Question 1

Use odd and even identities to simplify the expression.
-cos (-x) tan (-x)

Accepted Answer

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

Question 2

Solve the problem. Round to the nearest whole unit.
-The angle of elevation of the top of a pole as seen from a point 23 ft away from the base is double its angle of elevation as seen from a point 34 ft farther from the pole. Find the height of the pole above the level of the
Observer's eyes.

Accepted Answer

A)  25 ft 
B)  11 ft 
C)  30 ft 
D)  57 ft 
A)  25 ft 
B)  11 ft 
C)  30 ft 
D)  57 ft

Question 3

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 - 3 cos x

Accepted Answer

A)    ,phase shift     
B)    ,phase shift     
C)    ,phase shift     
D)    ,phase shift     
A)    ,phase shift     
B)    ,phase shift     
C)    ,phase shift     
D)    ,phase shift

Question 4

hundredth.
-  x + cos x + 1 = 0

Accepted Answer

A)  {0, 4.71, 5.71} 
B)  {1.57, 2.57, 3.14} 
C)  {3.14, 3.72, 4.71} 
D)  {0, 0.57, 1.57} 
A)  {0, 4.71, 5.71} 
B)  {1.57, 2.57, 3.14} 
C)  {3.14, 3.72, 4.71} 
D)  {0, 0.57, 1.57}

Question 5

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

Accepted Answer

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

Question 6

Find the exact value using a double-angle identity.
-cos(90°)

Accepted Answer

A)  1 
B)    
C)  0 
D)    
A)  1 
B)    
C)  0 
D)

Question 7

Use a sum or difference identity to find the exact value.
-sin

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

Identify the equation as either an identity or not.
-cos x csc x tan x = 1

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Express the given trigonometric function in terms of the indicated function.
-cos   in terms of cot

Accepted Answer

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

Question 14

Find all real numbers that satisfy the equation.
-sin

Accepted Answer

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

Question 15

Find the product.
-

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Prove the identity.
-

Accepted Answer

The answer of Prove the identity.
- ...

Question 18

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

Accepted Answer

A)  {60°, 300°} 
B)  {150°, 210°} 
C)  {210°, 330°} 
D)  {60°, 120°} 
A)  {60°, 300°} 
B)  {150°, 210°} 
C)  {210°, 330°} 
D)  {60°, 120°}

Question 19

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Prove that the equation is an identity.
-  = - cos14k cot 5k

Accepted Answer

The answer of SHORT ANSWER. Write the word or phrase...

Question 20

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

Accepted Answer

A)  {70.5°, 289.5°} 
B)  {60°, 120°} 
C)  {70.5°, 109.5°} 
D)  {60°, 300°} 
A)  {70.5°, 289.5°} 
B)  {60°, 120°} 
C)  {70.5°, 109.5°} 
D)  {60°, 300°}

Use odd and even identities to simplify the expression. -cos (-x) tan (-x)

Solve the problem. Round to the nearest whole unit. -The angle of elevation of the top of a pole as seen from a point 23 ft away from the base is double its angle of elevation as seen from a point 34 ft farther from the pole. Find the height of the pole above the level of the Observer's eyes.

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 - 3 cos x

hundredth. - x + cos x + 1 = 0

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

Find the exact value using a double-angle identity. -cos(90°)

Use a sum or difference identity to find the exact value. -sin

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

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

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

Identify the equation as either an identity or not. -cos x csc x tan x = 1

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

Express the given trigonometric function in terms of the indicated function. -cos in terms of cot

Find all real numbers that satisfy the equation. -sin

Find the product. -

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

Prove the identity. -

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prove that the equation is an identity. - = - cos14k cot 5k

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

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

Exam 6: Trigonometric Identities and Conditional Equations

Use odd and even identities to simplify the expression. -cos (-x) tan (-x)

Solve the problem. Round to the nearest whole unit. -The angle of elevation of the top of a pole as seen from a point 23 ft away from the base is double its angle of elevation as seen from a point 34 ft farther from the pole. Find the height of the pole above the level of the Observer's eyes.

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 - 3 cos x

hundredth. - x + cos x + 1 = 0

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

Find the exact value using a double-angle identity. -cos(90°)

Use a sum or difference identity to find the exact value. -sin

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

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

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

Identify the equation as either an identity or not. -cos x csc x tan x = 1

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

Express the given trigonometric function in terms of the indicated function. -cos in terms of cot

Find all real numbers that satisfy the equation. -sin

Find the product. -

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

Prove the identity. -

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

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Prove that the equation is an identity. - = - cos14k cot 5k

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

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