Question 1

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

Accepted Answer

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

Question 2

Find all real numbers in the interval   that satisfy the equation.
-  + 2 cos x + 1 = 0

Accepted Answer

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

Question 3

Choose the expression which is equivalent to the given expression.
-

Accepted Answer

A)  cos 32° 
B)  tan 32° 
C)  cot 8° 
D)  tan 8° 
A)  cos 32° 
B)  tan 32° 
C)  cot 8° 
D)  tan 8°

Question 4

Simplify the expression by using a sum or difference identity.
-sin(18°) cos (-4°) - cos(18°) sin (-4°)

Accepted Answer

A)  cos 22° 
B)  sin 22° 
C)  cos 14° 
D)  sin 14° 
A)  cos 22° 
B)  sin 22° 
C)  cos 14° 
D)  sin 14°

Question 5

Find all angles in [0°, 360°) that satisfy the equation.
-2 sin

Accepted Answer

A)  30°, 150°, 210°, 330° 
B)  60°, 120°, 240°, 300° 
C)  30°, 60°, 210°, 240° 
D)  60°, 150°, 240°, 300° 
A)  30°, 150°, 210°, 330° 
B)  60°, 120°, 240°, 300° 
C)  30°, 60°, 210°, 240° 
D)  60°, 150°, 240°, 300°

Question 6

Use trigonometric identities to find the exact value.
-

Accepted Answer

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

Question 7

Show that the equation is not an identity by listing the value(s) of the variable from among   for which
the equation is false.
-

Accepted Answer

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

Question 8

Multiply and simplify.
-(sin x - cos x)(sec x + csc x)

Accepted Answer

A)  tan x - sin x 
B)  tan x - cot x 
C)  cot x + csc x 
D)  cos x - cot x 
A)  tan x - sin x 
B)  tan x - cot x 
C)  cot x + csc x 
D)  cos x - cot x

Question 9

Choose the expression which is equivalent to the given expression.
-

Accepted Answer

A)  tan 38° 
B)    
C)    
D)  sin 38° 
A)  tan 38° 
B)    
C)    
D)  sin 38°

Question 10

Find the exact value of the sum.
-sin   - sin

Accepted Answer

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

Question 11

Simplify the expression by using a sum or difference identity.
-sin (10°) cos (110°) + cos (10°) sin (110°)

Accepted Answer

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

Question 12

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

Accepted Answer

A)  {225°, 315°} 
B)  {45°, 315°} 
C)  {45°, 225°} 
D)  {135°, 225°} 
A)  {225°, 315°} 
B)  {45°, 315°} 
C)  {45°, 225°} 
D)  {135°, 225°}

Question 13

For the following equation, graph   on the same screen on your calculator. From the graphs, make
a conjecture as to whether the equation is an identity. If so, prove your conjecture.
-tan x + cot x = 2 csc 2x

Accepted Answer

The statement is an

Question 14

Use a sum-to-product identity to rewrite the expression.
-cos 22° - cos 50°

Accepted Answer

A)  2 sin 36° sin 14° 
B)  -2 sin 36° sin 14° 
C)  -2 cos 36° cos 14° 
D)  2 sin 36° cos 14° 
A)  2 sin 36° sin 14° 
B)  -2 sin 36° sin 14° 
C)  -2 cos 36° cos 14° 
D)  2 sin 36° cos 14°

Question 15

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a
degree.
-

Accepted Answer

A)  {20°, 140°, 260°} 
B)  {20°, 80°, 140°, 200°, 260°, 320°} 
C)  {10°, 70°, 130°, 190°, 250°, 310°} 
D)  {10°, 130°, 250°} 
A)  {20°, 140°, 260°} 
B)  {20°, 80°, 140°, 200°, 260°, 320°} 
C)  {10°, 70°, 130°, 190°, 250°, 310°} 
D)  {10°, 130°, 250°}

Question 16

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

Accepted Answer

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

Question 17

Simplify the expression by using a sum or difference identity.
-

Accepted Answer

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

Question 18

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

Accepted Answer

A)  37.5°, 127.5°, 217.5°, 307.5° 
B)  37.5°, 52.5°, 127.5°, 142.5°, 217.5°, 232.5°, 307.5°, 322.5° 
C)  30°, 60°, 120°, 150°, 210°, 240°, 300°, 330° 
D)  30°, 120°, 210°, 300° 
A)  37.5°, 127.5°, 217.5°, 307.5° 
B)  37.5°, 52.5°, 127.5°, 142.5°, 217.5°, 232.5°, 307.5°, 322.5° 
C)  30°, 60°, 120°, 150°, 210°, 240°, 300°, 330° 
D)  30°, 120°, 210°, 300°

Question 19

Factor the trigonometric expression.
-

Accepted Answer

A)    
B)  (cot x - csc x)(cot x + csc x) 
C)    
D)    
A)    
B)  (cot x - csc x)(cot x + csc x) 
C)    
D)

Question 20

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-Why is it not possible to find a formula for tan (

Accepted Answer

The range

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

Find all real numbers in the interval that satisfy the equation. - + 2 cos x + 1 = 0

Choose the expression which is equivalent to the given expression. -

Simplify the expression by using a sum or difference identity. -sin(18°) cos (-4°) - cos(18°) sin (-4°)

Find all angles in [0°, 360°) that satisfy the equation. -2 sin

Use trigonometric identities to find the exact value. -

Show that the equation is not an identity by listing the value(s) of the variable from among for which the equation is false. -

Multiply and simplify. -(sin x - cos x)(sec x + csc x)

Choose the expression which is equivalent to the given expression. -

Find the exact value of the sum. -sin - sin

Simplify the expression by using a sum or difference identity. -sin (10°) cos (110°) + cos (10°) sin (110°)

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

For the following equation, graph on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -tan x + cot x = 2 csc 2x

Use a sum-to-product identity to rewrite the expression. -cos 22° - cos 50°

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. -

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

Simplify the expression by using a sum or difference identity. -

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

Factor the trigonometric expression. -

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Why is it not possible to find a formula for tan (

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Exam 6: Trigonometric Identities and Conditional Equations

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

Find all real numbers in the interval that satisfy the equation. - + 2 cos x + 1 = 0

Choose the expression which is equivalent to the given expression. -

Simplify the expression by using a sum or difference identity. -sin(18°) cos (-4°) - cos(18°) sin (-4°)

Find all angles in [0°, 360°) that satisfy the equation. -2 sin

Use trigonometric identities to find the exact value. -

Show that the equation is not an identity by listing the value(s) of the variable from among for which the equation is false. -

Multiply and simplify. -(sin x - cos x)(sec x + csc x)

Choose the expression which is equivalent to the given expression. -

Find the exact value of the sum. -sin - sin

Simplify the expression by using a sum or difference identity. -sin (10°) cos (110°) + cos (10°) sin (110°)

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

For the following equation, graph on the same screen on your calculator. From the graphs, make a conjecture as to whether the equation is an identity. If so, prove your conjecture. -tan x + cot x = 2 csc 2x

Use a sum-to-product identity to rewrite the expression. -cos 22° - cos 50°

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. -

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

Simplify the expression by using a sum or difference identity. -

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

Factor the trigonometric expression. -

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -Why is it not possible to find a formula for tan (

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