Question 1

Complement of $50 \frac { 2 } { 3 } ^ { \circ }$

Accepted Answer

A)  $129 \frac { 1 } { 3 }$ o 
B)  $309 \frac { 1 } { 3 } ^ { \circ }$ 
C)  $39 \frac { 1 } { 3 } ^ { \circ }$ 
D)  $219 \frac { 1 } { 3 } ^ { \circ }$ 
A)  $129 \frac { 1 } { 3 }$ o 
B)  $309 \frac { 1 } { 3 } ^ { \circ }$ 
C)  $39 \frac { 1 } { 3 } ^ { \circ }$ 
D)  $219 \frac { 1 } { 3 } ^ { \circ }$ C

Question 2

Solve the right triangle.
-a = 3.3 in., A = 68.5°, C = 90°

Accepted Answer

A) b = 1.3 in., B = 21.5°, c = 3.5 in. 
B) b = 3.2 in., B = 21.5°, c = 4.6 in. 
C) b = 0.2 in., B = 21.5°, c = 3.3 in. 
D) b = 3.2 in., B = 21.5°, c = 3.5 in. 
A) b = 1.3 in., B = 21.5°, c = 3.5 in. 
B) b = 3.2 in., B = 21.5°, c = 4.6 in. 
C) b = 0.2 in., B = 21.5°, c = 3.3 in. 
D) b = 3.2 in., B = 21.5°, c = 3.5 in. A

Question 3

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\sin \theta = - \frac { \sqrt { 2 } } { 2 }$

Accepted Answer

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

Question 4

Find the exact function value if it exists.
-csc 0°

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Find the exact function value if it exists.
-sin 90°

Accepted Answer

A) Undefined 
B) 1 
C)  $\frac { 1 } { 2 }$ 
D) 0 
A) Undefined 
B) 1 
C)  $\frac { 1 } { 2 }$ 
D) 0

Question 7

$\tan \left( 420 ^ { \circ } \right)$

Accepted Answer

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

Question 8

Write the expression in terms of its cofunction.
-sin 5.1°

Accepted Answer

A) cos 95.1° 
B) cos 84.9° 
C) cos 5.1° 
D) cos 85.9° 
A) cos 95.1° 
B) cos 84.9° 
C) cos 5.1° 
D) cos 85.9°

Question 9

Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
-31°41'

Accepted Answer

A) 31.82° 
B) 31.41° 
C) 32.68° 
D) 31.68° 
A) 31.82° 
B) 31.41° 
C) 32.68° 
D) 31.68°

Question 10

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\tan \mathrm { A }$ and $\cot \mathrm { A }$.

Accepted Answer

A)  $\tan \mathrm { A } = \frac { 5 } { 12 } ; \cot \mathrm { A } = \frac { 12 } { 5 }$ 
B)  $\tan \mathrm { A } = \frac { 13 } { 5 } ; \cot \mathrm { A } = \frac { 13 } { 12 }$ 
C)  $\tan \mathrm { A } = \frac { 5 } { 13 } ; \cot \mathrm { A } = \frac { 12 } { 13 }$ 
D)  $\tan \mathrm { A } = \frac { 12 } { 5 } ; \cot \mathrm { A } = \frac { 5 } { 12 }$ 
A)  $\tan \mathrm { A } = \frac { 5 } { 12 } ; \cot \mathrm { A } = \frac { 12 } { 5 }$ 
B)  $\tan \mathrm { A } = \frac { 13 } { 5 } ; \cot \mathrm { A } = \frac { 13 } { 12 }$ 
C)  $\tan \mathrm { A } = \frac { 5 } { 13 } ; \cot \mathrm { A } = \frac { 12 } { 13 }$ 
D)  $\tan \mathrm { A } = \frac { 12 } { 5 } ; \cot \mathrm { A } = \frac { 5 } { 12 }$

Question 11

Use the fundamental identities to find the value of the trigonometric function.
-$\cot \gamma$, if $\csc \gamma = - \frac { 13 } { 3 }$, with $\gamma$ in quadrant III

Accepted Answer

A)  $\frac { 4 \sqrt { 10 } } { 3 }$ 
B)  $- \frac { 3 \sqrt { 10 } } { 40 }$ 
C)  $- \frac { 13 \sqrt { 10 } } { 40 }$ 
D)  $- \frac { 4 \sqrt { 10 } } { 3 }$ 
A)  $\frac { 4 \sqrt { 10 } } { 3 }$ 
B)  $- \frac { 3 \sqrt { 10 } } { 40 }$ 
C)  $- \frac { 13 \sqrt { 10 } } { 40 }$ 
D)  $- \frac { 4 \sqrt { 10 } } { 3 }$

Question 12

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement.
-tan ϴ= 0.6269

Accepted Answer

A) 32.08° 
B) 38.82° 
C) -38.82° 
D) 128.82° 
A) 32.08° 
B) 38.82° 
C) -38.82° 
D) 128.82°

Question 13

Perform the calculation.
-90° - 32°17'41''

Accepted Answer

A) 57°43'19'' 
B) 57°42'19'' 
C) 57°42'18'' 
D) 58°43'19'' 
A) 57°43'19'' 
B) 57°42'19'' 
C) 57°42'18'' 
D) 58°43'19''

Question 14

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°

Accepted Answer

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

Question 15

Find the reference angle for the given angle.
-A = -430°

Accepted Answer

A) 160° 
B) 70° 
C) 20° 
D) 110° 
A) 160° 
B) 70° 
C) 20° 
D) 110°

Question 16

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative.
-III, xr

Accepted Answer

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

Question 17

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions.
-$\cot \theta > 0$ and $\sin \theta < 0$

Accepted Answer

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

Question 18

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\sin \theta$, if $\csc \theta = 9.5$

Accepted Answer

A)  $- \frac { 2 } { 19 }$ 
B)  $\frac { 2 } { 19 }$ 
C)  $\frac { 19 } { 2 }$ 
D)  $\frac { 17 } { 19 }$ 
A)  $- \frac { 2 } { 19 }$ 
B)  $\frac { 2 } { 19 }$ 
C)  $\frac { 19 } { 2 }$ 
D)  $\frac { 17 } { 19 }$

Question 19

Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 24° 23'. He then
Drives 1 mile (1 mile = 5280 ft)more and measures the angle of elevation to be 33° 12'. Find the
Height of the mountain to the nearest foot.

Accepted Answer

A) 778,723 ft 
B) 7887 ft 
C) 7787 ft 
D) 77,872 ft 
A) 778,723 ft 
B) 7887 ft 
C) 7787 ft 
D) 77,872 ft

Question 20

Use a calculator to find the function value to four decimal places.
-tan 716°

Accepted Answer

A) 0.9976 
B) 0.4877 
C) -0.0699 
D) -0.6745 
A) 0.9976 
B) 0.4877 
C) -0.0699 
D) -0.6745

Complement of $50 \frac { 2 } { 3 } ^ { \circ }$

Solve the right triangle. -a = 3.3 in., A = 68.5°, C = 90°

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ - $\sin \theta = - \frac { \sqrt { 2 } } { 2 }$

Find the exact function value if it exists. -csc 0°

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

Find the exact function value if it exists. -sin 90°

$\tan \left( 420 ^ { \circ } \right)$

Write the expression in terms of its cofunction. -sin 5.1°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -31°41'

Use the fundamental identities to find the value of the trigonometric function. - $\cot \gamma$ , if $\csc \gamma = - \frac { 13 } { 3 }$ , with $\gamma$ in quadrant III

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -tan ϴ= 0.6269

Perform the calculation. -90° - 32°17'41''

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°

Find the reference angle for the given angle. -A = -430°

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -III, xr

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\cot \theta > 0$ and $\sin \theta < 0$

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\sin \theta$ , if $\csc \theta = 9.5$

Use a calculator to find the function value to four decimal places. -tan 716°

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

Exam 14: Trigonometry Formerly

Complement of 5023∘50 \frac { 2 } { 3 } ^ { \circ }5032​∘

Solve the right triangle. -a = 3.3 in., A = 68.5°, C = 90°

Find the exact function value if it exists. -csc 0°

Use the fundamental identities to find the value of the trigonometric function. - sin⁡θ\sin \thetasinθ , if cos⁡θ=23\cos \theta = \frac { 2 } { 3 }cosθ=32​ and θ\thetaθ is in quadrant IV.

Find the exact function value if it exists. -sin 90°

tan⁡(420∘)\tan \left( 420 ^ { \circ } \right)tan(420∘)

Write the expression in terms of its cofunction. -sin 5.1°

Convert the angle to decimal degrees and round to the nearest hundredth of a degree. -31°41'

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find tan⁡A\tan \mathrm { A }tanA and cot⁡A\cot \mathrm { A }cotA .

Use the fundamental identities to find the value of the trigonometric function. - cot⁡γ\cot \gammacotγ , if csc⁡γ=−133\csc \gamma = - \frac { 13 } { 3 }cscγ=−313​ , with γ\gammaγ in quadrant III

Find a value of ϴsuch that 0 ϴ 90° and ϴsatisfies the statement. -tan ϴ= 0.6269

Perform the calculation. -90° - 32°17'41''

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°

Find the reference angle for the given angle. -A = -430°

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. -III, xr

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - cot⁡θ>0\cot \theta > 0cotθ>0 and sin⁡θ<0\sin \theta < 0sinθ<0

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - sin⁡θ\sin \thetasinθ , if csc⁡θ=9.5\csc \theta = 9.5cscθ=9.5

Use a calculator to find the function value to four decimal places. -tan 716°

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Geometry

Counting Methods

Probability

Statistics

Personal Financial Management

Graph Theory

Voting and Apportionment

Filters

Complement of $50 \frac { 2 } { 3 } ^ { \circ }$

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

$\tan \left( 420 ^ { \circ } \right)$

Use the fundamental identities to find the value of the trigonometric function. - $\cot \gamma$ , if $\csc \gamma = - \frac { 13 } { 3 }$ , with $\gamma$ in quadrant III

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - $\cot \theta > 0$ and $\sin \theta < 0$

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\sin \theta$ , if $\csc \theta = 9.5$