi - 1.2 \approx 1.9$ 
E)  no complement; no supplement 
A)  complement: $1.2$; supplement: $\pi - 1.2 \approx 1.9$ 
B)  complement: $\frac { \pi } { 2 } - 2.5 \approx 0.4$; no supplement 
C)  complement: $\frac { \pi } { 2 } - 1.2 \approx 0.4$; supplement: $\pi - 1.2 \approx 1.9$ 
D)  no complement; supplement: $\pi - 1.2 \approx 1.9$ 
E)  no complement; no supplement

Question 10

Determine a pair of coterminal angles (in radian measure) to the angle $\frac { \pi } { 2 }$.

Accepted Answer

A)  $\frac { 3 \pi } { 2 } , - \frac { \pi } { 2 }$ 
B)  $\frac { 5 \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $\frac { 7 \pi } { 2 } , - \frac { \pi } { 2 }$ 
D)  $\frac { 5 \pi } { 2 } , - \frac { 3 \pi } { 2 }$ 
E)  $\frac { 5 \pi } { 2 } , - \frac { \pi } { 2 }$ 
A)  $\frac { 3 \pi } { 2 } , - \frac { \pi } { 2 }$ 
B)  $\frac { 5 \pi } { 2 } , \frac { 3 \pi } { 2 }$ 
C)  $\frac { 7 \pi } { 2 } , - \frac { \pi } { 2 }$ 
D)  $\frac { 5 \pi } { 2 } , - \frac { 3 \pi } { 2 }$ 
E)  $\frac { 5 \pi } { 2 } , - \frac { \pi } { 2 }$

Question 11

Find the exact value of the given trigonometric function of the angle $\theta$ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: $\sin \theta$

Accepted Answer

A)  $8 \sqrt { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  1 
E)  $\frac { \sqrt { 2 } } { 8 }$ 
A)  $8 \sqrt { 2 }$ 
B)  $\sqrt { 2 }$ 
C)  $\frac { \sqrt { 2 } } { 2 }$ 
D)  1 
E)  $\frac { \sqrt { 2 } } { 8 }$

Question 12

Use the figure and a straightedge to approximate the value of $\cos 1.75$.

Accepted Answer

A)  $1.00$ 
B)  $0.98$ 
C)  $- 0.18$ 
D)  $- 5.52$ 
E)  $- 5.61$ 
A)  $1.00$ 
B)  $0.98$ 
C)  $- 0.18$ 
D)  $- 5.52$ 
E)  $- 5.61$

Question 13

Determine the exact value, if it exists, of $\sec ( - \pi )$.

Accepted Answer

A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $- 1$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  1 
E)  The value does not exist. 
A)  $- \frac { \sqrt { 3 } } { 2 }$ 
B)  $- 1$ 
C)  $\frac { \sqrt { 3 } } { 2 }$ 
D)  1 
E)  The value does not exist.

Question 14

Approximate $\sin ^ { - 1 } ( - 0.82 )$. Round your answer to four decimal places.

Accepted Answer

A)  $- 1.0401$ 
B)  $- 1.3677$ 
C)  $- 0.7311$ 
D)  $- 0.9614$ 
E)  $- 0.9389$ 
A)  $- 1.0401$ 
B)  $- 1.3677$ 
C)  $- 0.7311$ 
D)  $- 0.9614$ 
E)  $- 0.9389$

Question 15

The circular blade of a saw has a diameter of 7 inches and rotates at 2500 revolutions per minute. Find the angular speed in radians per second.

Accepted Answer

A)  $\frac { 875 \pi } { 3 }$ radians per second 
B)  $\frac { 250 \pi } { 3 }$ radians per second 
C)  $\frac { 1750 \pi } { 3 }$ radians per second 
D)  $\frac { 125 \pi } { 3 }$ radians per second 
E)  $14 \pi$ radians per second 
A)  $\frac { 875 \pi } { 3 }$ radians per second 
B)  $\frac { 250 \pi } { 3 }$ radians per second 
C)  $\frac { 1750 \pi } { 3 }$ radians per second 
D)  $\frac { 125 \pi } { 3 }$ radians per second 
E)  $14 \pi$ radians per second

Question 16

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.)
$\sin 78.9 ^ { \circ }$

Accepted Answer

A)  $- 0.3524$ 
B)  $0.1146$ 
C)  $0.9813$ 
D)  $0.1925$ 
E)  $5.0970$ 
A)  $- 0.3524$ 
B)  $0.1146$ 
C)  $0.9813$ 
D)  $0.1925$ 
E)  $5.0970$

Question 17

Determine the graph of $y = \frac { 1 } { 5 } \cos ( x )$.

Accepted Answer

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

Question 18

Find the frequency of the simple harmonic motion described by the function below.
$d = - 3 \cos ( 18 \pi t )$

Accepted Answer

A)  9 
B)  $- \frac { 2 \pi } { 3 }$ 
C)  $18 \pi$ 
D)  $- \frac { 2 } { 3 }$ 
E)  $- 3$ 
A)  9 
B)  $- \frac { 2 \pi } { 3 }$ 
C)  $18 \pi$ 
D)  $- \frac { 2 } { 3 }$ 
E)  $- 3$

Question 19

The circular blade of a saw has a diameter of $6.5$ inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Accepted Answer

A)  $113.45$ feet per second 
B)  $680.68$ feet per second 
C)  $9.03$ feet per second 
D)  $56.72$ feet per second 
E)  $209.44$ feet per second 
A)  $113.45$ feet per second 
B)  $680.68$ feet per second 
C)  $9.03$ feet per second 
D)  $56.72$ feet per second 
E)  $209.44$ feet per second

Question 20

Evaluate the tangent of the angle without using a calculator.
$- 120 ^ { \circ }$

Accepted Answer

A)  $\sqrt { 3 }$ 
B)  $- \frac { \sqrt { 3 } } { 3 }$ 
C)  $\frac { \sqrt { 3 } } { 3 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0 
A)  $\sqrt { 3 }$ 
B)  $- \frac { \sqrt { 3 } } { 3 }$ 
C)  $\frac { \sqrt { 3 } } { 3 }$ 
D)  $\frac { 1 } { 2 }$ 
E)  0

Determine the quadrant in which the angle $- 170.8 ^ { \circ }$ lies.

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$ . radius: $r = 10$ inches arc length: $s = 47$ inches

Find the indicated trigonometric value in the specified quadrant. Function Quadrant Trigonometric Value $\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \theta$

Determine the graph of $y = \cos \left( \frac { 5 x } { 3 } \right)$ .

Determine the period and amplitude of $y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)$ .

Use a calculator to evaluate $\tan 4.8$ . Round your answer to four decimal places.

Rewrite the given angle in radian measure as a multiple of $\pi$ . (Do not use a calculator.) $- 110 ^ { \circ }$

Find the reference angle for the angle $6.1$ radians. Round your answer to one decimal place.

Find (if possible) the complement and supplement of the given angle. $1.2$

Determine a pair of coterminal angles (in radian measure) to the angle $\frac { \pi } { 2 }$ .

Use the figure and a straightedge to approximate the value of $\cos 1.75$ . $Use the figure and a straightedge to approximate the value of \cos 1.75 .$

Determine the exact value, if it exists, of $\sec ( - \pi )$ .

Approximate $\sin ^ { - 1 } ( - 0.82 )$ . Round your answer to four decimal places.

The circular blade of a saw has a diameter of 7 inches and rotates at 2500 revolutions per minute. Find the angular speed in radians per second.

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\sin 78.9 ^ { \circ }$

Determine the graph of $y = \frac { 1 } { 5 } \cos ( x )$ .

Find the frequency of the simple harmonic motion described by the function below. $d = - 3 \cos ( 18 \pi t )$

The circular blade of a saw has a diameter of $6.5$ inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Evaluate the tangent of the angle without using a calculator. $- 120 ^ { \circ }$

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

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Exam 4: Trigonometric Functions

Determine the quadrant in which the angle −170.8∘- 170.8 ^ { \circ }−170.8∘ lies.

Find the radian measure of the central angle of a circle of radius rrr that intercepts an arc of length sss . radius: r=10r = 10r=10 inches arc length: s=47s = 47s=47 inches

Find the indicated trigonometric value in the specified quadrant. Function Quadrant Trigonometric Value csc⁡θ=−112 IV sec⁡θ\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \thetacscθ=−211​ IV secθ

Determine the graph of y=cos⁡(5x3)y = \cos \left( \frac { 5 x } { 3 } \right)y=cos(35x​) .

Determine the period and amplitude of y=5cos⁡(x13+π5)y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)y=5cos(13x​+5π​) .

Use a calculator to evaluate tan⁡4.8\tan 4.8tan4.8 . Round your answer to four decimal places.

Rewrite the given angle in radian measure as a multiple of π\piπ . (Do not use a calculator.) −110∘- 110 ^ { \circ }−110∘

Find the reference angle for the angle 6.16.16.1 radians. Round your answer to one decimal place.

Find (if possible) the complement and supplement of the given angle. 1.21.21.2

Determine a pair of coterminal angles (in radian measure) to the angle π2\frac { \pi } { 2 }2π​ .

Find the exact value of the given trigonometric function of the angle θ\thetaθ shown in the figure. (Use the Pythagorean Theorem to find the third side of the triangle.) Find: sin⁡θ\sin \thetasinθ

Use the figure and a straightedge to approximate the value of cos⁡1.75\cos 1.75cos1.75 .

Determine the exact value, if it exists, of sec⁡(−π)\sec ( - \pi )sec(−π) .

Approximate sin⁡−1(−0.82)\sin ^ { - 1 } ( - 0.82 )sin−1(−0.82) . Round your answer to four decimal places.

The circular blade of a saw has a diameter of 7 inches and rotates at 2500 revolutions per minute. Find the angular speed in radians per second.

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) sin⁡78.9∘\sin 78.9 ^ { \circ }sin78.9∘

Determine the graph of y=15cos⁡(x)y = \frac { 1 } { 5 } \cos ( x )y=51​cos(x) .

Find the frequency of the simple harmonic motion described by the function below. d=−3cos⁡(18πt)d = - 3 \cos ( 18 \pi t )d=−3cos(18πt)

The circular blade of a saw has a diameter of 6.56.56.5 inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Evaluate the tangent of the angle without using a calculator. −120∘- 120 ^ { \circ }−120∘

Functions and Their Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Limits and an Introduction to Calculus

Filters

Determine the quadrant in which the angle $- 170.8 ^ { \circ }$ lies.

Find the radian measure of the central angle of a circle of radius $r$ that intercepts an arc of length $s$ . radius: $r = 10$ inches arc length: $s = 47$ inches

Find the indicated trigonometric value in the specified quadrant. Function Quadrant Trigonometric Value $\csc \theta = - \frac { 11 } { 2 } \quad \text { IV } \quad \sec \theta$

Determine the graph of $y = \cos \left( \frac { 5 x } { 3 } \right)$ .

Determine the period and amplitude of $y = 5 \cos \left( \frac { x } { 13 } + \frac { \pi } { 5 } \right)$ .

Use a calculator to evaluate $\tan 4.8$ . Round your answer to four decimal places.

Rewrite the given angle in radian measure as a multiple of $\pi$ . (Do not use a calculator.) $- 110 ^ { \circ }$

Find the reference angle for the angle $6.1$ radians. Round your answer to one decimal place.

Find (if possible) the complement and supplement of the given angle. $1.2$

Determine a pair of coterminal angles (in radian measure) to the angle $\frac { \pi } { 2 }$ .

Use the figure and a straightedge to approximate the value of $\cos 1.75$ . $Use the figure and a straightedge to approximate the value of \cos 1.75 .$

Determine the exact value, if it exists, of $\sec ( - \pi )$ .

Approximate $\sin ^ { - 1 } ( - 0.82 )$ . Round your answer to four decimal places.

Use a calculator to evaluate the function. Round your answers to four decimal places. (Be sure the calculator is in the correct angle mode.) $\sin 78.9 ^ { \circ }$

Determine the graph of $y = \frac { 1 } { 5 } \cos ( x )$ .

Find the frequency of the simple harmonic motion described by the function below. $d = - 3 \cos ( 18 \pi t )$

The circular blade of a saw has a diameter of $6.5$ inches and rotates at 2000 revolutions per minute. Find the linear speed of the saw teeth in feet per second. Round your answer to two decimal places.

Evaluate the tangent of the angle without using a calculator. $- 120 ^ { \circ }$