Question 1

Factor the trigonometric expression.
-

Accepted Answer

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

Question 2

Use an identity to find the exact value of the expression.
-sin 135° - 30°

Accepted Answer

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

Question 3

Solve the problem. Round to the nearest whole unit.
-A 25-inch tall picture hangs on a wall so that its lower edge is 27 inches higher than the eyes of an observer. How far from the wall must the observer stand in order to make the angle subtended by the picture equal to 1/3
Of the angle of elevation of the top?

Accepted Answer

A)  30 in. 
B)  42 in. 
C)  36 in. 
D)  24 in. 
A)  30 in. 
B)  42 in. 
C)  36 in. 
D)  24 in.

Question 4

Find the exact value using a double-angle identity.
-tan(480°)

Accepted Answer

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

Question 5

Use an appropriate identity to find the exact value of the expression.
-cos (-105°)

Accepted Answer

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

Question 6

Find the exact value by using a half-angle identity.
-tan 165°

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Find all angles in degrees that satisfy the equation.
-sin x = -1

Accepted Answer

Question 10

Solve the problem.
-It can be shown that if the angle of elevation from an observer to the top of an object is A and the angle of elevation d ft closer is B, then the height of the object is given by   Find A if h = 50 ft, d = 80 ft, and B = 22°. Give your answer in degrees to the nearest hundredth.

Accepted Answer

A)  18.96° 
B)  13.79° 
C)  16.41° 
D)  11.11° 
A)  18.96° 
B)  13.79° 
C)  16.41° 
D)  11.11°

Question 11

Prove the identity.
-2 cot 2x cos x = csc x - 2 sin x

Accepted Answer

The answer of Prove the identity.
-2 cot 2x cos x...

Question 12

Simplify the expression by using a sum or difference identity.
-sin (95°) cos (35°) - cos (95°) sin (35°)

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

Identify the equation as either an identity or not.
-  = 2 sin 2x

Accepted Answer

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

Question 15

Write the expression in terms of sines and/or cosines, and then simplify.
-(tan x csc x + 1)(sec x - 1)

Accepted Answer

A)  tan x + sec x - sin x - 1 
B)  sec x - cos x 
C)    
D)    
A)  tan x + sec x - sin x - 1 
B)  sec x - cos x 
C)    
D)

Question 16

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

Accepted Answer

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

Question 17

Use identities to simplify the expression.
-cot x sec x sin x

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Find the exact value by using a half-angle identity.
-tan 15°

Accepted Answer

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

Factor the trigonometric expression. -

Use an identity to find the exact value of the expression. -sin 135° - 30°

Find the exact value using a double-angle identity. -tan(480°)

Use an appropriate identity to find the exact value of the expression. -cos (-105°)

Find the exact value by using a half-angle identity. -tan 165°

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

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

Find all angles in degrees that satisfy the equation. -sin x = -1

Solve the problem. -It can be shown that if the angle of elevation from an observer to the top of an object is A and the angle of elevation d ft closer is B, then the height of the object is given by Find A if h = 50 ft, d = 80 ft, and B = 22°. Give your answer in degrees to the nearest hundredth.

Prove the identity. -2 cot 2x cos x = csc x - 2 sin x

Simplify the expression by using a sum or difference identity. -sin (95°) cos (35°) - cos (95°) sin (35°)

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

Identify the equation as either an identity or not. - = 2 sin 2x

Write the expression in terms of sines and/or cosines, and then simplify. -(tan x csc x + 1)(sec x - 1)

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

Use identities to simplify the expression. -cot x sec x sin x

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

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

Find the exact value by using a half-angle identity. -tan 15°

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Exam 6: Trigonometric Identities and Conditional Equations

Factor the trigonometric expression. -

Use an identity to find the exact value of the expression. -sin 135° - 30°

Find the exact value using a double-angle identity. -tan(480°)

Use an appropriate identity to find the exact value of the expression. -cos (-105°)

Find the exact value by using a half-angle identity. -tan 165°

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

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

Find all angles in degrees that satisfy the equation. -sin x = -1

Solve the problem. -It can be shown that if the angle of elevation from an observer to the top of an object is A and the angle of elevation d ft closer is B, then the height of the object is given by Find A if h = 50 ft, d = 80 ft, and B = 22°. Give your answer in degrees to the nearest hundredth.

Prove the identity. -2 cot 2x cos x = csc x - 2 sin x

Simplify the expression by using a sum or difference identity. -sin (95°) cos (35°) - cos (95°) sin (35°)

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

Identify the equation as either an identity or not. - = 2 sin 2x

Write the expression in terms of sines and/or cosines, and then simplify. -(tan x csc x + 1)(sec x - 1)

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

Use identities to simplify the expression. -cot x sec x sin x

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

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

Find the exact value by using a half-angle identity. -tan 15°

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