Question 1

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-$136 ^ { \circ } 6 ^ { \prime } 30 ^ { \prime \prime }$

Accepted Answer

A)  $136.11 ^ { \circ }$ 
B)  $136.07 ^ { \circ }$ 
C)  $136.17 ^ { \circ }$ 
D)  $136.12 ^ { \circ }$ 
A)  $136.11 ^ { \circ }$ 
B)  $136.07 ^ { \circ }$ 
C)  $136.17 ^ { \circ }$ 
D)  $136.12 ^ { \circ }$

Question 2

Solve the problem.
-A person is watching a car from the top of a building. The car is traveling on a straight road directly toward the building. When first noticed, the angle of depression to the car is $22 ^ { \circ } 50 ^ { \prime }$. When the car stops, the angle of depression is $47 ^ { \circ } 16 ^ { \prime }$. The building is 270 feet tall. How far did the car travel from when it was first noticed until it stopped? Round to the nearest foot.

Accepted Answer

A)  $418 \mathrm { ft }$ 
B)  $592 \mathrm { ft }$ 
C)  $371 \mathrm { ft }$ 
D)  $392 \mathrm { ft }$ 
A)  $418 \mathrm { ft }$ 
B)  $592 \mathrm { ft }$ 
C)  $371 \mathrm { ft }$ 
D)  $392 \mathrm { ft }$

Question 3

Find the exact value of the expression.
-$\sin 3105 ^ { \circ }$

Accepted Answer

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

Question 4

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal
places, if necessary.
-csc θ = 1.6208757

Accepted Answer

A)  38.0937809° 
B)  31.6725297° 
C)  58.3274703° 
D)  51.9062191° 
A)  38.0937809° 
B)  31.6725297° 
C)  58.3274703° 
D)  51.9062191°

Question 5

Provide an appropriate response.
-Find the supplement of an angle whose measure is 155°.

Accepted Answer

A)  $- 65 ^ { \circ }$ 
B)  $335 ^ { \circ }$ 
C)  $245 ^ { \circ }$ 
D)  $25 ^ { \circ }$ 
A)  $- 65 ^ { \circ }$ 
B)  $335 ^ { \circ }$ 
C)  $245 ^ { \circ }$ 
D)  $25 ^ { \circ }$

Question 6

Solve the right triangle. If two sides are given, give angles in degrees and minutes.
- 
$$\mathrm { B } = 58.45 ^ { \circ } , \mathrm { a } = 615.7 \mathrm {~m}$$
Give side lengths to two decimal places.

Accepted Answer

A)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 1002.77 \mathrm {~m} ; \mathrm { c } = 1189.35 \mathrm {~m}$ 
B)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 941.20 \mathrm {~m} ; \mathrm { c } = 1176.70 \mathrm {~m}$ 
C)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 1064.34 \mathrm {~m} ; \mathrm { c } = 1163.13 \mathrm {~m}$ 
D)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 1002.77 \mathrm {~m} ; \mathrm { c } = 1176.70 \mathrm {~m}$ 
A)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 1002.77 \mathrm {~m} ; \mathrm { c } = 1189.35 \mathrm {~m}$ 
B)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 941.20 \mathrm {~m} ; \mathrm { c } = 1176.70 \mathrm {~m}$ 
C)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 1064.34 \mathrm {~m} ; \mathrm { c } = 1163.13 \mathrm {~m}$ 
D)  $\mathrm { A } = 31.55 ^ { \circ } ; \mathrm { b } = 1002.77 \mathrm {~m} ; \mathrm { c } = 1176.70 \mathrm {~m}$

Question 7

Use the fundamental identities to find the value of the trigonometric function.
-Find $\csc \theta$, given that $\cot \theta = - \sqrt { 3 }$ and $\theta$ is in quadrant II.

Accepted Answer

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

Question 8

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.
-$8 x + 9 y = 0 , x \geq 0 ; \quad$ Find $\cot \theta$

Accepted Answer

A)  $\frac { 9 } { 8 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { \sqrt { 145 } } { 8 }$ 
A)  $\frac { 9 } { 8 }$ 
B)  $- \frac { 8 } { 9 }$ 
C)  $- \frac { 9 } { 8 }$ 
D)  $\frac { \sqrt { 145 } } { 8 }$

Question 9

Evaluate the expression.
-$\cos 360 ^ { \circ } - 6 \sin 90 ^ { \circ }$

Accepted Answer

A)  $- 5$ 
B)  $- 6$ 
C)  0 
D)  1 
A)  $- 5$ 
B)  $- 6$ 
C)  0 
D)  1

Question 10

Evaluate the expression.
-$\csc 450 ^ { \circ }$

Accepted Answer

A)  1 
B)  Undefined 
C)  0 
D)  2 
A)  1 
B)  Undefined 
C)  0 
D)  2

Question 11

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.
-$\tan \theta$, given that $\cot \theta = - \frac { 7 } { 8 }$

Accepted Answer

A)  $\frac { 15 } { 8 }$ 
B)  $- \frac { 7 } { 8 }$ 
C)  $\frac { 8 } { 7 }$ 
D)  $- \frac { 8 } { 7 }$ 
A)  $\frac { 15 } { 8 }$ 
B)  $- \frac { 7 } { 8 }$ 
C)  $\frac { 8 } { 7 }$ 
D)  $- \frac { 8 } { 7 }$

Question 12

Perform the calculation.
-$$180 ^ { \circ } - 121 ^ { \circ } 36 ^ { \prime } 21 ^ { \prime \prime }$$

Accepted Answer

A)  $59 ^ { \circ } 23 ^ { \prime } 39 ^ { \prime \prime }$ 
B)  $58 ^ { \circ } 24 ^ { \prime } 39 ^ { \prime \prime }$ 
C)  $59 ^ { \circ } 24 ^ { \prime } 39 ^ { \prime \prime }$ 
D)  $58 ^ { \circ } 23 ^ { \prime } 39 ^ { \prime \prime }$ 
A)  $59 ^ { \circ } 23 ^ { \prime } 39 ^ { \prime \prime }$ 
B)  $58 ^ { \circ } 24 ^ { \prime } 39 ^ { \prime \prime }$ 
C)  $59 ^ { \circ } 24 ^ { \prime } 39 ^ { \prime \prime }$ 
D)  $58 ^ { \circ } 23 ^ { \prime } 39 ^ { \prime \prime }$

Question 13

Provide an appropriate response.
-Find the complement of an angle whose measure is 36°27′56′′.

Accepted Answer

A)  $53 ^ { \circ } 32 ^ { \prime } 4 ^ { \prime \prime }$ 
B)  $54 ^ { \circ } 33 ^ { \prime } 4 ^ { \prime \prime }$ 
C)  $53 ^ { \circ } 32 ^ { \prime } 3 ^ { \prime \prime }$ 
D)  $53 ^ { \circ } 33 ^ { \prime } 4 ^ { \prime \prime }$ 
A)  $53 ^ { \circ } 32 ^ { \prime } 4 ^ { \prime \prime }$ 
B)  $54 ^ { \circ } 33 ^ { \prime } 4 ^ { \prime \prime }$ 
C)  $53 ^ { \circ } 32 ^ { \prime } 3 ^ { \prime \prime }$ 
D)  $53 ^ { \circ } 33 ^ { \prime } 4 ^ { \prime \prime }$

Question 14

Solve the problem.
-Find the exact value of $x$ in the figure.

Accepted Answer

A)  $10 \sqrt { 6 }$ 
B)  $\frac { 20 \sqrt { 3 } } { 3 }$ 
C)  $\frac { 20 \sqrt { 6 } } { 3 }$ 
D)  $10 \sqrt { 3 }$ 
A)  $10 \sqrt { 6 }$ 
B)  $\frac { 20 \sqrt { 3 } } { 3 }$ 
C)  $\frac { 20 \sqrt { 6 } } { 3 }$ 
D)  $10 \sqrt { 3 }$

Question 15

Find the exact value of the expression.
-$\cot \left( - 2295 ^ { \circ } \right)$

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Use the fundamental identities to find the value of the trigonometric function.
-Find $\cos \theta$, given that $\sin \theta = - \frac { 5 } { 13 }$ and $\theta$ is in quadrant III.

Accepted Answer

A)  $- \frac { 5 } { 12 }$ 
B)  $\frac { 12 } { 5 }$ 
C)  $- \frac { 13 } { 5 }$ 
D)  $- \frac { 12 } { 13 }$ 
A)  $- \frac { 5 } { 12 }$ 
B)  $\frac { 12 } { 5 }$ 
C)  $- \frac { 13 } { 5 }$ 
D)  $- \frac { 12 } { 13 }$

Question 18

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 $\mathrm { b } = 12$ and $c = 20$

Accepted Answer

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

Question 19

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

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)  $\frac { 2 \sqrt { 3 } } { 3 }$

Question 20

If n is an integer, n ∙ 180° represents an integer multiple of 180°, and (2n + 1) ∙ 90° represents an odd integer multiple of
90°. Decide whether the expression is equal to 0, 1, -1, or is undefined.
-$\tan \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$

Accepted Answer

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

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. - $136 ^ { \circ } 6 ^ { \prime } 30 ^ { \prime \prime }$

Find the exact value of the expression. - $\sin 3105 ^ { \circ }$

Find a value of θ in [0°, 90°] that satisfies the statement. Leave answer in decimal degrees rounded to seven decimal places, if necessary. -csc θ = 1.6208757

Provide an appropriate response. -Find the supplement of an angle whose measure is 155°.

Use the fundamental identities to find the value of the trigonometric function. -Find $\csc \theta$ , given that $\cot \theta = - \sqrt { 3 }$ and $\theta$ is in quadrant II.

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. - $8 x + 9 y = 0 , x \geq 0 ; \quad$ Find $\cot \theta$

Evaluate the expression. - $\cos 360 ^ { \circ } - 6 \sin 90 ^ { \circ }$

Evaluate the expression. - $\csc 450 ^ { \circ }$

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. - $\tan \theta$ , given that $\cot \theta = - \frac { 7 } { 8 }$

Perform the calculation. - $180 ^ { \circ } - 121 ^ { \circ } 36 ^ { \prime } 21 ^ { \prime \prime }$

Provide an appropriate response. -Find the complement of an angle whose measure is 36°27′56′′.

Solve the problem. -Find the exact value of $x$ in the figure.

Find the exact value of the expression. - $\cot \left( - 2295 ^ { \circ } \right)$

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

Use the fundamental identities to find the value of the trigonometric function. -Find $\cos \theta$ , given that $\sin \theta = - \frac { 5 } { 13 }$ and $\theta$ is in quadrant III.

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

If n is an integer, n ∙ 180° represents an integer multiple of 180°, and (2n + 1) ∙ 90° represents an odd integer multiple of 90°. Decide whether the expression is equal to 0, 1, -1, or is undefined. - $\tan \left( ( 2 n + 1 ) \cdot 90 ^ { \circ } \right)$

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. - 136∘6′30′′136 ^ { \circ } 6 ^ { \prime } 30 ^ { \prime \prime }136∘6′30′′

Find the exact value of the expression. - sin⁡3105∘\sin 3105 ^ { \circ }sin3105∘