Question 1

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\csc \theta$, if $\sin \theta = \frac { 1 } { 9 }$

Accepted Answer

A)  $- 9$ 
B)  $\frac { 1 } { 9 }$ 
C)  9 
D)  $- \frac { 1 } { 9 }$ 
A)  $- 9$ 
B)  $\frac { 1 } { 9 }$ 
C)  9 
D)  $- \frac { 1 } { 9 }$

Question 2

Perform the calculation.
-85°46' + 30°58'

Accepted Answer

A) 116°104' 
B) 45°104' 
C) 45°44' 
D) 116°44' 
A) 116°104' 
B) 45°104' 
C) 45°44' 
D) 116°44'

Question 3

Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C. Find the exact value of the indicated
trigonometric function. You may need to use the Pythagorean theorem to find the unknown side length. Rationalize the
denominator if necessary.
-Find $\sec B$ when $a = 5$ and $b = 9$.

Accepted Answer

A)  $\frac { 5 \sqrt { 106 } } { 9 }$ 
B)  $\frac { \sqrt { 106 } } { 5 }$ 
C)  $\frac { 9 \sqrt { 106 } } { 106 }$ 
D)  $\frac { 5 \sqrt { 106 } } { 106 }$ 
A)  $\frac { 5 \sqrt { 106 } } { 9 }$ 
B)  $\frac { \sqrt { 106 } } { 5 }$ 
C)  $\frac { 9 \sqrt { 106 } } { 106 }$ 
D)  $\frac { 5 \sqrt { 106 } } { 106 }$

Question 4

Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C. Find the exact value of the indicated
trigonometric function. You may need to use the Pythagorean theorem to find the unknown side length. Rationalize the
denominator if necessary.
-Find $\sin \mathrm { A }$ when $\mathrm { a } = 8$ and $\mathrm { b } = 3$.

Accepted Answer

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

Question 5

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

Accepted Answer

A)  $b = 517.74$ feet 
B)  $b = 564.47$ feet 
C)  $b = 508.88$ feet 
D)  $b = 515.27$ feet 
A)  $b = 517.74$ feet 
B)  $b = 564.47$ feet 
C)  $b = 508.88$ feet 
D)  $b = 515.27$ feet

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.
-$( 12,16 )$; find $\csc \theta$.

Accepted Answer

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

Question 7

Convert the angle to degrees, minutes, and seconds.
-105.89°

Accepted Answer

A) 105°54'24'' 
B) 105°53'24'' 
C) 105°53'89'' 
D) 105°51'89'' 
A) 105°54'24'' 
B) 105°53'24'' 
C) 105°53'89'' 
D) 105°51'89''

Question 8

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

Accepted Answer

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

Question 9

Find the signs of the six trigonometric functions for the given angle.
-268°

Accepted Answer

A) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
B) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
C) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
D) Negative: all 
A) Positive: cosine and secant; negative: sine, tangent, cotangent, cosecant 
B) Positive: sine and cosecant; negative: cosine, tangent, cotangent, secant 
C) Positive: tangent and cotangent; negative: sine, cosine, secant, cosecant 
D) Negative: all

Question 10

Find the angle of smallest possible positive measure coterminal with the given angle.
-409°

Accepted Answer

A) 204.5° 
B) 39° 
C) 229° 
D) 49° 
A) 204.5° 
B) 39° 
C) 229° 
D) 49°

Question 11

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

Accepted Answer

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

Question 12

Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C. Find the exact value of the indicated
trigonometric function. You may need to use the Pythagorean theorem to find the unknown side length. Rationalize the
denominator if necessary.
-Find $\csc B$ when $a = 3$ and $b = 2$.

Accepted Answer

A)  $\frac { \sqrt { 13 } } { 2 }$ 
B)  $\frac { 2 \sqrt { 13 } } { 13 }$ 
C)  $\frac { 3 \sqrt { 13 } } { 13 }$ 
D)  $\frac { \sqrt { 13 } } { 3 }$ 
A)  $\frac { \sqrt { 13 } } { 2 }$ 
B)  $\frac { 2 \sqrt { 13 } } { 13 }$ 
C)  $\frac { 3 \sqrt { 13 } } { 13 }$ 
D)  $\frac { \sqrt { 13 } } { 3 }$

Question 13

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

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 14

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

Accepted Answer

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

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\csc \theta$ , if $\sin \theta = \frac { 1 } { 9 }$

Perform the calculation. -85°46' + 30°58'

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

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. - $( 12,16 )$ ; find $\csc \theta$ .

Convert the angle to degrees, minutes, and seconds. -105.89°

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

Find the signs of the six trigonometric functions for the given angle. -268°

Find the angle of smallest possible positive measure coterminal with the given angle. -409°

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

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

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

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 the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - csc⁡θ\csc \thetacscθ , if sin⁡θ=19\sin \theta = \frac { 1 } { 9 }sinθ=91​