Question 1

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\sin 20 ^ { \circ } 5 ^ { \prime }$

Accepted Answer

A)  $0.3433865$ 
B)  $0.3533865$ 
C)  $0.3423865$ 
D)  $0.3333865$ 
A)  $0.3433865$ 
B)  $0.3533865$ 
C)  $0.3423865$ 
D)  $0.3333865$

Question 2

Solve the problem.
-A ship travels $89 \mathrm {~km}$ on a bearing of $25 ^ { \circ }$, and then travels on a bearing of $115 ^ { \circ }$ for $115 \mathrm {~km}$. Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Accepted Answer

A)  $38 \mathrm {~km}$ 
B)  $204 \mathrm {~km}$ 
C)  $145 \mathrm {~km}$ 
D)  $81 \mathrm {~km}$ 
A)  $38 \mathrm {~km}$ 
B)  $204 \mathrm {~km}$ 
C)  $145 \mathrm {~km}$ 
D)  $81 \mathrm {~km}$

Question 3

Solve the problem.
-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 $2500 - \mathrm { lb }$ car traveling downhill on a $6 ^ { \circ }$ grade $\left( \theta = - 6 ^ { \circ } \right)$ ?

Accepted Answer

A)  $- 2506 \mathrm { lb }$ 
B)  $261 \mathrm { lb }$ 
C)  $2506 \mathrm { lb }$ 
D)  $- 261 \mathrm { lb }$ 
A)  $- 2506 \mathrm { lb }$ 
B)  $261 \mathrm { lb }$ 
C)  $2506 \mathrm { lb }$ 
D)  $- 261 \mathrm { lb }$

Question 4

Evaluate the expression.
-$9 \tan 180 ^ { \circ } + 3 \csc 270 ^ { \circ }$

Accepted Answer

A)  0 
B)  3 
C)  $- 3$ 
D)  Undefined 
A)  0 
B)  3 
C)  $- 3$ 
D)  Undefined

Question 5

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.
-III, $\frac { r } { x }$

Accepted Answer

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

Question 6

Solve the problem.
-From a balloon 839 feet high, the angle of depression to the ranger headquarters is $77 ^ { \circ } 18 ^ { \prime }$. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Accepted Answer

A)  $179 \mathrm { ft }$ 
B)  $184 \mathrm { ft }$ 
C)  $194 \mathrm { ft }$ 
D)  $189 \mathrm { ft }$ 
A)  $179 \mathrm { ft }$ 
B)  $184 \mathrm { ft }$ 
C)  $194 \mathrm { ft }$ 
D)  $189 \mathrm { ft }$

Question 7

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 $\theta _ { . }$
-$( - 4,0 )$

Accepted Answer

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

Question 8

Solve the problem.
-In 1838, the German mathematician and astronomer Friedrich Wilhelm Bessel was the first person to calculate the distance to a star other than the Sun. He accomplished this by first determining the parallax of the star, 61 Cygni, at $0.314$ arc seconds (Parallax is the change in position of the star measured against background stars as Earth orbits the Sun. See illustration.) If the distance from Earth to the Sun is about $150,000,000 \mathrm {~km}$ and $\theta = 0.314$ seconds $= \frac { 0.314 } { 60 }$ minutes $= \frac { 0.314 } { 60 \cdot 60 }$ degrees, determine the distance $\mathrm { d }$ from Earth to 61 Cygni using Bessel's figures. Express the answer in scientific notation.

Accepted Answer

A)  $1.05 \times 10 ^ { 14 } \mathrm {~km}$ 
B)  $9.85 \times 10 ^ { 13 } \mathrm {~km}$ 
C)  $2.28 \times 10 ^ { 13 } \mathrm {~km}$ 
D)  $1.97 \times 10 ^ { 14 } \mathrm {~km}$ 
A)  $1.05 \times 10 ^ { 14 } \mathrm {~km}$ 
B)  $9.85 \times 10 ^ { 13 } \mathrm {~km}$ 
C)  $2.28 \times 10 ^ { 13 } \mathrm {~km}$ 
D)  $1.97 \times 10 ^ { 14 } \mathrm {~km}$

Question 9

Solve the problem.
-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 2750 -lb car on a level road $\left( \theta = 0 ^ { \circ } \right)$ ?

Accepted Answer

A)  $- 2750 \mathrm { lb }$ 
B)  $0 \mathrm { lb }$ 
C)  $2750 \mathrm { lb }$ 
D)  undefined 
A)  $- 2750 \mathrm { lb }$ 
B)  $0 \mathrm { lb }$ 
C)  $2750 \mathrm { lb }$ 
D)  undefined

Question 10

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle.
-$\sec 30.4 ^ { \circ }$

Accepted Answer

A)  $\cos 149.6 ^ { \circ }$ 
B)  $\cos 59.6 ^ { \circ }$ 
C)  $\csc 30.4 ^ { \circ }$ 
D)  $\csc 59.6 ^ { \circ }$ 
A)  $\cos 149.6 ^ { \circ }$ 
B)  $\cos 59.6 ^ { \circ }$ 
C)  $\csc 30.4 ^ { \circ }$ 
D)  $\csc 59.6 ^ { \circ }$

Question 11

Find the exact value of the expression.
-$\sin \left( - 240 ^ { \circ } \right)$

Accepted Answer

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

Question 12

Solve the right triangle.
-$$\mathrm { B } = 32.7 ^ { \circ } , \mathrm { c } = 4.6 \mathrm {~mm} , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.

Accepted Answer

A)  $\mathrm { a } = 3.9 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 2.5 \mathrm {~mm}$ 
B)  $\mathrm { a } = 3.1 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 3.4 \mathrm {~mm}$ 
C)  $\mathrm { a } = 3.9 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 3.1 \mathrm {~mm}$ 
D)  $\mathrm { a } = 2.5 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 3.9 \mathrm {~mm}$ 
A)  $\mathrm { a } = 3.9 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 2.5 \mathrm {~mm}$ 
B)  $\mathrm { a } = 3.1 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 3.4 \mathrm {~mm}$ 
C)  $\mathrm { a } = 3.9 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 3.1 \mathrm {~mm}$ 
D)  $\mathrm { a } = 2.5 \mathrm {~mm} , \mathrm {~A} = 57.3 ^ { \circ } , \mathrm { b } = 3.9 \mathrm {~mm}$

Question 13

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 $\csc B$ when $a = 5$ and $b = 4$.

Accepted Answer

A)  $\frac { \sqrt { 41 } } { 5 }$ 
B)  $\frac { \sqrt { 41 } } { 4 }$ 
C)  $\frac { 5 \sqrt { 41 } } { 41 }$ 
D)  $\frac { 4 \sqrt { 41 } } { 41 }$ 
A)  $\frac { \sqrt { 41 } } { 5 }$ 
B)  $\frac { \sqrt { 41 } } { 4 }$ 
C)  $\frac { 5 \sqrt { 41 } } { 41 }$ 
D)  $\frac { 4 \sqrt { 41 } } { 41 }$

Question 14

Find the angle of least positive measure coterminal with the given angle.
-$577 ^ { \circ }$

Accepted Answer

A)  $397 ^ { \circ }$ 
B)  $288.5 ^ { \circ }$ 
C)  $207 ^ { \circ }$ 
D)  $217 ^ { \circ }$ 
A)  $397 ^ { \circ }$ 
B)  $288.5 ^ { \circ }$ 
C)  $207 ^ { \circ }$ 
D)  $217 ^ { \circ }$

Question 15

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.
-$( 0 , - 7 )$

Accepted Answer

A)  $0 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$ 
B)  $0 ^ { \circ } ; \mathrm { N } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
C)  $180 ^ { \circ } ; \mathrm { N } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
D)  $180 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$ 
A)  $0 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$ 
B)  $0 ^ { \circ } ; \mathrm { N } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
C)  $180 ^ { \circ } ; \mathrm { N } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { N } 0 ^ { \circ } \mathrm { E }$ 
D)  $180 ^ { \circ } ; \mathrm { S } 0 ^ { \circ } \mathrm { W }$ or $\mathrm { S } 0 ^ { \circ } \mathrm { E }$

Question 16

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

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.
-$- 85 ^ { \circ }$

Accepted Answer

A)  $185 ^ { \circ }$ and $- 355 ^ { \circ }$
  
B)  $175 ^ { \circ }$ and $- 5 ^ { \circ }$
  
C)  $275 ^ { \circ }$ and $- 445 ^ { \circ }$
  
D)  $85 ^ { \circ }$ and $- 105 ^ { \circ }$
  
A)  $185 ^ { \circ }$ and $- 355 ^ { \circ }$
  
B)  $175 ^ { \circ }$ and $- 5 ^ { \circ }$
  
C)  $275 ^ { \circ }$ and $- 445 ^ { \circ }$
  
D)  $85 ^ { \circ }$ and $- 105 ^ { \circ }$

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 $\theta _ { . }$
-$( 6,2 )$

Accepted Answer

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

Question 19

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given
value is a decimal, round your answer to three decimal places.
-$\cos \theta$, given that $\sec \theta = - 4$

Accepted Answer

A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $- \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 4 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  $- \frac { 1 } { 4 }$ 
D)  $- \frac { 1 } { 3 }$

Question 20

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$339 ^ { \circ } 18 ^ { \prime } 55 ^ { \prime \prime }$

Accepted Answer

A)  $339.28 ^ { \circ }$ 
B)  $339.32 ^ { \circ }$ 
C)  $339.38 ^ { \circ }$ 
D)  $339.33 ^ { \circ }$ 
A)  $339.28 ^ { \circ }$ 
B)  $339.32 ^ { \circ }$ 
C)  $339.38 ^ { \circ }$ 
D)  $339.33 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sin 20 ^ { \circ } 5 ^ { \prime }$

Solve the problem. -A ship travels $89 \mathrm {~km}$ on a bearing of $25 ^ { \circ }$ , and then travels on a bearing of $115 ^ { \circ }$ for $115 \mathrm {~km}$ . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Evaluate the expression. - $9 \tan 180 ^ { \circ } + 3 \csc 270 ^ { \circ }$

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. -III, $\frac { r } { x }$

Solve the problem. -From a balloon 839 feet high, the angle of depression to the ranger headquarters is $77 ^ { \circ } 18 ^ { \prime }$ . How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - $\sec 30.4 ^ { \circ }$

Find the exact value of the expression. - $\sin \left( - 240 ^ { \circ } \right)$

Solve the right triangle. - $\mathrm { B } = 32.7 ^ { \circ } , \mathrm { c } = 4.6 \mathrm {~mm} , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

Find the angle of least positive measure coterminal with the given angle. - $577 ^ { \circ }$

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. - $( 0 , - 7 )$

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. - $- 85 ^ { \circ }$

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - $\cos \theta$ , given that $\sec \theta = - 4$

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $339 ^ { \circ } 18 ^ { \prime } 55 ^ { \prime \prime }$

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

Filters

Exam 5: Trigonometric Functions

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - sin⁡20∘5′\sin 20 ^ { \circ } 5 ^ { \prime }sin20∘5′

Solve the problem. -A ship travels 89 km89 \mathrm {~km}89 km on a bearing of 25∘25 ^ { \circ }25∘ , and then travels on a bearing of 115∘115 ^ { \circ }115∘ for 115 km115 \mathrm {~km}115 km . Find the distance from the starting point to the end of the trip, to the nearest kilometer.

Evaluate the expression. - 9tan⁡180∘+3csc⁡270∘9 \tan 180 ^ { \circ } + 3 \csc 270 ^ { \circ }9tan180∘+3csc270∘

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. -III, rx\frac { r } { x }xr​

Solve the problem. -From a balloon 839 feet high, the angle of depression to the ranger headquarters is 77∘18′77 ^ { \circ } 18 ^ { \prime }77∘18′ . How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the least positive measure and the given point is on the terminal side of θ.\theta _ { . }θ.​ - (−4,0)( - 4,0 )(−4,0)

Write the function in terms of its cofunction. Assume that any angle in which an unknown appears is an acute angle. - sec⁡30.4∘\sec 30.4 ^ { \circ }sec30.4∘

Find the exact value of the expression. - sin⁡(−240∘)\sin \left( - 240 ^ { \circ } \right)sin(−240∘)

Solve the right triangle. - B=32.7∘,c=4.6 mm,C=90∘\mathrm { B } = 32.7 ^ { \circ } , \mathrm { c } = 4.6 \mathrm {~mm} , \mathrm { C } = 90 ^ { \circ }B=32.7∘,c=4.6 mm,C=90∘ Round values to one decimal place.

Find the angle of least positive measure coterminal with the given angle. - 577∘577 ^ { \circ }577∘

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. - (0,−7)( 0 , - 7 )(0,−7)

Use the fundamental identities to find the value of the trigonometric function. -Find sin⁡θ\sin \thetasinθ , given that cos⁡θ=23\cos \theta = \frac { 2 } { 3 }cosθ=32​ and θ\thetaθ 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. - −85∘- 85 ^ { \circ }−85∘

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the least positive measure and the given point is on the terminal side of θ.\theta _ { . }θ.​ - (6,2)( 6,2 )(6,2)

Use the appropriate identity to find the indicated function value. Rationalize the denominator, if applicable. If the given value is a decimal, round your answer to three decimal places. - cos⁡θ\cos \thetacosθ , given that sec⁡θ=−4\sec \theta = - 4secθ=−4

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - 339∘18′55′′339 ^ { \circ } 18 ^ { \prime } 55 ^ { \prime \prime }339∘18′55′′