Question 1

Use a sum-to-product identity to rewrite the expression.
-sin (11t + 8) + sin (2t - 4)

Accepted Answer

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

Question 2

Find the exact value using a double-angle identity.
-sin

Accepted Answer

A)    
B)    
C)    
D)  0 
A)    
B)    
C)    
D)  0

Question 3

Identify the equation as either an identity or not.
-

Accepted Answer

A)  Not an identity 
B)  Identity 
A)  Not an identity 
B)  Identity

Question 4

Use an appropriate identity to find the exact value of the expression.
-

Accepted Answer

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

Question 5

Use identities to simplify the expression.
-

Accepted Answer

A)  0 
B)    
C)    
D)  1 
A)  0 
B)    
C)    
D)  1

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-How does the graph of y = cos (-x) compare to that of y = cos x?

Accepted Answer

It is the

Question 7

Find all angles in [0°, 360°) that satisfy the equation.
-csc

Accepted Answer

A)  15°, 105°, 135°, 225°, 255°, 345° 
B)  15°, 45°, 135°, 165°, 255°, 285° 
C)  15°, 135°, 255° 
D)  37.5°, 127.5°, 217.5°, 307.5° 
A)  15°, 105°, 135°, 225°, 255°, 345° 
B)  15°, 45°, 135°, 165°, 255°, 285° 
C)  15°, 135°, 255° 
D)  37.5°, 127.5°, 217.5°, 307.5°

Question 8

Find the exact value of the expression using the provided information.
-Find sin(B - C)   , with B in quadrant IV, and sin   , with C in quadrant II.

Accepted Answer

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

Question 9

Prove the identity.
-

Accepted Answer

The answer of Prove the identity.
- ...

Question 10

Find the exact value of the sum.
-sin 75° - sin 15°

Accepted Answer

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

Question 11

Prove the identity.
-

Accepted Answer

The answer of Prove the identity.
- ...

Question 12

Identify the equation as either an identity or not.
-

Accepted Answer

A)  Not an identity 
B)  Identity 
A)  Not an identity 
B)  Identity

Question 13

Find the exact value by using a sum or difference identity.
-tan

Accepted Answer

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

Question 14

Simplify the expression by using a sum or difference identity.
-cos (13°) cos(87°) + cos(-77°) sin(-87°)

Accepted Answer

A)  cos 100° 
B)  1 
C)  0 
D)  sin 100° 
A)  cos 100° 
B)  1 
C)  0 
D)  sin 100°

Question 15

Write in terms of the cofunction of a complementary angle.
-tan (90° - 19°)

Accepted Answer

A)  cot 19° 
B)  cos 71° 
C)  sin 19° 
D)  cot 71° 
A)  cot 19° 
B)  cos 71° 
C)  sin 19° 
D)  cot 71°

Question 16

Use an appropriate identity to find the exact value of the expression.
-cos (75°)

Accepted Answer

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

Question 17

Find the exact value using a double-angle identity.
-tan

Accepted Answer

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

Question 18

Use odd and even identities to simplify the expression.
-cos (-x) cos x - sin (-x) sin x

Accepted Answer

A)  2 
B)    
C)  1 
D)    
A)  2 
B)    
C)  1 
D)

Question 19

Solve the problem.
-A block hanging from a spring is free to oscillate. If a 1-kg block attached to the spring is given an upward velocity of 0.4 m/sec from a point 0.2 m above its resting position, then at any time t in seconds its position in
Meters is given by x = -0.4 sin t - 0.2 cos t. Find the maximum distance that the block travels from its resting
Position.

Accepted Answer

A)  0.4 m 
B)    
C)  0.2 m 
D)    
A)  0.4 m 
B)    
C)  0.2 m 
D)

Question 20

Simplify the expression.
-

Accepted Answer

A)  sin x - 1 
B)  sin x 
C)  - sin x 
D)  1 - sin x 
A)  sin x - 1 
B)  sin x 
C)  - sin x 
D)  1 - sin x

Use a sum-to-product identity to rewrite the expression. -sin (11t + 8) + sin (2t - 4)

Find the exact value using a double-angle identity. -sin

Identify the equation as either an identity or not. -

Use an appropriate identity to find the exact value of the expression. -

Use identities to simplify the expression. -

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -How does the graph of y = cos (-x) compare to that of y = cos x?

Find all angles in [0°, 360°) that satisfy the equation. -csc

Find the exact value of the expression using the provided information. -Find sin(B - C) , with B in quadrant IV, and sin , with C in quadrant II.

Prove the identity. -

Find the exact value of the sum. -sin 75° - sin 15°

Prove the identity. -

Identify the equation as either an identity or not. -

Find the exact value by using a sum or difference identity. -tan

Simplify the expression by using a sum or difference identity. -cos (13°) cos(87°) + cos(-77°) sin(-87°)

Write in terms of the cofunction of a complementary angle. -tan (90° - 19°)

Use an appropriate identity to find the exact value of the expression. -cos (75°)

Find the exact value using a double-angle identity. -tan

Use odd and even identities to simplify the expression. -cos (-x) cos x - sin (-x) sin x

Simplify the expression. -

Equations, Inequalities, and Modeling

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Exam 6: Trigonometric Identities and Conditional Equations

Use a sum-to-product identity to rewrite the expression. -sin (11t + 8) + sin (2t - 4)

Find the exact value using a double-angle identity. -sin

Identify the equation as either an identity or not. -

Use an appropriate identity to find the exact value of the expression. -

Use identities to simplify the expression. -

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -How does the graph of y = cos (-x) compare to that of y = cos x?

Find all angles in [0°, 360°) that satisfy the equation. -csc

Find the exact value of the expression using the provided information. -Find sin(B - C) , with B in quadrant IV, and sin , with C in quadrant II.

Prove the identity. -

Find the exact value of the sum. -sin 75° - sin 15°

Prove the identity. -

Identify the equation as either an identity or not. -

Find the exact value by using a sum or difference identity. -tan

Simplify the expression by using a sum or difference identity. -cos (13°) cos(87°) + cos(-77°) sin(-87°)

Write in terms of the cofunction of a complementary angle. -tan (90° - 19°)

Use an appropriate identity to find the exact value of the expression. -cos (75°)

Find the exact value using a double-angle identity. -tan

Use odd and even identities to simplify the expression. -cos (-x) cos x - sin (-x) sin x

Simplify the expression. -

Equations, Inequalities, and Modeling

Functions and Graphs

Polynomial and Rational Functions

Exponential and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

The Conic Sections

Sequences, Series, and Probability

Basic Algebra Review

Filters