Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Find the exact value of the sum.
-cos 105° - cos 15°

Accepted Answer

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

Question 4

Find the exact value, given that sin A = -4/5 with A in quadrant IV, tan B = 7/24 with B in quadrant III, and cos C = - 5/13
with C in quadrant II.
-tan 2A

Accepted Answer

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

Question 5

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 6

Prove that the equation is an identity.
-

Accepted Answer

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

Question 7

Prove that the equation is an identity.
-

Accepted Answer

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

Question 8

Find the exact value using a double-angle identity.
-tan(120°)

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Use a sum-to-product identity to rewrite the expression.
-cos   + cos

Accepted Answer

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

Question 11

Use a product-to-sum identity to rewrite the expression.
-sin 41° cos 28°

Accepted Answer

A)  0.5(cos(13°) - cos(69°)) 
B)  0.5(cos(69°) + cos(13°)) 
C)  0.5(sin(13°) - sin(69°)) 
D)  0.5(sin(69°) + sin(13°)) 
A)  0.5(cos(13°) - cos(69°)) 
B)  0.5(cos(69°) + cos(13°)) 
C)  0.5(sin(13°) - sin(69°)) 
D)  0.5(sin(69°) + sin(13°))

Question 12

Prove that the equation is an identity.
-tan x csc x -   cos x = 0

Accepted Answer

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

Question 13

Find all real numbers in the interval   that satisfy the equation.
-  + 3 sin x = 2 Round any approximations to the nearest tenth of a radian.

Accepted Answer

A)  0.3, 2.4, 2.8, 3.9 
B)  0.3, 2.4, 3.5, 5.9 
C)  0.3, 2.8, 3.9, 5.6 
D)  0.3, 3.5, 3.9, 5.6 
A)  0.3, 2.4, 2.8, 3.9 
B)  0.3, 2.4, 3.5, 5.9 
C)  0.3, 2.8, 3.9, 5.6 
D)  0.3, 3.5, 3.9, 5.6

Question 14

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

Accepted Answer

A)  cos 26° 
B)  tan 26° 
C)  cot 26° 
D)  sin 26° 
A)  cos 26° 
B)  tan 26° 
C)  cot 26° 
D)  sin 26°

Question 15

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

Accepted Answer

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

Question 16

Simplify the expression by using a sum or difference identity.
-sin 16° cos 29° + cos 16° sin 29°

Accepted Answer

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

Question 17

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a
degree.
-  - 8 sin x - 4 = 0

Accepted Answer

A)  {208.2°, 331.8°} 
B)  {28.2°, 151.8°, 208.2°, 331.8°} 
C)  {28.2°, 151.8°} 
D)  No solution 
A)  {208.2°, 331.8°} 
B)  {28.2°, 151.8°, 208.2°, 331.8°} 
C)  {28.2°, 151.8°} 
D)  No solution

Question 18

Use identities to simplify the expression.
-

Accepted Answer

A)  - cot x 
B)  tan x 
C)    
D)  cot x 
A)  - cot x 
B)  tan x 
C)    
D)  cot x

Question 19

Simplify the expression.
-

Accepted Answer

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

Question 20

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

Accepted Answer

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

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

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

Find the exact value of the sum. -cos 105° - cos 15°

Find the exact value, given that sin A = -4/5 with A in quadrant IV, tan B = 7/24 with B in quadrant III, and cos C = - 5/13 with C in quadrant II. -tan 2A

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

Prove that the equation is an identity. -

Prove that the equation is an identity. -

Find the exact value using a double-angle identity. -tan(120°)

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

Use a sum-to-product identity to rewrite the expression. -cos + cos

Use a product-to-sum identity to rewrite the expression. -sin 41° cos 28°

Prove that the equation is an identity. -tan x csc x - cos x = 0

Find all real numbers in the interval that satisfy the equation. - + 3 sin x = 2 Round any approximations to the nearest tenth of a radian.

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

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

Simplify the expression by using a sum or difference identity. -sin 16° cos 29° + cos 16° sin 29°

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. - - 8 sin x - 4 = 0

Use identities to simplify the expression. -

Simplify the expression. -

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

Equations, Inequalities, and Modeling

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Exam 6: Trigonometric Identities and Conditional Equations

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

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

Find the exact value of the sum. -cos 105° - cos 15°

Find the exact value, given that sin A = -4/5 with A in quadrant IV, tan B = 7/24 with B in quadrant III, and cos C = - 5/13 with C in quadrant II. -tan 2A

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

Prove that the equation is an identity. -

Prove that the equation is an identity. -

Find the exact value using a double-angle identity. -tan(120°)

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

Use a sum-to-product identity to rewrite the expression. -cos + cos

Use a product-to-sum identity to rewrite the expression. -sin 41° cos 28°

Prove that the equation is an identity. -tan x csc x - cos x = 0

Find all real numbers in the interval that satisfy the equation. - + 3 sin x = 2 Round any approximations to the nearest tenth of a radian.

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

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

Simplify the expression by using a sum or difference identity. -sin 16° cos 29° + cos 16° sin 29°

Find all values of x in the interval [0°, 360°) that satisfy the equation. Round approximate answers to the nearest tenth of a degree. - - 8 sin x - 4 = 0

Use identities to simplify the expression. -

Simplify the expression. -

Choose the expression which is equivalent to the given 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