Question 1

Find the exact value of the expression.
-$\tan 30 ^ { \circ }$

Accepted Answer

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

Question 2

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 $\theta$
-$( - 7 , - 2 ) ;$ Find $\cot \theta$

Accepted Answer

A)  $- \frac { 2 } { 7 }$ 
B)  $\frac { 7 } { 2 }$ 
C)  $- 1$ 
D)  $\frac { 2 } { 7 }$ 
A)  $- \frac { 2 } { 7 }$ 
B)  $\frac { 7 } { 2 }$ 
C)  $- 1$ 
D)  $\frac { 2 } { 7 }$

Question 3

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$, where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). What is the grade resistance (to the nearest pound) of a 1750-lb car on a level road $\left( \theta = 0 ^ { \circ } \right)$ ?

Accepted Answer

A)  $- 1750 \mathrm { lb }$ 
B)  $1750 \mathrm { lb }$ 
C)  undefined 
D)  $0 \mathrm { lb }$ 
A)  $- 1750 \mathrm { lb }$ 
B)  $1750 \mathrm { lb }$ 
C)  undefined 
D)  $0 \mathrm { lb }$

Question 4

Convert the angle to degrees, minutes, and seconds.
-$91.32 ^ { \circ }$

Accepted Answer

A)  $91 ^ { \circ } 19 ^ { \prime } 12 ^ { \prime \prime }$ 
B)  $91 ^ { \circ } 19 ^ { \prime } 32 ^ { \prime \prime }$ 
C)  $91 ^ { \circ } 19 ^ { \prime } 0 ^ { \prime \prime }$ 
D)  $91 ^ { \circ } 19 ^ { \prime } 18 ^ { \prime \prime }$ 
A)  $91 ^ { \circ } 19 ^ { \prime } 12 ^ { \prime \prime }$ 
B)  $91 ^ { \circ } 19 ^ { \prime } 32 ^ { \prime \prime }$ 
C)  $91 ^ { \circ } 19 ^ { \prime } 0 ^ { \prime \prime }$ 
D)  $91 ^ { \circ } 19 ^ { \prime } 18 ^ { \prime \prime }$

Question 5

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-The grade resistance $\mathrm { F }$ of a car traveling up or down a hill is modeled by the equation $\mathrm { F } = \mathrm { W } \sin \theta$, where $W$ is the weight of the car and $\theta$ is the angle of the hill's grade $( \theta > 0$ for uphill travel, $\theta < 0$ for downhill travel). A 2025-lb car has just rolled off a sheer vertical cliff $\left( \theta = - 90 ^ { \circ } \right)$. What is the car's grade resistance?

Accepted Answer

A)  $0 \mathrm { lb }$ 
B)  undefined 
C)  $2025 \mathrm { lb }$ 
D)  $- 2025 \mathrm { lb }$ 
A)  $0 \mathrm { lb }$ 
B)  undefined 
C)  $2025 \mathrm { lb }$ 
D)  $- 2025 \mathrm { lb }$

Question 6

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\tan 55 ^ { \circ } 6 ^ { \prime }$

Accepted Answer

A)  $1.4337664$ 
B)  $1.4343664$ 
C)  $1.4334664$ 
D)  $1.4340664$ 
A)  $1.4337664$ 
B)  $1.4343664$ 
C)  $1.4334664$ 
D)  $1.4340664$

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

Question 8

Find the reference angle for the given angle.
-106°

Accepted Answer

A)  16° 
B)  74° 
C)  84° 
D)  26° 
A)  16° 
B)  74° 
C)  84° 
D)  26°

Question 9

Find the exact value of the expression.
-$\sec 240 ^ { \circ }$

Accepted Answer

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

Question 10

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-$42 ^ { \circ }$

Accepted Answer

A)  $42 ^ { \circ } + \mathrm { n } \cdot 180 ^ { \circ }$ 
B)  $42 ^ { \circ } + \mathrm { n } \cdot 90 ^ { \circ }$ 
C)  $42 ^ { \circ } + \mathrm { n } \cdot 360 ^ { \circ }$ 
D)  $42 ^ { \circ } + \mathrm { n } \cdot 720 ^ { \circ }$ 
A)  $42 ^ { \circ } + \mathrm { n } \cdot 180 ^ { \circ }$ 
B)  $42 ^ { \circ } + \mathrm { n } \cdot 90 ^ { \circ }$ 
C)  $42 ^ { \circ } + \mathrm { n } \cdot 360 ^ { \circ }$ 
D)  $42 ^ { \circ } + \mathrm { n } \cdot 720 ^ { \circ }$

Question 11

Without using a calculator, give the exact trigonometric function value with rational denominator.
-Find the exact value of x in the figure.

Accepted Answer

A)  $\frac { 34 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 34 \sqrt { 6 } } { 3 }$ 
C)  $17 \sqrt { 6 }$ 
D)  $17 \sqrt { 3 }$ 
A)  $\frac { 34 \sqrt { 3 } } { 3 }$ 
B)  $\frac { 34 \sqrt { 6 } } { 3 }$ 
C)  $17 \sqrt { 6 }$ 
D)  $17 \sqrt { 3 }$

Question 12

Use the fundamental identities to find the value of the trigonometric function.
-Find $\sin \theta$, given that $\cos \theta = \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

Accepted Answer

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

Question 13

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

Question 14

Perform the calculation.
-$180 ^ { \circ } - 148 ^ { \circ } 52 ^ { \prime } 16 ^ { \prime \prime }$

Accepted Answer

A)  $31 ^ { \circ } 7 ^ { \prime } 44 ^ { \prime \prime }$ 
B)  $32 ^ { \circ } 7 ^ { \prime } 44 ^ { \prime \prime }$ 
C)  $31 ^ { \circ } 8 ^ { \prime } 44 ^ { \prime \prime }$ 
D)  $32 ^ { \circ } 8 ^ { \prime } 44 ^ { \prime \prime }$ 
A)  $31 ^ { \circ } 7 ^ { \prime } 44 ^ { \prime \prime }$ 
B)  $32 ^ { \circ } 7 ^ { \prime } 44 ^ { \prime \prime }$ 
C)  $31 ^ { \circ } 8 ^ { \prime } 44 ^ { \prime \prime }$ 
D)  $32 ^ { \circ } 8 ^ { \prime } 44 ^ { \prime \prime }$

Question 15

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\sec \theta = 2.6013225$

Accepted Answer

A)  $22.6077284 ^ { \circ }$ 
B)  $67.3922716 ^ { \circ }$ 
C)  $21.0277507 ^ { \circ }$ 
D)  $51.3556884 ^ { \circ }$ 
A)  $22.6077284 ^ { \circ }$ 
B)  $67.3922716 ^ { \circ }$ 
C)  $21.0277507 ^ { \circ }$ 
D)  $51.3556884 ^ { \circ }$

Question 16

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-Any offset between a stationary radar gun and a moving target creates a "cosine effect" that reduces the radar mileage reading by the cosine of the angle between the gun and the vehicle. That is, the radar speed
Reading is the product of the actual reading and the cosine of the angle. Find the radar reading to the
Nearest hundredth for the auto shown in the figure.

Accepted Answer

A)  $98.93 \mathrm { mph }$ 
B)  $35.12 \mathrm { mph }$ 
C)  $91.49 \mathrm { mph }$ 
D)  $97.07 \mathrm { mph }$ 
A)  $98.93 \mathrm { mph }$ 
B)  $35.12 \mathrm { mph }$ 
C)  $91.49 \mathrm { mph }$ 
D)  $97.07 \mathrm { mph }$

Question 17

Find the exact value of the expression.
-$$\sin \theta = - \frac { 1 } { 2 }$$

Accepted Answer

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

Question 18

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or
negative.
-$\text { II, } \frac { \mathrm { r } } { \mathrm { x } }$

Accepted Answer

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

Question 19

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-$\sin 54 ^ { \circ }$

Accepted Answer

A)  $\cos 54 ^ { \circ }$ 
B)  $\sin 144 ^ { \circ }$ 
C)  $\csc 36 ^ { \circ }$ 
D)  $\cos 36 ^ { \circ }$ 
A)  $\cos 54 ^ { \circ }$ 
B)  $\sin 144 ^ { \circ }$ 
C)  $\csc 36 ^ { \circ }$ 
D)  $\cos 36 ^ { \circ }$

Question 20

Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\sec 45 ^ { \circ }$

Accepted Answer

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

Find the exact value of the expression. - $\tan 30 ^ { \circ }$

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 $\theta$ - $( - 7 , - 2 ) ;$ Find $\cot \theta$

Convert the angle to degrees, minutes, and seconds. - $91.32 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\tan 55 ^ { \circ } 6 ^ { \prime }$

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. - $65 ^ { \circ }$

Find the reference angle for the given angle. -106°

Find the exact value of the expression. - $\sec 240 ^ { \circ }$

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $42 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. -Find the exact value of x in the figure.

Use the fundamental identities to find the value of the trigonometric function. -Find $\sin \theta$ , given that $\cos \theta = \frac { 2 } { 3 }$ and $\theta$ is in quadrant IV.

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. - $160 ^ { \circ }$

Perform the calculation. - $180 ^ { \circ } - 148 ^ { \circ } 52 ^ { \prime } 16 ^ { \prime \prime }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sec \theta = 2.6013225$

Find the exact value of the expression. - $\sin \theta = - \frac { 1 } { 2 }$

If r is a positive number and the point (x, y) is in the indicated quadrant, decide whether the given ratio is positive or negative. - $\text { II, } \frac { \mathrm { r } } { \mathrm { x } }$

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\sin 54 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sec 45 ^ { \circ }$

Review of Basic Concepts

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

Filters

Exam 6: Trigonometric Functions

Find the exact value of the expression. - tan⁡30∘\tan 30 ^ { \circ }tan30∘

Suppose that θ\thetaθ is in standard position and the given point is on the terminal side of θ\thetaθ . Give the exact value of the indicated trig function for θ\thetaθ - (−7,−2);( - 7 , - 2 ) ;(−7,−2); Find cot⁡θ\cot \thetacotθ

Convert the angle to degrees, minutes, and seconds. - 91.32∘91.32 ^ { \circ }91.32∘

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - tan⁡55∘6′\tan 55 ^ { \circ } 6 ^ { \prime }tan55∘6′

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∘