Question 1

Identify the equation as either an identity or not.
-tan   = tan A

Accepted Answer

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

Question 2

Use an identity to find the exact value of the expression.
-tan 135° + 150°

Accepted Answer

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

Question 3

Solve the problem.
-A generator produces an alternating current according to the equation I = 16 sin   where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 8?

Accepted Answer

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

Question 4

Prove that the equation is an identity.
-

Accepted Answer

The answer of Prove that the equation is an identity.
-...

Question 5

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 6

Simplify the expression by using a sum or difference identity.
-cos(13°) cos (-3°) - sin(13°) sin (-3°)

Accepted Answer

A)  sin 16° 
B)  cos 10° 
C)  sin 10° 
D)  cos 16° 
A)  sin 16° 
B)  cos 10° 
C)  sin 10° 
D)  cos 16°

Question 7

Use identities to find the exact value of the trigonometric function.
-Find cos   if tan   .

Accepted Answer

A)    
B)  -37 
C)    
D)    
A)    
B)  -37 
C)    
D)

Question 8

Solve the equation.
-

Accepted Answer

A)  142.4° 
B)  179.2° 
C)  3.6° 
D)  145.4° 
A)  142.4° 
B)  179.2° 
C)  3.6° 
D)  145.4°

Question 9

Use a half-angle identity to find an exact value for the following, given the information about x.
-Find sin   , given that sin x = -   and 270° < x <360°.

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Find all real numbers that satisfy the equation.
-sin x = -

Accepted Answer

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

Question 12

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

Accepted Answer

A)  tan 36° 
B)  tan 9° 
C)    
D)    
A)  tan 36° 
B)  tan 9° 
C)    
D)

Question 13

Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
-A student claims that the equation tan   is an identity, since by letting   = 0° we get 0 + 1 = 1, a true
statement. Comment on this student's reasoning.

Accepted Answer

For the equation to be an iden

Question 14

Write in terms of the cofunction of a complementary angle.
-

Accepted Answer

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

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)  {30°, 90°, 150°, 210°, 270°, 330°} 
B)  {30°, 90°, 150°} 
C)  {0°, 30°, 150°, 180°, 210°, 330°} 
D)  {60°, 90°, 120°, 240°, 270°, 300°} 
A)  {30°, 90°, 150°, 210°, 270°, 330°} 
B)  {30°, 90°, 150°} 
C)  {0°, 30°, 150°, 180°, 210°, 330°} 
D)  {60°, 90°, 120°, 240°, 270°, 300°}

Question 16

Decide whether the expression is or is not an identity.
-

Accepted Answer

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

Question 17

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

Accepted Answer

A)  {33°, 57°, 147°, 237°, 327°} 
B)  {0°, 45°, 90°, 135°, 180°, 225°, 270°} 
C)  {0°, 90°, 180°, 270°} 
D)  {0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°} 
A)  {33°, 57°, 147°, 237°, 327°} 
B)  {0°, 45°, 90°, 135°, 180°, 225°, 270°} 
C)  {0°, 90°, 180°, 270°} 
D)  {0°, 45°, 90°, 135°, 180°, 225°, 270°, 315°}

Question 18

Use a half-angle identity to find an exact value for the following, given the information about x.
-Find tan   given that cos   and x terminates in 180° < x < 270°.

Accepted Answer

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

Question 19

Identify the equation as either an identity or not.
-tan   = -tan A

Accepted Answer

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

Question 20

Find the exact value by using a half-angle identity.
-tan

Accepted Answer

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

Identify the equation as either an identity or not. -tan = tan A

Use an identity to find the exact value of the expression. -tan 135° + 150°

Solve the problem. -A generator produces an alternating current according to the equation I = 16 sin where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 8?

Prove that the equation is an identity. -

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

Simplify the expression by using a sum or difference identity. -cos(13°) cos (-3°) - sin(13°) sin (-3°)

Use identities to find the exact value of the trigonometric function. -Find cos if tan .

Solve the equation. -

Use a half-angle identity to find an exact value for the following, given the information about x. -Find sin , given that sin x = - and 270° < x <360°.

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

Find all real numbers that satisfy the equation. -sin x = -

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

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -A student claims that the equation tan is an identity, since by letting = 0° we get 0 + 1 = 1, a true statement. Comment on this student's reasoning.

Write in terms of the cofunction of a complementary angle. -

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

Decide whether the expression is or is not an identity. -

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

Use a half-angle identity to find an exact value for the following, given the information about x. -Find tan given that cos and x terminates in 180° < x < 270°.

Identify the equation as either an identity or not. -tan = -tan A

Find the exact value by using a half-angle identity. -tan

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Exam 6: Trigonometric Identities and Conditional Equations

Identify the equation as either an identity or not. -tan = tan A

Use an identity to find the exact value of the expression. -tan 135° + 150°

Solve the problem. -A generator produces an alternating current according to the equation I = 16 sin where t is time in seconds and I is the current in amperes. What is the smallest time t such that I = 8?

Prove that the equation is an identity. -

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

Simplify the expression by using a sum or difference identity. -cos(13°) cos (-3°) - sin(13°) sin (-3°)

Use identities to find the exact value of the trigonometric function. -Find cos if tan .

Solve the equation. -

Use a half-angle identity to find an exact value for the following, given the information about x. -Find sin , given that sin x = - and 270° < x <360°.

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

Find all real numbers that satisfy the equation. -sin x = -

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

Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. -A student claims that the equation tan is an identity, since by letting = 0° we get 0 + 1 = 1, a true statement. Comment on this student's reasoning.

Write in terms of the cofunction of a complementary angle. -

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

Decide whether the expression is or is not an identity. -

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

Use a half-angle identity to find an exact value for the following, given the information about x. -Find tan given that cos and x terminates in 180° < x < 270°.

Identify the equation as either an identity or not. -tan = -tan A

Find the exact value by using a half-angle identity. -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