Question 1

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$26 ^ { \circ } 5 ^ { \prime }$

Accepted Answer

A)  $26.10 ^ { \circ }$ 
B)  $27.08 ^ { \circ }$ 
C)  $26.05 ^ { \circ }$ 
D)  $26.08 ^ { \circ }$ 
A)  $26.10 ^ { \circ }$ 
B)  $27.08 ^ { \circ }$ 
C)  $26.05 ^ { \circ }$ 
D)  $26.08 ^ { \circ }$

Question 2

Find the measure of each angle in the problem.
-Complementary angles with measures 2x and 7x - 9 degrees

Accepted Answer

A)  $42 ^ { \circ }$ and $138 ^ { \circ }$ 
B)  $11 ^ { \circ }$ and $79 ^ { \circ }$ 
C)  $22 ^ { \circ }$ and $68 ^ { \circ }$ 
D)  $24 ^ { \circ }$ and $66 ^ { \circ }$ 
A)  $42 ^ { \circ }$ and $138 ^ { \circ }$ 
B)  $11 ^ { \circ }$ and $79 ^ { \circ }$ 
C)  $22 ^ { \circ }$ and $68 ^ { \circ }$ 
D)  $24 ^ { \circ }$ and $66 ^ { \circ }$

Question 3

Solve the problem.
-A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is $15 ^ { \circ } 8 ^ { \prime }$. When the boat stops, the angle of depression is $55 ^ { \circ } 7 ^ { \prime }$. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round to the nearest foot.

Accepted Answer

A)  $623 \mathrm { ft }$ 
B)  $585 \mathrm { ft }$ 
C)  $645 \mathrm { ft }$ 
D)  $600 \mathrm { ft }$ 
A)  $623 \mathrm { ft }$ 
B)  $585 \mathrm { ft }$ 
C)  $645 \mathrm { ft }$ 
D)  $600 \mathrm { ft }$

Question 4

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.
-$160 ^ { \circ }$

Accepted Answer

A) $340 ^ { \circ }$ and $- 20 ^ { \circ }$
  
B)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
C)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
D)  $340 ^ { \circ }$ and $- 20 ^ { \circ }$
  
A) $340 ^ { \circ }$ and $- 20 ^ { \circ }$
  
B)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
C)  $520 ^ { \circ }$ and $- 200 ^ { \circ }$
  
D)  $340 ^ { \circ }$ and $- 20 ^ { \circ }$

Question 5

Solve the right triangle.
-$$\mathrm { a } = 2.2 \text { in., } \mathrm { A } = 59.4 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.

Accepted Answer

A)  $b = 0.2$ in., $B = 30.6 ^ { \circ } , c = 2.2$ in. 
B)  $b = 1.3$ in., $B = 30.6 ^ { \circ } , c = 2.6$ in. 
C)  $b = 2.7$ in., $B = 30.6 ^ { \circ } , c = 3.5$ in. 
D)  $b = 2.7$ in., $B = 30.6 ^ { \circ } , c = 2.6$ in. 
A)  $b = 0.2$ in., $B = 30.6 ^ { \circ } , c = 2.2$ in. 
B)  $b = 1.3$ in., $B = 30.6 ^ { \circ } , c = 2.6$ in. 
C)  $b = 2.7$ in., $B = 30.6 ^ { \circ } , c = 3.5$ in. 
D)  $b = 2.7$ in., $B = 30.6 ^ { \circ } , c = 2.6$ in.

Question 6

Find the reference angle for the given angle.
-$81 ^ { \circ }$

Accepted Answer

A)  $99 ^ { \circ }$ 
B)  $81 ^ { \circ }$ 
C)  $9 ^ { \circ }$ 
D)  $171 ^ { \circ }$ 
A)  $99 ^ { \circ }$ 
B)  $81 ^ { \circ }$ 
C)  $9 ^ { \circ }$ 
D)  $171 ^ { \circ }$

Question 7

Solve the problem.
-A conservation officer needs to know the width of a river in order to set instruments correctly for study of pollutants in the river. From point $\mathrm { A }$, the conservation officer walks 110 feet downstrean and sights point $B$ on the opposite bank to determine that $\theta = 60 ^ { \circ }$ (see figure). How wide is the river (round to the nearest foot)?

Accepted Answer

A)  $95 \mathrm { ft }$ 
B)  $220 \mathrm { ft }$ 
C)  $64 \mathrm { ft }$ 
D)  $191 \mathrm { ft }$ 
A)  $95 \mathrm { ft }$ 
B)  $220 \mathrm { ft }$ 
C)  $64 \mathrm { ft }$ 
D)  $191 \mathrm { ft }$

Question 8

Convert the angle to degrees, minutes, and seconds.
-$127.53 ^ { \circ }$

Accepted Answer

A)  $127 ^ { \circ } 31 ^ { \prime } 53 ^ { \prime \prime }$ 
B)  $127 ^ { \circ } 32 ^ { \prime } 48 ^ { \prime \prime }$ 
C)  $127 ^ { \circ } 29 ^ { \prime } 53 ^ { \prime \prime }$ 
D)  $127 ^ { \circ } 31 ^ { \prime } 48 ^ { \prime \prime }$ 
A)  $127 ^ { \circ } 31 ^ { \prime } 53 ^ { \prime \prime }$ 
B)  $127 ^ { \circ } 32 ^ { \prime } 48 ^ { \prime \prime }$ 
C)  $127 ^ { \circ } 29 ^ { \prime } 53 ^ { \prime \prime }$ 
D)  $127 ^ { \circ } 31 ^ { \prime } 48 ^ { \prime \prime }$

Question 9

Evaluate the expression.
-$$\tan ( - 540 ) ^ { \circ }$$

Accepted Answer

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

Question 10

Identify the quadrant for the angle θ satisfying the following conditions.
-$\sin \theta > 0$ and $\cos \theta < 0$

Accepted Answer

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

Question 11

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.
-$130 ^ { \circ }$

Accepted Answer

A) $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
B)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
C)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
D)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
A) $310 ^ { \circ }$ and $- 50 ^ { \circ }$
  
B)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
C)  $490 ^ { \circ }$ and $- 230 ^ { \circ }$
  
D)  $310 ^ { \circ }$ and $- 50 ^ { \circ }$

Question 12

Solve the problem.
-A wheel makes 234 revolutions per minute. How many revolutions does it make per second?

Accepted Answer

A)  1404 revolutions per second 
B)  3.9 revolutions per second 
C)  7.8 revolutions per second 
D)  2.34 revolutions per second 
A)  1404 revolutions per second 
B)  3.9 revolutions per second 
C)  7.8 revolutions per second 
D)  2.34 revolutions per second

Question 13

Solve the right triangle.
-$$\mathrm { a } = 3.5 \mathrm {~cm} , \mathrm {~b} = 1.5 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.

Accepted Answer

A)  $\mathrm { A } = 25.4 ^ { \circ } , \mathrm { B } = 64.6 ^ { \circ } , \mathrm { c } = 5.0 \mathrm {~cm}$ 
B)  $\mathrm { A } = 66.8 ^ { \circ } , \mathrm { B } = 23.2 ^ { \circ } , \mathrm { c } = 3.8 \mathrm {~cm}$ 
C)  $\mathrm { A } = 23.2 ^ { \circ } , \mathrm { B } = 66.8 ^ { \circ } , \mathrm { c } = 3.8 \mathrm {~cm}$ 
D)  $\mathrm { A } = 62.3 ^ { \circ } , \mathrm { B } = 27.7 ^ { \circ } , \mathrm { c } = 3.8 \mathrm {~cm}$ 
A)  $\mathrm { A } = 25.4 ^ { \circ } , \mathrm { B } = 64.6 ^ { \circ } , \mathrm { c } = 5.0 \mathrm {~cm}$ 
B)  $\mathrm { A } = 66.8 ^ { \circ } , \mathrm { B } = 23.2 ^ { \circ } , \mathrm { c } = 3.8 \mathrm {~cm}$ 
C)  $\mathrm { A } = 23.2 ^ { \circ } , \mathrm { B } = 66.8 ^ { \circ } , \mathrm { c } = 3.8 \mathrm {~cm}$ 
D)  $\mathrm { A } = 62.3 ^ { \circ } , \mathrm { B } = 27.7 ^ { \circ } , \mathrm { c } = 3.8 \mathrm {~cm}$

Question 14

Identify the quadrant for the angle θ satisfying the following conditions.
-sec θ < 0 and tan θ < 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 15

Solve the problem.
-A 38 -foot ladder is leaning against the side of a building. If the ladder makes an angle of $22 ^ { \circ } 17 ^ { \prime }$ with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place when necessary.

Accepted Answer

A)  $5.04 \mathrm { ft }$ 
B)  $20.11 \mathrm { ft }$ 
C)  $14.41 \mathrm { ft }$ 
D)  $15.71 \mathrm { ft }$ 
A)  $5.04 \mathrm { ft }$ 
B)  $20.11 \mathrm { ft }$ 
C)  $14.41 \mathrm { ft }$ 
D)  $15.71 \mathrm { ft }$

Question 16

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-$\tan \theta = 0.49179429$

Accepted Answer

A)  $206.187696 ^ { \circ }$ 
B)  $63.812304 ^ { \circ }$ 
C)  $26.187696 ^ { \circ }$ 
D)  $333812304 ^ { \circ }$ 
A)  $206.187696 ^ { \circ }$ 
B)  $63.812304 ^ { \circ }$ 
C)  $26.187696 ^ { \circ }$ 
D)  $333812304 ^ { \circ }$

Question 17

An equation of the terminal side of an angle θ in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of θ. Do not use a calculator.
-$- 9 x + y = 0 , x \geq 0 ; \quad$ Find $\sin \theta$

Accepted Answer

A)  9 
B)  $\frac { 9 \sqrt { 82 } } { 82 }$ 
C)  $\frac { 1 } { 9 }$ 
D)  $\frac { \sqrt { 82 } } { 82 }$ 
A)  9 
B)  $\frac { 9 \sqrt { 82 } } { 82 }$ 
C)  $\frac { 1 } { 9 }$ 
D)  $\frac { \sqrt { 82 } } { 82 }$

Question 18

Sketch an angle $\theta$ in standard position such that $\theta$ has the least positive measure and the given point is on the terminal
side of $\theta _ { . }$
-$$( - 5 , - 3 )$$

Accepted Answer

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

Question 19

Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length
using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle.
Rationalize the denominator if applicable.
-Find $\sin \mathrm { A }$ when $\mathrm { a } = 9$ and $\mathrm { b } = 5$.

Accepted Answer

A)  $\frac { 9 \sqrt { 106 } } { 106 }$ 
B)  $\frac { 5 \sqrt { 106 } } { 106 }$ 
C)  $\frac { \sqrt { 106 } } { 5 }$ 
D)  $\frac { \sqrt { 106 } } { 9 }$ 
A)  $\frac { 9 \sqrt { 106 } } { 106 }$ 
B)  $\frac { 5 \sqrt { 106 } } { 106 }$ 
C)  $\frac { \sqrt { 106 } } { 5 }$ 
D)  $\frac { \sqrt { 106 } } { 9 }$

Question 20

Perform the calculation.
-$79 ^ { \circ } 29 ^ { \prime } - 23 ^ { \circ } 36 ^ { \prime }$

Accepted Answer

A)  $56 ^ { \circ } 36 ^ { \prime }$ 
B)  $56 ^ { \circ } 7 ^ { \prime }$ 
C)  $55 ^ { \circ } 53 ^ { \prime }$ 
D)  $102 ^ { \circ } 65 ^ { \prime }$ 
A)  $56 ^ { \circ } 36 ^ { \prime }$ 
B)  $56 ^ { \circ } 7 ^ { \prime }$ 
C)  $55 ^ { \circ } 53 ^ { \prime }$ 
D)  $102 ^ { \circ } 65 ^ { \prime }$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $26 ^ { \circ } 5 ^ { \prime }$

Find the measure of each angle in the problem. -Complementary angles with measures 2x and 7x - 9 degrees

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. - $160 ^ { \circ }$

Solve the right triangle. - $\mathrm { a } = 2.2 \text { in., } \mathrm { A } = 59.4 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Find the reference angle for the given angle. - $81 ^ { \circ }$

Convert the angle to degrees, minutes, and seconds. - $127.53 ^ { \circ }$

Evaluate the expression. - $\tan ( - 540 ) ^ { \circ }$

Identify the quadrant for the angle θ satisfying the following conditions. - $\sin \theta > 0$ and $\cos \theta < 0$

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. - $130 ^ { \circ }$

Solve the problem. -A wheel makes 234 revolutions per minute. How many revolutions does it make per second?

Solve the right triangle. - $\mathrm { a } = 3.5 \mathrm {~cm} , \mathrm {~b} = 1.5 \mathrm {~cm} , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Identify the quadrant for the angle θ satisfying the following conditions. -sec θ < 0 and tan θ < 0

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. - $\tan \theta = 0.49179429$

An equation of the terminal side of an angle θ in standard position is given along with a restriction on x. Find the indicated trigonometric function value of θ. Do not use a calculator. - $- 9 x + y = 0 , x \geq 0 ; \quad$ Find $\sin \theta$

Perform the calculation. - $79 ^ { \circ } 29 ^ { \prime } - 23 ^ { \circ } 36 ^ { \prime }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

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Exam 5: Trigonometric Functions

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 26∘5′26 ^ { \circ } 5 ^ { \prime }26∘5′

Find the measure of each angle in the problem. -Complementary angles with measures 2x and 7x - 9 degrees

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. - 160∘160 ^ { \circ }160∘

Solve the right triangle. - a=2.2 in., A=59.4∘,C=90∘\mathrm { a } = 2.2 \text { in., } \mathrm { A } = 59.4 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }a=2.2 in., A=59.4∘,C=90∘ Round values to one decimal place.

Find the reference angle for the given angle. - 81∘81 ^ { \circ }81∘

Convert the angle to degrees, minutes, and seconds. - 127.53∘127.53 ^ { \circ }127.53∘

Evaluate the expression. - tan⁡(−540)∘\tan ( - 540 ) ^ { \circ }tan(−540)∘

Identify the quadrant for the angle θ satisfying the following conditions. - sin⁡θ>0\sin \theta > 0sinθ>0 and cos⁡θ<0\cos \theta < 0cosθ<0

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. - 130∘130 ^ { \circ }130∘