Question 1

Use odd and even identities to simplify the expression.
-

Accepted Answer

A)  0 
B)  -2 csc x 
C)  -2 sin x 
D)  2 csc x 
A)  0 
B)  -2 csc x 
C)  -2 sin x 
D)  2 csc x

Question 2

Factor the trigonometric expression.
-

Accepted Answer

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

Question 3

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

Accepted Answer

A)  tan 16° 
B)  cos 16° 
C)  sin 4° 
D)  tan 4° 
A)  tan 16° 
B)  cos 16° 
C)  sin 4° 
D)  tan 4°

Question 4

Write in terms of the cofunction of a complementary angle.
-csc (90° - 8°)

Accepted Answer

A)  sin 82° 
B)  sec 82° 
C)  sin 8° 
D)  sec 8° 
A)  sin 82° 
B)  sec 82° 
C)  sin 8° 
D)  sec 8°

Question 5

Prove that the equation is an identity.
-tan x + cot x = sec x csc x

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Solve the problem.
-A block hanging from a spring is free to oscillate. If a 1-kg block attached to the spring is given an upward velocity of 0.7 m/sec from a point 0.8 m below its resting position, then at any time t in seconds its position in
Meters is given by x = -0.7 sin t + 0.8 cos t. Find the maximum distance that the block travels from its resting
Position.

Accepted Answer

A)  1.13 m 
B)  2.26 m 
C)    
D)    
A)  1.13 m 
B)  2.26 m 
C)    
D)

Question 8

Solve the problem.
-A block hanging from a spring is free to oscillate. If a 1-kg block attached to the spring is given a downward velocity of 0.8 m/sec from a point 0.7 m below its resting position, then at any time t in seconds its position in
Meters is given by x = 0.8 sin t + 0.7 cos t. Find the maximum distance that the block travels from its resting
Position.

Accepted Answer

A)    
B)  1.13 m 
C)  2.26 m 
D)    
A)    
B)  1.13 m 
C)  2.26 m 
D)

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Factor the trigonometric expression.
-16   - 8 sec y + 1

Accepted Answer

A)    
B)  (4 sec y - 1)(4 sec y + 1) 
C)    
D)    
A)    
B)  (4 sec y - 1)(4 sec y + 1) 
C)    
D)

Question 12

For the given function, determine the amplitude and find the phase shift.
-y = 15 sin x + 20 cos x Give the phase shift in radians rounded to the nearest thousandth.

Accepted Answer

A)  35, 0.644 
B)  25, 0.927 
C)  25, - 0.644 
D)  25, - 0.927 
A)  35, 0.644 
B)  25, 0.927 
C)  25, - 0.644 
D)  25, - 0.927

Question 13

Use a product-to-sum identity to rewrite the expression.
-cos(13k) cos (6k)

Accepted Answer

A)  0.5(cos(7k) - cos(19k)) 
B)  0.5(sin(7k) - sin(19k)) 
C)  0.5(cos(7k) + cos(19k)) 
D)  0.5(sin(7k) + sin(19k)) 
A)  0.5(cos(7k) - cos(19k)) 
B)  0.5(sin(7k) - sin(19k)) 
C)  0.5(cos(7k) + cos(19k)) 
D)  0.5(sin(7k) + sin(19k))

Question 14

Solve the equation.
-

Accepted Answer

A)  31.9° 
B)  29.9° 
C)  50.2 
D)  27.9° 
A)  31.9° 
B)  29.9° 
C)  50.2 
D)  27.9°

Question 15

Solve the equation.
-

Accepted Answer

A)  284.8 
B)  282.2 
C)  352.3 
D)  23.9 
A)  284.8 
B)  282.2 
C)  352.3 
D)  23.9

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Determine whether the function is odd, even, or neither.
-f(   ) = 1 +

Accepted Answer

A)  Odd 
B)  Neither 
C)  Even 
A)  Odd 
B)  Neither 
C)  Even

Question 20

Prove that the equation is an identity.
-

Accepted Answer

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

Use odd and even identities to simplify the expression. -

Factor the trigonometric expression. -

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

Write in terms of the cofunction of a complementary angle. -csc (90° - 8°)

Prove that the equation is an identity. -tan x + cot x = sec x csc x

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

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

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

Factor the trigonometric expression. -16 - 8 sec y + 1

For the given function, determine the amplitude and find the phase shift. -y = 15 sin x + 20 cos x Give the phase shift in radians rounded to the nearest thousandth.

Use a product-to-sum identity to rewrite the expression. -cos(13k) cos (6k)

Solve the equation. -

Solve the equation. -

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

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

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

Determine whether the function is odd, even, or neither. -f( ) = 1 +

Prove that the equation is an identity. -

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Exam 6: Trigonometric Identities and Conditional Equations

Use odd and even identities to simplify the expression. -

Factor the trigonometric expression. -

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

Write in terms of the cofunction of a complementary angle. -csc (90° - 8°)

Prove that the equation is an identity. -tan x + cot x = sec x csc x

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

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

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

Factor the trigonometric expression. -16 - 8 sec y + 1

For the given function, determine the amplitude and find the phase shift. -y = 15 sin x + 20 cos x Give the phase shift in radians rounded to the nearest thousandth.

Use a product-to-sum identity to rewrite the expression. -cos(13k) cos (6k)

Solve the equation. -

Solve the equation. -

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

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

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

Determine whether the function is odd, even, or neither. -f( ) = 1 +

Prove that the equation is an identity. -

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