Question 1

Without using a calculator, give the exact trigonometric function value with rational denominator.
-Find a formula for the area of the figure in terms of s.

Accepted Answer

A)  $\sqrt { 6 } s ^ { 2 }$ 
B)  $\frac { \sqrt { 6 } } { 4 } s ^ { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }$ 
D)  $\frac { \sqrt { 3 } } { 6 } \mathrm {~s} ^ { 2 }$ 
A)  $\sqrt { 6 } s ^ { 2 }$ 
B)  $\frac { \sqrt { 6 } } { 4 } s ^ { 2 }$ 
C)  $\frac { \sqrt { 3 } } { 2 } \mathrm {~s} ^ { 2 }$ 
D)  $\frac { \sqrt { 3 } } { 6 } \mathrm {~s} ^ { 2 }$

Question 2

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
-$208 ^ { \circ }$

Accepted Answer

A)  $208 ^ { \circ } + \mathrm { n } \cdot 360 ^ { \circ }$ 
B)  $208 ^ { \circ } + 2 n \pi$ 
C)  $208 ^ { \circ } + \mathrm { n } \cdot 90 ^ { \circ }$ 
D)  $208 ^ { \circ } + \mathrm { n } \cdot 180 ^ { \circ }$ 
A)  $208 ^ { \circ } + \mathrm { n } \cdot 360 ^ { \circ }$ 
B)  $208 ^ { \circ } + 2 n \pi$ 
C)  $208 ^ { \circ } + \mathrm { n } \cdot 90 ^ { \circ }$ 
D)  $208 ^ { \circ } + \mathrm { n } \cdot 180 ^ { \circ }$

Question 3

Without using a calculator, give the exact trigonometric function value with rational denominator.
-$\sec 30 ^ { \circ }$

Accepted Answer

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

Question 4

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\csc 38 ^ { \circ } 22 ^ { \prime }$

Accepted Answer

A)  $1.6101057$ 
B)  $1.6121057$ 
C)  $1.6131057$ 
D)  $1.6111057$ 
A)  $1.6101057$ 
B)  $1.6121057$ 
C)  $1.6131057$ 
D)  $1.6111057$

Question 5

Decide whether the statement is possible or impossible for an angle $\theta .$
-$\sec \theta = 0.87$

Accepted Answer

A)  Impossible 
B)  Possible 
A)  Impossible 
B)  Possible

Question 6

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 $\sec B$ when $a = 3$ and $b = 8$.

Accepted Answer

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

Question 7

Find the exact value of the expression.
-$\cos 210 ^ { \circ }$

Accepted Answer

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

Question 8

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary.
-$\sin \theta = 0.30738671$

Accepted Answer

A)  $197.901812 ^ { \circ }$ 
B)  $72.0981881 ^ { \circ }$ 
C)  $162.098188 ^ { \circ }$ 
D)  $17.9018119 ^ { \circ }$ 
A)  $197.901812 ^ { \circ }$ 
B)  $72.0981881 ^ { \circ }$ 
C)  $162.098188 ^ { \circ }$ 
D)  $17.9018119 ^ { \circ }$

Question 9

Solve the problem.
-The angle of elevation from a point on the ground to the top of a tower is $35 ^ { \circ } 42 ^ { \prime }$. The angle of elevation from a point 152 feet farther back from the tower is $24 ^ { \circ } 30 ^ { \prime }$. Find the height of the tower. Round to the nearest foot.

Accepted Answer

A)  $185 \mathrm { ft }$ 
B)  $189 \mathrm { ft }$ 
C)  $1894 \mathrm { ft }$ 
D)  $200 \mathrm { ft }$ 
A)  $185 \mathrm { ft }$ 
B)  $189 \mathrm { ft }$ 
C)  $1894 \mathrm { ft }$ 
D)  $200 \mathrm { ft }$

Question 10

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-$$A = 79 ^ { \circ } 32 ^ { \prime } , c = 264 \mathrm {~m} , C = 90 ^ { \circ }$$
Round side lengths to two decimal places, if necessary.

Accepted Answer

A)  $B = 11 ^ { \circ } 18 ^ { \prime } , a = 259.81 \mathrm {~m} , \mathrm {~b} = 47.96 \mathrm {~m}$ 
B)  $B = 10 ^ { \circ } 32 ^ { \prime } , a = 260.81 \mathrm {~m} , \mathrm {~b} = 40.96 \mathrm {~m}$ 
C)  $\mathrm { B } = 10 ^ { \circ } 28 ^ { \prime } , \mathrm { a } = 259.81 \mathrm {~m} , \mathrm {~b} = 54.96 \mathrm {~m}$ 
D)  $B = 10 ^ { \circ } 28 ^ { \prime } , a = 259.61 \mathrm {~m} , \mathrm {~b} = 47.96 \mathrm {~m}$ 
A)  $B = 11 ^ { \circ } 18 ^ { \prime } , a = 259.81 \mathrm {~m} , \mathrm {~b} = 47.96 \mathrm {~m}$ 
B)  $B = 10 ^ { \circ } 32 ^ { \prime } , a = 260.81 \mathrm {~m} , \mathrm {~b} = 40.96 \mathrm {~m}$ 
C)  $\mathrm { B } = 10 ^ { \circ } 28 ^ { \prime } , \mathrm { a } = 259.81 \mathrm {~m} , \mathrm {~b} = 54.96 \mathrm {~m}$ 
D)  $B = 10 ^ { \circ } 28 ^ { \prime } , a = 259.61 \mathrm {~m} , \mathrm {~b} = 47.96 \mathrm {~m}$

Question 11

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 $\theta$
-$( 6,8 ) ;$ Find $\cos \theta$

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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

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 14

Provide an appropriate response.
-Find the complement of an angle whose measure is $34 ^ { \circ } 24 ^ { \prime } 40 ^ { \prime \prime }$.

Accepted Answer

A)  $55 ^ { \circ } 35 ^ { \prime } 20 ^ { \prime \prime }$ 
B)  $55 ^ { \circ } 36 ^ { \prime } 20 ^ { \prime \prime }$ 
C)  $55 ^ { \circ } 35 ^ { \prime } 19 ^ { \prime \prime }$ 
D)  $56 ^ { \circ } 36 ^ { \prime } 20 ^ { \prime \prime }$ 
A)  $55 ^ { \circ } 35 ^ { \prime } 20 ^ { \prime \prime }$ 
B)  $55 ^ { \circ } 36 ^ { \prime } 20 ^ { \prime \prime }$ 
C)  $55 ^ { \circ } 35 ^ { \prime } 19 ^ { \prime \prime }$ 
D)  $56 ^ { \circ } 36 ^ { \prime } 20 ^ { \prime \prime }$

Question 15

Use the fundamental identities to find the value of the trigonometric function.
-Find $\sin \theta$, given that $\cos \theta = \frac { 4 } { 7 }$ and $\theta$ is in quadrant IV.

Accepted Answer

A)  $- \frac { \sqrt { 33 } } { 4 }$ 
B)  $- \frac { 7 } { 4 }$ 
C)  $- \sqrt { 33 }$ 
D)  $- \frac { \sqrt { 33 } } { 7 }$ 
A)  $- \frac { \sqrt { 33 } } { 4 }$ 
B)  $- \frac { 7 } { 4 }$ 
C)  $- \sqrt { 33 }$ 
D)  $- \frac { \sqrt { 33 } } { 7 }$

Question 16

Find the measure of each angle in the problem.
-

Accepted Answer

A)  $50 ^ { \circ }$ and $40 ^ { \circ }$ 
B)  $200 ^ { \circ }$ and $160 ^ { \circ }$ 
C)  $95 ^ { \circ }$ and $85 ^ { \circ }$ 
D)  $100 ^ { \circ }$ and $80 ^ { \circ }$ 
A)  $50 ^ { \circ }$ and $40 ^ { \circ }$ 
B)  $200 ^ { \circ }$ and $160 ^ { \circ }$ 
C)  $95 ^ { \circ }$ and $85 ^ { \circ }$ 
D)  $100 ^ { \circ }$ and $80 ^ { \circ }$

Question 17

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

Accepted Answer

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

Question 18

Provide an appropriate response.
-Find the complement of an angle whose measure is 8°.

Accepted Answer

A)  82° 
B)  98° 
C)  8° 
D)  172° 
A)  82° 
B)  98° 
C)  8° 
D)  172°

Question 19

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
-$$\mathrm { a } = 2.6 \text { in., } \mathrm { A } = 48.5 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$$
Round values to one decimal place.

Accepted Answer

A)  $b = 1.2$ in., $B = 41.5 ^ { \circ } , c = 2.9$ in. 
B)  $b = 4.2$ in., $B = 41.5 ^ { \circ } , c = 4.9$ in. 
C)  $b = 2.3$ in., $B = 41.5 ^ { \circ } , c = 3.5$ in. 
D)  $b = 4.2$ in., $B = 41.5 ^ { \circ } , c = 3.5$ in. 
A)  $b = 1.2$ in., $B = 41.5 ^ { \circ } , c = 2.9$ in. 
B)  $b = 4.2$ in., $B = 41.5 ^ { \circ } , c = 4.9$ in. 
C)  $b = 2.3$ in., $B = 41.5 ^ { \circ } , c = 3.5$ in. 
D)  $b = 4.2$ in., $B = 41.5 ^ { \circ } , c = 3.5$ in.

Question 20

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.
-$( 0,2 )$

Accepted Answer

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

Without using a calculator, give the exact trigonometric function value with rational denominator. -Find a formula for the area of the figure in terms of s.

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - $208 ^ { \circ }$

Without using a calculator, give the exact trigonometric function value with rational denominator. - $\sec 30 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\csc 38 ^ { \circ } 22 ^ { \prime }$

Decide whether the statement is possible or impossible for an angle $\theta .$ - $\sec \theta = 0.87$

Find the exact value of the expression. - $\cos 210 ^ { \circ }$

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - $\sin \theta = 0.30738671$

Solve the problem. -The angle of elevation from a point on the ground to the top of a tower is $35 ^ { \circ } 42 ^ { \prime }$ . The angle of elevation from a point 152 feet farther back from the tower is $24 ^ { \circ } 30 ^ { \prime }$ . Find the height of the tower. Round to the nearest foot.

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $A = 79 ^ { \circ } 32 ^ { \prime } , c = 264 \mathrm {~m} , C = 90 ^ { \circ }$ Round side lengths to two decimal places, if necessary.

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 $\theta$ - $( 6,8 ) ;$ Find $\cos \theta$

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

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

Provide an appropriate response. -Find the complement of an angle whose measure is $34 ^ { \circ } 24 ^ { \prime } 40 ^ { \prime \prime }$ .

Use the fundamental identities to find the value of the trigonometric function. -Find $\sin \theta$ , given that $\cos \theta = \frac { 4 } { 7 }$ and $\theta$ is in quadrant IV.

Find the measure of each angle in the problem. -

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

Provide an appropriate response. -Find the complement of an angle whose measure is 8°.

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - $\mathrm { a } = 2.6 \text { in., } \mathrm { A } = 48.5 ^ { \circ } , \mathrm { C } = 90 ^ { \circ }$ Round values to one decimal place.

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. - $( 0,2 )$

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

Without using a calculator, give the exact trigonometric function value with rational denominator. -Find a formula for the area of the figure in terms of s.

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. - 208∘208 ^ { \circ }208∘

Without using a calculator, give the exact trigonometric function value with rational denominator. - sec⁡30∘\sec 30 ^ { \circ }sec30∘

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - csc⁡38∘22′\csc 38 ^ { \circ } 22 ^ { \prime }csc38∘22′

Decide whether the statement is possible or impossible for an angle θ.\theta .θ. - sec⁡θ=0.87\sec \theta = 0.87secθ=0.87

Find the exact value of the expression. - cos⁡210∘\cos 210 ^ { \circ }cos210∘

Use a calculator to find the function value. Give your answer rounded to seven decimal places, if necessary. - sin⁡θ=0.30738671\sin \theta = 0.30738671sinθ=0.30738671

Solve the right triangle. If two sides are given, give angles in degrees and minutes. - A=79∘32′,c=264 m,C=90∘A = 79 ^ { \circ } 32 ^ { \prime } , c = 264 \mathrm {~m} , C = 90 ^ { \circ }A=79∘32′,c=264 m,C=90∘ Round side lengths to two decimal places, if necessary.

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 - (6,8);( 6,8 ) ;(6,8); Find cos⁡θ\cos \thetacosθ

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

Find the exact value of the expression. - sin⁡θ=−22\sin \theta = - \frac { \sqrt { 2 } } { 2 }sinθ=−22​​

Provide an appropriate response. -Find the complement of an angle whose measure is 34∘24′40′′34 ^ { \circ } 24 ^ { \prime } 40 ^ { \prime \prime }34∘24′40′′ .

Use the fundamental identities to find the value of the trigonometric function. -Find sin⁡θ\sin \thetasinθ , given that cos⁡θ=47\cos \theta = \frac { 4 } { 7 }cosθ=74​ and θ\thetaθ is in quadrant IV.