Question 1

Provide an appropriate response.
-Find the supplement of an angle whose measure is 74°57′.

Accepted Answer

A)  $106 ^ { \circ } 3 ^ { \prime }$ 
B)  $15 ^ { \circ } 3 ^ { \prime }$ 
C)  $105 ^ { \circ } 3 ^ { \prime }$ 
D)  $105 ^ { \circ } 57 ^ { \prime }$ 
A)  $106 ^ { \circ } 3 ^ { \prime }$ 
B)  $15 ^ { \circ } 3 ^ { \prime }$ 
C)  $105 ^ { \circ } 3 ^ { \prime }$ 
D)  $105 ^ { \circ } 57 ^ { \prime }$

Question 2

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value.
-$\tan \theta = 1$

Accepted Answer

A)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
B)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
D)  $135 ^ { \circ }$ and $225 ^ { \circ }$ 
A)  $45 ^ { \circ }$ and $315 ^ { \circ }$ 
B)  $225 ^ { \circ }$ and $315 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $225 ^ { \circ }$ 
D)  $135 ^ { \circ }$ and $225 ^ { \circ }$

Question 3

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

Accepted Answer

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

Question 4

Evaluate the expression.
-$$\cos \left( - 180 ^ { \circ } \right)$$

Accepted Answer

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

Question 5

Find the reference angle for the given angle.
-$399 ^ { \circ }$

Accepted Answer

A)  $39 ^ { \circ }$ 
B)  $141 ^ { \circ }$ 
C)  $129 ^ { \circ }$ 
D)  $51 ^ { \circ }$ 
A)  $39 ^ { \circ }$ 
B)  $141 ^ { \circ }$ 
C)  $129 ^ { \circ }$ 
D)  $51 ^ { \circ }$

Question 6

Solve the problem.
-In one area, the lowest angle of elevation of the sun in winter is $23 ^ { \circ } 17 ^ { \prime }$. Find the minimum distance $x$ that a plant needing full sun can be placed from a fence that is $4.5$ feet high. Round your answer to the tenths place when necessary.

Accepted Answer

A)  $13.9 \mathrm { ft }$ 
B)  $10.7 \mathrm { ft }$ 
C)  $10.5 \mathrm { ft }$ 
D)  $10.1 \mathrm { ft }$ 
A)  $13.9 \mathrm { ft }$ 
B)  $10.7 \mathrm { ft }$ 
C)  $10.5 \mathrm { ft }$ 
D)  $10.1 \mathrm { ft }$

Question 7

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.
-$65 ^ { \circ }$

Accepted Answer

A)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
B)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
C)  $425 ^ { \circ }$ and $- 295 ^ { \circ }$
  
D) $425 ^ { \circ }$ and $- 295 ^ { \circ }$
  
A)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
B)  $245 ^ { \circ }$ and $- 115 ^ { \circ }$
  
C)  $425 ^ { \circ }$ and $- 295 ^ { \circ }$
  
D) $425 ^ { \circ }$ and $- 295 ^ { \circ }$

Question 8

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

Accepted Answer

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

Question 9

Find the exact value of the expression.
-$\csc 840 ^ { \circ }$

Accepted Answer

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

Question 10

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $90 ^ { \circ }$ and $270 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $55 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $135 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$ 
A)  $90 ^ { \circ }$ and $270 ^ { \circ }$ 
B)  $45 ^ { \circ }$ and $55 ^ { \circ }$ 
C)  $45 ^ { \circ }$ and $135 ^ { \circ }$ 
D)  $60 ^ { \circ }$ and $120 ^ { \circ }$

Question 11

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 $\cos \mathrm { A }$ when $\mathrm { a } = \sqrt { 5 }$ and $\mathrm { c } = 14$.

Accepted Answer

A)  $\frac { 191 } { 5 }$ 
B)  $\frac { 5 } { 14 }$ 
C)  $\frac { \sqrt { 5 } } { 14 }$ 
D)  $\frac { \sqrt { 191 } } { 14 }$ 
A)  $\frac { 191 } { 5 }$ 
B)  $\frac { 5 } { 14 }$ 
C)  $\frac { \sqrt { 5 } } { 14 }$ 
D)  $\frac { \sqrt { 191 } } { 14 }$

Question 12

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an
airplane located at that point. Express the bearing using both methods.
-$( 5 , - 5 )$

Accepted Answer

A)  $135 ^ { \circ } ; \mathrm { N } 45 ^ { \circ } \mathrm { W }$ 
B)  $135 ^ { \circ } ; \mathrm { S } 45 ^ { \circ } \mathrm { E }$ 
C)  $45 ^ { \circ } ; \mathrm { N } 45 ^ { \circ } \mathrm { W }$ 
D)  $45 ^ { \circ } ; \mathrm { S } 45 ^ { \circ } \mathrm { E }$ 
A)  $135 ^ { \circ } ; \mathrm { N } 45 ^ { \circ } \mathrm { W }$ 
B)  $135 ^ { \circ } ; \mathrm { S } 45 ^ { \circ } \mathrm { E }$ 
C)  $45 ^ { \circ } ; \mathrm { N } 45 ^ { \circ } \mathrm { W }$ 
D)  $45 ^ { \circ } ; \mathrm { S } 45 ^ { \circ } \mathrm { E }$

Question 13

Solve the problem.
-If an automobile is traveling at velocity $\mathrm { V }$ (in feet per second), the safe radius $\mathrm { R }$ for a curve with superelevation $\alpha$ is given by the formula $\mathrm { R } = \frac { \mathrm { V } ^ { 2 } } { \mathrm {~g} ( \mathrm { f } + \tan \alpha ) }$, where $\mathrm { f }$ and $g$ are constants. A road is being constructed for automobiles traveling at 47 miles per hour. If $\alpha = 4 ^ { \circ } , g = 31.5$, and $f = 0.16$, calculate $R$. Round to the nearest foot. (Hint: 1 mile $= 5280$ feet)

Accepted Answer

A)  $R = 656 \mathrm { ft }$ 
B)  $R = 1106 \mathrm { ft }$ 
C)  $R = 640 \mathrm { ft }$ 
D)  $\mathrm { R } = 676 \mathrm { ft }$ 
A)  $R = 656 \mathrm { ft }$ 
B)  $R = 1106 \mathrm { ft }$ 
C)  $R = 640 \mathrm { ft }$ 
D)  $\mathrm { R } = 676 \mathrm { ft }$

Question 14

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$327 ^ { \circ } 36 ^ { \prime } 26 ^ { \prime \prime }$

Accepted Answer

A)  $327.67 ^ { \circ }$ 
B)  $327.62 ^ { \circ }$ 
C)  $327.57 ^ { \circ }$ 
D)  $327.61 ^ { \circ }$ 
A)  $327.67 ^ { \circ }$ 
B)  $327.62 ^ { \circ }$ 
C)  $327.57 ^ { \circ }$ 
D)  $327.61 ^ { \circ }$

Question 15

Evaluate the expression.
-$\cot ^ { 2 } 90 ^ { \circ } - \sec 180 ^ { \circ }$

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  $- 1$ 
A)  1 
B)  2 
C)  0 
D)  $- 1$

Question 16

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

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 17

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.
-$50 ^ { \circ }$

Accepted Answer

A)  $230 ^ { \circ }$ and $- 130 ^ { \circ }$
  
B)  $230 ^ { \circ }$ and $- 130 ^ { \circ }$
  
C)  $410 ^ { \circ }$ and $- 310 ^ { \circ }$
  
D) $410^{\circ} \text { and }-310^{\circ}$
  
A)  $230 ^ { \circ }$ and $- 130 ^ { \circ }$
  
B)  $230 ^ { \circ }$ and $- 130 ^ { \circ }$
  
C)  $410 ^ { \circ }$ and $- 310 ^ { \circ }$
  
D) $410^{\circ} \text { and }-310^{\circ}$

Question 18

Perform the calculation.
-$90 ^ { \circ } - 32 ^ { \circ } 16 ^ { \prime } 43 ^ { \prime \prime }$

Accepted Answer

A)  $57 ^ { \circ } 43 ^ { \prime } 17 ^ { \prime \prime }$ 
B)  $58 ^ { \circ } 44 ^ { \prime } 17 ^ { \prime \prime }$ 
C)  $57 ^ { \circ } 43 ^ { \prime } 16 ^ { \prime \prime }$ 
D)  $57 ^ { \circ } 44 ^ { \prime } 17 ^ { \prime \prime }$ 
A)  $57 ^ { \circ } 43 ^ { \prime } 17 ^ { \prime \prime }$ 
B)  $58 ^ { \circ } 44 ^ { \prime } 17 ^ { \prime \prime }$ 
C)  $57 ^ { \circ } 43 ^ { \prime } 16 ^ { \prime \prime }$ 
D)  $57 ^ { \circ } 44 ^ { \prime } 17 ^ { \prime \prime }$

Question 19

Convert the angle to degrees, minutes, and seconds.
-$39.32 ^ { \circ }$

Accepted Answer

A)  $39 ^ { \circ } 19 ^ { \prime } 2 ^ { \prime \prime }$ 
B)  $39 ^ { \circ } 19 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $39 ^ { \circ } 29 ^ { \prime } 12 ^ { \prime \prime }$ 
D)  $39 ^ { \circ } 29 ^ { \prime } 2 ^ { \prime \prime }$ 
A)  $39 ^ { \circ } 19 ^ { \prime } 2 ^ { \prime \prime }$ 
B)  $39 ^ { \circ } 19 ^ { \prime } 12 ^ { \prime \prime }$ 
C)  $39 ^ { \circ } 29 ^ { \prime } 12 ^ { \prime \prime }$ 
D)  $39 ^ { \circ } 29 ^ { \prime } 2 ^ { \prime \prime }$

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.
-$115 ^ { \circ }$

Accepted Answer

A)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
C)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
D)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
A)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
C)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
D)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$

Provide an appropriate response. -Find the supplement of an angle whose measure is 74°57′.

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - $\tan \theta = 1$

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

Evaluate the expression. - $\cos \left( - 180 ^ { \circ } \right)$

Find the reference angle for the given angle. - $399 ^ { \circ }$

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. - $65 ^ { \circ }$

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

Find the exact value of the expression. - $\csc 840 ^ { \circ }$

Find the measure of each angle in the problem. -

An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an airplane located at that point. Express the bearing using both methods. - $( 5 , - 5 )$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $327 ^ { \circ } 36 ^ { \prime } 26 ^ { \prime \prime }$

Evaluate the expression. - $\cot ^ { 2 } 90 ^ { \circ } - \sec 180 ^ { \circ }$

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

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. - $50 ^ { \circ }$

Perform the calculation. - $90 ^ { \circ } - 32 ^ { \circ } 16 ^ { \prime } 43 ^ { \prime \prime }$

Convert the angle to degrees, minutes, and seconds. - $39.32 ^ { \circ }$

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. - $115 ^ { \circ }$

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

Filters

Exam 5: Trigonometric Functions

Provide an appropriate response. -Find the supplement of an angle whose measure is 74°57′.

Find all values of θ, if θ is in the interval [0, 360°) and has the given function value. - tan⁡θ=1\tan \theta = 1tanθ=1

Identify the quadrant for the angle θ satisfying the following conditions. - cos⁡θ<0\cos \theta < 0cosθ<0 and csc⁡θ<0\csc \theta < 0cscθ<0

Evaluate the expression. - cos⁡(−180∘)\cos \left( - 180 ^ { \circ } \right)cos(−180∘)

Find the reference angle for the given angle. - 399∘399 ^ { \circ }399∘

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. - 65∘65 ^ { \circ }65∘

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

Find the exact value of the expression. - csc⁡840∘\csc 840 ^ { \circ }csc840∘