Question 1

Find the exact function value if it exists.
-sin 270°

Accepted Answer

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

Question 2

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-207°

Accepted Answer

A) 207° + n · 360° 
B) 207° + n · 90° 
C) 207° + n · 180° 
D) 207° + 2nπ 
A) 207° + n · 360° 
B) 207° + n · 90° 
C) 207° + n · 180° 
D) 207° + 2nπ

Question 3

Solve for the requested quantity.
-Find all missing sides and angles. Round to the nearest tenth.

$\mathrm { c } = 29.7$
$B = 39.6 ^ { \circ }$

Accepted Answer

A)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 38.5 , \mathrm {~b} = 46.6$ 
B)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 22.9 , \mathrm {~b} = 18.9$ 
C)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 35.9 , \mathrm {~b} = 46.6$ 
D)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 46.6 , \mathrm {~b} = 38.5$ 
A)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 38.5 , \mathrm {~b} = 46.6$ 
B)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 22.9 , \mathrm {~b} = 18.9$ 
C)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 35.9 , \mathrm {~b} = 46.6$ 
D)  $\mathrm { A } = 50.4 ^ { \circ } , \mathrm { a } = 46.6 , \mathrm {~b} = 38.5$

Question 4

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( 3,8 )$; find $\sin \theta$

Accepted Answer

A)  $\frac { 3 \sqrt { 73 } } { 73 }$ 
B)  $\frac { 8 } { 3 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $\frac { 8 \sqrt { 73 } } { 73 }$ 
A)  $\frac { 3 \sqrt { 73 } } { 73 }$ 
B)  $\frac { 8 } { 3 }$ 
C)  $\frac { 3 } { 8 }$ 
D)  $\frac { 8 \sqrt { 73 } } { 73 }$

Question 5

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( 9,0 )$; find $\sec \theta$

Accepted Answer

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

Question 6

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-337°18'37''

Accepted Answer

A) 337.27 
B) 337.32 
C) 337.31 
D) 337.37 
A) 337.27 
B) 337.32 
C) 337.31 
D) 337.37

Question 7

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-tan ϴ= 2.007

Accepted Answer

A) -19.35° 
B) 63.51° 
C) 423.51° 
D) 243.51° 
A) -19.35° 
B) 63.51° 
C) 423.51° 
D) 243.51°

Question 8

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\cos \theta = \frac { 1 } { 2 }$

Accepted Answer

A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
C)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
D)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
C)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
D)  $210 ^ { \circ }$ and $330 ^ { \circ }$

Question 9

Sketch an angle $\theta$ in standard position such that $\theta$ has the smallest possible positive measure and the given point is on the terminal side of $\theta$.
-P = (-1, -3)

Accepted Answer

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

Question 10

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

Accepted Answer

A)  $\sin B = \frac { 7 } { 24 } ; \tan B = \frac { 7 } { 25 }$ 
B)  $\sin B = \frac { 7 } { 25 } ; \tan B = \frac { 7 } { 24 }$ 
C)  $\sin B = \frac { 24 } { 25 } ; \tan B = \frac { 24 } { 7 }$ 
D)  $\sin B = \frac { 25 } { 7 } ; \tan B = \frac { 24 } { 7 }$ 
A)  $\sin B = \frac { 7 } { 24 } ; \tan B = \frac { 7 } { 25 }$ 
B)  $\sin B = \frac { 7 } { 25 } ; \tan B = \frac { 7 } { 24 }$ 
C)  $\sin B = \frac { 24 } { 25 } ; \tan B = \frac { 24 } { 7 }$ 
D)  $\sin B = \frac { 25 } { 7 } ; \tan B = \frac { 24 } { 7 }$

Question 11

Use a calculator to find the function value to four decimal places.
-sin 31.1°

Accepted Answer

A) 0.6032 
B) 0.5165 
C) 0.3107 
D) 0.8563 
A) 0.6032 
B) 0.5165 
C) 0.3107 
D) 0.8563

Question 12

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$. Give the exact value of the indicated trig function for $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( 9,12 )$; find $\cos \theta$.

Accepted Answer

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

Question 13

$\sec \left( - 90 ^ { \circ } \right)$

Accepted Answer

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

Question 14

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\sin \theta = \frac { \sqrt { 3 } } { 2 }$

Accepted Answer

A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $150 ^ { \circ }$ and $210 ^ { \circ }$ 
A)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
B)  $210 ^ { \circ }$ and $330 ^ { \circ }$ 
C)  $60 ^ { \circ }$ and $300 ^ { \circ }$ 
D)  $150 ^ { \circ }$ and $210 ^ { \circ }$

Question 15

Use the fundamental identities to find the value of the trigonometric function.
-$\sec \theta$, if $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant $\mathrm { I }$.

Accepted Answer

A)  $- \frac { 3 } { 2 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$ 
A)  $- \frac { 3 } { 2 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
D)  $- \frac { \sqrt { 7 } } { 9 }$

Question 16

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions.
-$\sec \theta < 0$ and $\tan \theta < 0$

Accepted Answer

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

Question 17

Write the expression in terms of its cofunction.
-sec 71°

Accepted Answer

A) sec 19° 
B) cos 19° 
C) sin 71° 
D) csc 19° 
A) sec 19° 
B) cos 19° 
C) sin 71° 
D) csc 19°

Question 18

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-8°

Accepted Answer

A) 8° + n · 360° 
B) 8° + n · 720° 
C) 8° + n · 90° 
D) 8° + n · 180° 
A) 8° + n · 360° 
B) 8° + n · 720° 
C) 8° + n · 90° 
D) 8° + n · 180°

Question 19

Solve the right triangle.
-A = 36°, b = 56.8, C = 90°

Accepted Answer

A) B = 36°, a = 46, c = 41.3 
B) B = 54°, a = 41.3, c = 70.2 
C) B = 54°, a = 78.2, c = 96.6 
D) B = 36°, a = 78.2, c = 46 
A) B = 36°, a = 46, c = 41.3 
B) B = 54°, a = 41.3, c = 70.2 
C) B = 54°, a = 78.2, c = 96.6 
D) B = 36°, a = 78.2, c = 46

Question 20

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure
of two other angles, one positive and one negative, coterminal with the given angle.
-170°

Accepted Answer

A)  $350 ^ { \circ }$ and $- 10 ^ { \circ }$
  
B)  $530 ^ { \circ }$ and $- 190 ^ { \circ }$
  
C)  $530 ^ { \circ }$ and $- 190 ^ { \circ }$
  
D)  $350 ^ { \circ }$ and $- 10 ^ { \circ }$
  
A)  $350 ^ { \circ }$ and $- 10 ^ { \circ }$
  
B)  $530 ^ { \circ }$ and $- 190 ^ { \circ }$
  
C)  $530 ^ { \circ }$ and $- 190 ^ { \circ }$
  
D)  $350 ^ { \circ }$ and $- 10 ^ { \circ }$

Find the exact function value if it exists. -sin 270°

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -207°

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. $Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. \mathrm { c } = 29.7 B = 39.6 ^ { \circ }$ $\mathrm { c } = 29.7$ $B = 39.6 ^ { \circ }$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( 3,8 )$ ; find $\sin \theta$

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( 9,0 )$ ; find $\sec \theta$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -337°18'37''

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -tan ϴ= 2.007

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ - $\cos \theta = \frac { 1 } { 2 }$

Use a calculator to find the function value to four decimal places. -sin 31.1°

Suppose that $\theta$ is in standard position and the given point is on the terminal side of $\theta$ . Give the exact value of the indicated trig function for $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( 9,12 )$ ; find $\cos \theta$ .

$\sec \left( - 90 ^ { \circ } \right)$

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ - $\sin \theta = \frac { \sqrt { 3 } } { 2 }$

Use the fundamental identities to find the value of the trigonometric function. - $\sec \theta$ , if $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant $\mathrm { I }$ .

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\sec \theta < 0$ and $\tan \theta < 0$

Write the expression in terms of its cofunction. -sec 71°

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -8°

Solve the right triangle. -A = 36°, b = 56.8, C = 90°

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -170°

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Exam 14: Trigonometry Formerly

Find the exact function value if it exists. -sin 270°

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -207°

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. c=29.7\mathrm { c } = 29.7c=29.7 B=39.6∘B = 39.6 ^ { \circ }B=39.6∘

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -337°18'37''

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -tan ϴ= 2.007

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the smallest possible positive measure and the given point is on the terminal side of θ\thetaθ . -P = (-1, -3)

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find sin⁡B\sin \mathrm { B }sinB and tan⁡B\tan \mathrm { B }tanB .

Use a calculator to find the function value to four decimal places. -sin 31.1°

sec⁡(−90∘)\sec \left( - 90 ^ { \circ } \right)sec(−90∘)

Use the fundamental identities to find the value of the trigonometric function. - sec⁡θ\sec \thetasecθ , if tan⁡θ=34\tan \theta = \frac { 3 } { 4 }tanθ=43​ and θ\thetaθ is in quadrant I\mathrm { I }I .

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - sec⁡θ<0\sec \theta < 0secθ<0 and tan⁡θ<0\tan \theta < 0tanθ<0

Write the expression in terms of its cofunction. -sec 71°

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. -8°

Solve the right triangle. -A = 36°, b = 56.8, C = 90°

Draw the given angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, coterminal with the given angle. -170°

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. $Solve for the requested quantity. -Find all missing sides and angles. Round to the nearest tenth. \mathrm { c } = 29.7 B = 39.6 ^ { \circ }$ $\mathrm { c } = 29.7$ $B = 39.6 ^ { \circ }$

$\sec \left( - 90 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. - $\sec \theta$ , if $\tan \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant $\mathrm { I }$ .

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\sec \theta < 0$ and $\tan \theta < 0$