Question 1

Use a calculator to find the function value to four decimal places.
-tan 53.84°

Accepted Answer

A) 9.2653 
B) 1.3683 
C) 0.4419 
D) 0.5900 
A) 9.2653 
B) 1.3683 
C) 0.4419 
D) 0.5900

Question 2

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative.
-$\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

Accepted Answer

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

Question 3

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.
-115°

Accepted Answer

A)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
C)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
D) $475^{\circ} \text { and }-245^{\circ}$
  
A)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
B)  $295 ^ { \circ }$ and $- 65 ^ { \circ }$
  
C)  $475 ^ { \circ }$ and $- 245 ^ { \circ }$
  
D) $475^{\circ} \text { and }-245^{\circ}$

Question 4

Convert the angle to degrees, minutes, and seconds.
-46.87°

Accepted Answer

A) 46°52'87'' 
B) 46°52'0'' 
C) 46°52'12'' 
D) 46°52'18'' 
A) 46°52'87'' 
B) 46°52'0'' 
C) 46°52'12'' 
D) 46°52'18''

Question 5

A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed the angle of depression to the car is 43° 39' . When the car
Stops, the angle of depression is 21° 53' . The building is 230 feet tall. How far did the car travel
From when it was first noticed until it stopped? Round your answer to the hundredths place.

Accepted Answer

A) 531.62 ft 
B) 357.73 ft 
C) 310.45 ft 
D) 331.52 ft 
A) 531.62 ft 
B) 357.73 ft 
C) 310.45 ft 
D) 331.52 ft

Question 6

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 $\theta$. Rationalize the denominator if necessary. If the function is undefined, say so.
-$( - 5,12 )$; find $\sin \theta$

Accepted Answer

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

Question 7

Write the expression in terms of its cofunction.
-sin 38°

Accepted Answer

A) tan 52° 
B) cos 52° 
C) cot 52° 
D) cos 38° 
A) tan 52° 
B) cos 52° 
C) cot 52° 
D) cos 38°

Question 8

Solve for the requested quantity.
-Find c. Round your answer to the hundredths place.

Accepted Answer

A)  $\mathrm { c } = 726.47 \mathrm {~m}$ 
B)  $\mathrm { c } = 713.82 \mathrm {~m}$ 
C)  $\mathrm { c } = 693.82 \mathrm {~m}$ 
D)  $\mathrm { c } = 700.25 \mathrm {~m}$ 
A)  $\mathrm { c } = 726.47 \mathrm {~m}$ 
B)  $\mathrm { c } = 713.82 \mathrm {~m}$ 
C)  $\mathrm { c } = 693.82 \mathrm {~m}$ 
D)  $\mathrm { c } = 700.25 \mathrm {~m}$

Question 9

A blimp is 1700 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 83.3° and 25.5°, how far apart are the two stadiums to
The nearest meter?

Accepted Answer

A) 12,687 m 
B) 3364 m 
C) 2237m 
D) 3764 m 
A) 12,687 m 
B) 3364 m 
C) 2237m 
D) 3764 m

Question 10

Find the exact value of the function. Rationalize the denominator if necessary.
-sin 330°

Accepted Answer

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

Question 11

Find the exact value of the function. Rationalize the denominator if necessary.
-csc 240°

Accepted Answer

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

Question 12

Sketch an angle $\theta$ in standard position such that $\theta$ has the smallest possible positive measure and the given point is on the terminal side of $\theta$.
-P = (-4, 2)

Accepted Answer

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

Question 13

Find the exact value of the function. Rationalize the denominator if necessary.
-csc 330°

Accepted Answer

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

Question 14

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\tan \theta$, if $\cot \theta = - \frac { 4 } { 5 }$

Accepted Answer

A)  $- \frac { 4 } { 5 }$ 
B)  $- \frac { 5 } { 4 }$ 
C)  $\frac { 9 } { 5 }$ 
D)  $\frac { 5 } { 4 }$ 
A)  $- \frac { 4 } { 5 }$ 
B)  $- \frac { 5 } { 4 }$ 
C)  $\frac { 9 } { 5 }$ 
D)  $\frac { 5 } { 4 }$

Question 15

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

Accepted Answer

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

Question 16

Find the exact value of the function. Rationalize the denominator if necessary.
-sec 150°

Accepted Answer

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

Question 17

Use the fundamental identities to find the value of the trigonometric function.
-$\tan \theta$, if $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Accepted Answer

A)  $- \frac { \sqrt { 7 } } { 9 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { 3 \sqrt { 7 } } { 7 }$ 
A)  $- \frac { \sqrt { 7 } } { 9 }$ 
B)  $\frac { 5 } { 4 }$ 
C)  $- \frac { 3 } { 2 }$ 
D)  $- \frac { 3 \sqrt { 7 } } { 7 }$

Question 18

Supplement of 68°

Accepted Answer

A) 112° 
B) 157° 
C) 292° 
D) 202° 
A) 112° 
B) 157° 
C) 292° 
D) 202°

Question 19

Find the reference angle for the given angle.
-A = 362°

Accepted Answer

A) 2° 
B) 92° 
C) 178° 
D) 88° 
A) 2° 
B) 92° 
C) 178° 
D) 88°

Question 20

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms.
- 
Find $\sin B$ and $\tan B$.

Accepted Answer

A)  $\sin \mathrm { A } = \frac { \mathrm { b } } { \mathrm { c } } ; \tan \mathrm { A } = \frac { \mathrm { b } } { \mathrm { a } }$ 
B)  $\sin \mathrm { A } = \frac { \mathrm { c } } { \mathrm { b } } ; \tan \mathrm { A } = \frac { \mathrm { b } } { \mathrm { a } }$ 
C)  $\sin A = \frac { c } { a } ; \tan A = \frac { b } { a }$ 
D)  $\sin \mathrm { A } = \frac { \mathrm { a } } { \mathrm { c } } ; \tan \mathrm { A } = \frac { \mathrm { a } } { \mathrm { b } }$ 
A)  $\sin \mathrm { A } = \frac { \mathrm { b } } { \mathrm { c } } ; \tan \mathrm { A } = \frac { \mathrm { b } } { \mathrm { a } }$ 
B)  $\sin \mathrm { A } = \frac { \mathrm { c } } { \mathrm { b } } ; \tan \mathrm { A } = \frac { \mathrm { b } } { \mathrm { a } }$ 
C)  $\sin A = \frac { c } { a } ; \tan A = \frac { b } { a }$ 
D)  $\sin \mathrm { A } = \frac { \mathrm { a } } { \mathrm { c } } ; \tan \mathrm { A } = \frac { \mathrm { a } } { \mathrm { b } }$

Use a calculator to find the function value to four decimal places. -tan 53.84°

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. - $\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

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. -115°

Convert the angle to degrees, minutes, and seconds. -46.87°

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 $\theta$ . Rationalize the denominator if necessary. If the function is undefined, say so. - $( - 5,12 )$ ; find $\sin \theta$

Write the expression in terms of its cofunction. -sin 38°

Solve for the requested quantity. -Find c. Round your answer to the hundredths place.

A blimp is 1700 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 83.3° and 25.5°, how far apart are the two stadiums to The nearest meter?

Find the exact value of the function. Rationalize the denominator if necessary. -sin 330°

Find the exact value of the function. Rationalize the denominator if necessary. -csc 240°

Find the exact value of the function. Rationalize the denominator if necessary. -csc 330°

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\tan \theta$ , if $\cot \theta = - \frac { 4 } { 5 }$

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

Find the exact value of the function. Rationalize the denominator if necessary. -sec 150°

Use the fundamental identities to find the value of the trigonometric function. - $\tan \theta$ , if $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Supplement of 68°

Find the reference angle for the given angle. -A = 362°

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \sin B and \tan B .$ Find $\sin B$ and $\tan B$ .

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

Use a calculator to find the function value to four decimal places. -tan 53.84°

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. - I,ry\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }I,yr​

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. -115°

Convert the angle to degrees, minutes, and seconds. -46.87°

Write the expression in terms of its cofunction. -sin 38°

Solve for the requested quantity. -Find c. Round your answer to the hundredths place.

A blimp is 1700 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 83.3° and 25.5°, how far apart are the two stadiums to The nearest meter?

Find the exact value of the function. Rationalize the denominator if necessary. -sin 330°

Find the exact value of the function. Rationalize the denominator if necessary. -csc 240°

Sketch an angle θ\thetaθ in standard position such that θ\thetaθ has the smallest possible positive measure and the given point is on the terminal side of θ\thetaθ . -P = (-4, 2)

Find the exact value of the function. Rationalize the denominator if necessary. -csc 330°

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - tan⁡θ\tan \thetatanθ , if cot⁡θ=−45\cot \theta = - \frac { 4 } { 5 }cotθ=−54​

Identify the quadrant or quadrants for the angle ϴ satisfying the given conditions. - cos⁡θ>0\cos \theta > 0cosθ>0 and csc⁡θ<0\csc \theta < 0cscθ<0

Find the exact value of the function. Rationalize the denominator if necessary. -sec 150°

Use the fundamental identities to find the value of the trigonometric function. - tan⁡θ\tan \thetatanθ , if sin⁡θ=34\sin \theta = \frac { 3 } { 4 }sinθ=43​ and θ\thetaθ is in quadrant II.

Supplement of 68°

Find the reference angle for the given angle. -A = 362°

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find sin⁡B\sin BsinB and tan⁡B\tan BtanB .

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

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. - $\mathrm { I } , \frac { \mathrm { r } } { \mathrm { y } }$

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\tan \theta$ , if $\cot \theta = - \frac { 4 } { 5 }$

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

Use the fundamental identities to find the value of the trigonometric function. - $\tan \theta$ , if $\sin \theta = \frac { 3 } { 4 }$ and $\theta$ is in quadrant II.

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - $Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find \sin B and \tan B .$ Find $\sin B$ and $\tan B$ .