Question 1

Write the expression in terms of sines and/or cosines, and then simplify.
-

Accepted Answer

A)  sin x + csc x 
B)  csc x 
C)  sec x + sin x 
D)  cos x 
A)  sin x + csc x 
B)  csc x 
C)  sec x + sin x 
D)  cos x

Question 2

Choose the equivalent expression for the given expression.
-

Accepted Answer

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

Question 3

Identify the equation as either an identity or not.
-

Accepted Answer

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

Question 4

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift.
-y = -   sin x   cos x

Accepted Answer

A)  Amplitude 3, period   , phase shift     
B)  Amplitude 6, period   , phase shift -     
C)  Amplitude 6, period   , phase shift     
D)  Amplitude 6, period   phase shift     
A)  Amplitude 3, period   , phase shift     
B)  Amplitude 6, period   , phase shift -     
C)  Amplitude 6, period   , phase shift     
D)  Amplitude 6, period   phase shift

Question 5

Use a sum or difference identity to find the exact value.
-sin (285°)

Accepted Answer

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

Question 6

Find all real numbers in the interval   that satisfy the equation.
-tan x = 3 cot x

Accepted Answer

A)    
B)  No solution 
C)    
D)    
A)    
B)  No solution 
C)    
D)

Question 7

Find all real numbers in the interval   that satisfy the equation.
-  = 0

Accepted Answer

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

Question 8

Use an identity to write the expression as a single trigonometric function or as a single number.
-±

Accepted Answer

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

Question 9

Solve the equation.
-

Accepted Answer

A)  43.4 
B)  27.2 
C)  21.9 
D)  46.7 
A)  43.4 
B)  27.2 
C)  21.9 
D)  46.7

Question 10

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 11

Prove that the equation is an identity.
-

Accepted Answer

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

Question 12

Use a product-to-sum identity to rewrite the expression.
-cos 43° cos 20°

Accepted Answer

A)  0.5(sin (23°) + sin(63°)) 
B)  0.5(sin(63°) - sin (23°)) 
C)  0.5(cos (23°) + cos(63°)) 
D)  0.5(cos (23°) - cos(63°)) 
A)  0.5(sin (23°) + sin(63°)) 
B)  0.5(sin(63°) - sin (23°)) 
C)  0.5(cos (23°) + cos(63°)) 
D)  0.5(cos (23°) - cos(63°))

Question 13

Use the appropriate sum or difference identity to write the given expression as a function of x alone.
-cos

Accepted Answer

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

Question 14

Use an appropriate identity to find the exact value of the expression.
-cos (255°)

Accepted Answer

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

Question 15

Write the expression in terms of sines and/or cosines, and then simplify.
-cos x + tan x sin x

Accepted Answer

A)  csc x 
B)  sec x 
C)    
D)  sin x + cos x 
A)  csc x 
B)  sec x 
C)    
D)  sin x + cos x

Question 16

Find all real numbers in the interval   that satisfy the equation.
-4   = 4 cos x + 1

Accepted Answer

A)    
B)  No solution 
C)    
D)    
A)    
B)  No solution 
C)    
D)

Question 17

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

Accepted Answer

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

Question 18

Write in terms of the cofunction of a complementary angle.
-sin 73°

Accepted Answer

A)  cos 107° 
B)  csc 17° 
C)  cos 17° 
D)  csc 107° 
A)  cos 107° 
B)  csc 17° 
C)  cos 17° 
D)  csc 107°

Question 19

Prove that the equation is an identity.
-

Accepted Answer

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

Question 20

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

Accepted Answer

A)  {15°, 165°, 195°, 345°} 
B)  {105°, 165°, 285°, 345°} 
C)  {30°, 90°, 150°, 270°} 
D)  {0°, 120°, 180°, 240°} 
A)  {15°, 165°, 195°, 345°} 
B)  {105°, 165°, 285°, 345°} 
C)  {30°, 90°, 150°, 270°} 
D)  {0°, 120°, 180°, 240°}

Write the expression in terms of sines and/or cosines, and then simplify. -

Choose the equivalent expression for the given expression. -

Identify the equation as either an identity or not. -

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift. -y = - sin x cos x

Use a sum or difference identity to find the exact value. -sin (285°)

Find all real numbers in the interval that satisfy the equation. -tan x = 3 cot x

Find all real numbers in the interval that satisfy the equation. - = 0

Use an identity to write the expression as a single trigonometric function or as a single number. -±

Solve the equation. -

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.

Prove that the equation is an identity. -

Use a product-to-sum identity to rewrite the expression. -cos 43° cos 20°

Use the appropriate sum or difference identity to write the given expression as a function of x alone. -cos

Use an appropriate identity to find the exact value of the expression. -cos (255°)

Write the expression in terms of sines and/or cosines, and then simplify. -cos x + tan x sin x

Find all real numbers in the interval that satisfy the equation. -4 = 4 cos x + 1

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

Write in terms of the cofunction of a complementary angle. -sin 73°

Prove that the equation is an identity. -

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

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Exam 6: Trigonometric Identities and Conditional Equations

Write the expression in terms of sines and/or cosines, and then simplify. -

Choose the equivalent expression for the given expression. -

Identify the equation as either an identity or not. -

Graph the function by first writing it in the form y = A sin(x + C). State the amplitude, period, and phase shift. -y = - sin x cos x

Use a sum or difference identity to find the exact value. -sin (285°)

Find all real numbers in the interval that satisfy the equation. -tan x = 3 cot x

Find all real numbers in the interval that satisfy the equation. - = 0

Use an identity to write the expression as a single trigonometric function or as a single number. -±

Solve the equation. -

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.

Prove that the equation is an identity. -

Use a product-to-sum identity to rewrite the expression. -cos 43° cos 20°

Use the appropriate sum or difference identity to write the given expression as a function of x alone. -cos

Use an appropriate identity to find the exact value of the expression. -cos (255°)

Write the expression in terms of sines and/or cosines, and then simplify. -cos x + tan x sin x

Find all real numbers in the interval that satisfy the equation. -4 = 4 cos x + 1

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

Write in terms of the cofunction of a complementary angle. -sin 73°

Prove that the equation is an identity. -

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

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