Question 1

Use the fundamental identities to find the value of the trigonometric function.
-$\csc \theta$, if $\cot \theta = - \frac { 7 } { 10 }$, with $\theta$ in quadrant II

Accepted Answer

A)  $\frac { \sqrt { 149 } } { 10 }$ 
B)  $- \frac { 7 \sqrt { 149 } } { 149 }$ 
C)  $- \frac { \sqrt { 149 } } { 7 }$ 
D)  $\frac { 7 \sqrt { 149 } } { 149 }$ 
A)  $\frac { \sqrt { 149 } } { 10 }$ 
B)  $- \frac { 7 \sqrt { 149 } } { 149 }$ 
C)  $- \frac { \sqrt { 149 } } { 7 }$ 
D)  $\frac { 7 \sqrt { 149 } } { 149 }$

Question 2

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

Accepted Answer

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

Question 3

Use a calculator to find the function value to four decimal places.
-csc 30°9'

Accepted Answer

A) 1.991 
B) 1.992 
C) 1.993 
D) 1.99 
A) 1.991 
B) 1.992 
C) 1.993 
D) 1.99

Question 4

Find the exact function value if it exists.
-cos (-180°)

Accepted Answer

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

Question 5

Use a calculator to find the function value to four decimal places.
-cot 58.9°

Accepted Answer

A) 1.6577 
B) 0.6032 
C) 0.8563 
D) 1.0098 
A) 1.6577 
B) 0.6032 
C) 0.8563 
D) 1.0098

Question 6

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 $\tan \mathrm { A }$ when $\mathrm { a } = 2$ and $\mathrm { b } = 7$.

Accepted Answer

A)  $\frac { 7 \sqrt { 53 } } { 53 }$ 
B)  $\frac { 7 } { 2 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 2 \sqrt { 53 } } { 53 }$ 
A)  $\frac { 7 \sqrt { 53 } } { 53 }$ 
B)  $\frac { 7 } { 2 }$ 
C)  $\frac { 2 } { 7 }$ 
D)  $\frac { 2 \sqrt { 53 } } { 53 }$

Question 7

Solve the right triangle.
-a = 3.3 cm, b = 3.0 cm, C = 90°

Accepted Answer

A) A = 65.4°, B = 24.6°, c = 6.3 cm 
B) A = 42.3°, B = 47.7°, c = 4.5 cm 
C) A = 43.2°, B = 46.8°, c = 4.5 cm 
D) A = 47.7°, B = 42.3°, c = 4.5 cm 
A) A = 65.4°, B = 24.6°, c = 6.3 cm 
B) A = 42.3°, B = 47.7°, c = 4.5 cm 
C) A = 43.2°, B = 46.8°, c = 4.5 cm 
D) A = 47.7°, B = 42.3°, c = 4.5 cm

Question 8

Complement of 36°

Accepted Answer

A) 324° 
B) 144° 
C) 54° 
D) 72° 
A) 324° 
B) 144° 
C) 54° 
D) 72°

Question 9

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

Accepted Answer

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

Question 10

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary.
-$\tan \theta$, if $\cot \theta = \frac { \sqrt { 7 } } { 3 }$

Accepted Answer

A)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
B)  $\frac { \sqrt { 7 } } { 7 }$ 
C)  $\frac { \sqrt { 3 } } { 7 }$ 
D)  $\frac { 7 \sqrt { 7 } } { 3 }$ 
A)  $\frac { 3 \sqrt { 7 } } { 7 }$ 
B)  $\frac { \sqrt { 7 } } { 7 }$ 
C)  $\frac { \sqrt { 3 } } { 7 }$ 
D)  $\frac { 7 \sqrt { 7 } } { 3 }$

Question 11

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer.
--285°

Accepted Answer

A) -285° + n · 180° 
B) -285° + n · 90° 
C) -285° + 2nπ 
D) -285° + n · 360° 
A) -285° + n · 180° 
B) -285° + n · 90° 
C) -285° + 2nπ 
D) -285° + n · 360°

Question 12

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 19° 13'. When the boat stops, the
Angle of depression is 49° 18' . The lighthouse is 200 feet tall. How far did the boat travel from
When it was first noticed until it stopped? Round your answer to the hundredths place.

Accepted Answer

A) 386.46 ft 
B) 401.76ft 
C) 446.96 ft 
D) 424.26 ft 
A) 386.46 ft 
B) 401.76ft 
C) 446.96 ft 
D) 424.26 ft

Question 13

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

Accepted Answer

A)  $\sec \mathrm { A } = \frac { 8 } { 17 } ; \csc \mathrm { A } = \frac { 15 } { 17 }$ 
B)  $\sec A = \frac { 15 } { 8 } ; \csc A = \frac { 8 } { 15 }$ 
C)  $\sec \mathrm { A } = \frac { 17 } { 15 } ; \csc \mathrm { A } = \frac { 17 } { 8 }$ 
D)  $\sec \mathrm { A } = \frac { 17 } { 8 } ; \csc \mathrm { A } = \frac { 17 } { 15 }$ 
A)  $\sec \mathrm { A } = \frac { 8 } { 17 } ; \csc \mathrm { A } = \frac { 15 } { 17 }$ 
B)  $\sec A = \frac { 15 } { 8 } ; \csc A = \frac { 8 } { 15 }$ 
C)  $\sec \mathrm { A } = \frac { 17 } { 15 } ; \csc \mathrm { A } = \frac { 17 } { 8 }$ 
D)  $\sec \mathrm { A } = \frac { 17 } { 8 } ; \csc \mathrm { A } = \frac { 17 } { 15 }$

Question 14

Without using a calculator, give the exact trigonometric function value with rational denominator.
-cos 60°

Accepted Answer

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

Question 15

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

Accepted Answer

A)  Quadrants II or IV 
B)  Quadrants III or IV 
C)  Quadrant III 
D)  Quadrants II or III 
A)  Quadrants II or IV 
B)  Quadrants III or IV 
C)  Quadrant III 
D)  Quadrants II or III

Question 16

State in which quadrant the terminal side of the given angle lies.
-98°

Accepted Answer

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

Question 17

$\sin \left( 1140 ^ { \circ } \right)$

Accepted Answer

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

Question 18

Find the exact value of the function. Rationalize the denominator if necessary.
-cos (-630°)

Accepted Answer

A)  0 
B)  $\frac { \sqrt { 3 } } { 2 }$ 
C)  1 
D)  Undefined 
A)  0 
B)  $\frac { \sqrt { 3 } } { 2 }$ 
C)  1 
D)  Undefined

Question 19

Find the angle of smallest possible positive measure coterminal with the given angle.
--40°

Accepted Answer

A) 320° 
B) 50° 
C) 40° 
D) 230° 
A) 320° 
B) 50° 
C) 40° 
D) 230°

Question 20

$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-sec ϴis undefined

Accepted Answer

A) 90° 
B) 0° and 180° 
C) 0° 
D) 90° and 270° 
A) 90° 
B) 0° and 180° 
C) 0° 
D) 90° and 270°

Use the fundamental identities to find the value of the trigonometric function. - $\csc \theta$ , if $\cot \theta = - \frac { 7 } { 10 }$ , with $\theta$ in quadrant II

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

Use a calculator to find the function value to four decimal places. -csc 30°9'

Find the exact function value if it exists. -cos (-180°)

Use a calculator to find the function value to four decimal places. -cot 58.9°

Solve the right triangle. -a = 3.3 cm, b = 3.0 cm, C = 90°

Complement of 36°

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

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\tan \theta$ , if $\cot \theta = \frac { \sqrt { 7 } } { 3 }$

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. --285°

Without using a calculator, give the exact trigonometric function value with rational denominator. -cos 60°

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

State in which quadrant the terminal side of the given angle lies. -98°

$\sin \left( 1140 ^ { \circ } \right)$

Find the exact value of the function. Rationalize the denominator if necessary. -cos (-630°)

Find the angle of smallest possible positive measure coterminal with the given angle. --40°

$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$ -sec ϴis undefined

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Exam 14: Trigonometry Formerly

Use the fundamental identities to find the value of the trigonometric function. - csc⁡θ\csc \thetacscθ , if cot⁡θ=−710\cot \theta = - \frac { 7 } { 10 }cotθ=−107​ , with θ\thetaθ in quadrant II

Suppose that the point (x, y)is in the indicated quadrant. Decide whether the given ratio is positive or negative. - IV⁡,xy\operatorname { IV } , \frac { x } { y }IV,yx​

Use a calculator to find the function value to four decimal places. -csc 30°9'

Find the exact function value if it exists. -cos (-180°)

Use a calculator to find the function value to four decimal places. -cot 58.9°

Solve the right triangle. -a = 3.3 cm, b = 3.0 cm, C = 90°

Complement of 36°

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

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - tan⁡θ\tan \thetatanθ , if cot⁡θ=73\cot \theta = \frac { \sqrt { 7 } } { 3 }cotθ=37​​

Give an expression that generates all angles coterminal with the given angle. Let n represent any integer. --285°

Find the exact values of the indicated trigonometric functions. Write fractions in lowest terms. - Find sec⁡A\sec \mathrm { A }secA and csc⁡A\csc \mathrm { A }cscA .

Without using a calculator, give the exact trigonometric function value with rational denominator. -cos 60°

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

State in which quadrant the terminal side of the given angle lies. -98°

sin⁡(1140∘)\sin \left( 1140 ^ { \circ } \right)sin(1140∘)

Find the exact value of the function. Rationalize the denominator if necessary. -cos (-630°)

Find the angle of smallest possible positive measure coterminal with the given angle. --40°

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

Use the fundamental identities to find the value of the trigonometric function. - $\csc \theta$ , if $\cot \theta = - \frac { 7 } { 10 }$ , with $\theta$ in quadrant II

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

Use the appropriate reciprocal identity to find the function value. Rationalize the denominator if necessary. - $\tan \theta$ , if $\cot \theta = \frac { \sqrt { 7 } } { 3 }$

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

$\sin \left( 1140 ^ { \circ } \right)$