Question 1

Verify the identity.

Accepted Answer

A) Not identical 
B) Identical 
A) Not identical 
B) Identical A

Question 2

Verify the identity.

Accepted Answer

A) invalid 
B) valid 
A) invalid 
B) valid B

Question 3

Use the formula     to determine the period of f (x).

Accepted Answer

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

Question 4

Express as a sum or difference.

Accepted Answer

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

Question 5

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula   where D is the depth (in kilometers) below the surface of the focal point of the earthquake. For the San Francisco earthquake of 1906, S was 6 meters and D was 3.05 kilometers. Approximate M for d = 9 kilometers. Round the answer to the nearest hundredth.

Accepted Answer

A)    m 
B)    m 
C)    m 
D)    m 
E)    m 
A)    m 
B)    m 
C)    m 
D)    m 
E)    m

Question 6

Verify the identity.

Accepted Answer

A) Identical 
B) Not identical 
A) Identical 
B) Not identical

Question 7

A graph of   for   is shown in the figure. Find the exact values of the x-intercepts.

Accepted Answer

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

Question 8

Use the graph of f to find the simplest expression g(x) such that the equation   is an identity.

Accepted Answer

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

Question 9

Use the graph of f to find the simplest expression g(x) such that the equation   is an identity.

Accepted Answer

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

Question 10

Find all solutions of the equation.

Accepted Answer

A) 1 
B)    for every integer n. 
C)    for every integer n. 
D)    for every integer n. 
E)    for every integer n. 
A) 1 
B)    for every integer n. 
C)    for every integer n. 
D)    for every integer n. 
E)    for every integer n.

Question 11

Find the solutions of the equation that are in the interval

Accepted Answer

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

Question 12

Find all solutions of the equation.

Accepted Answer

A)    for every integer n. 
B)    for every integer n. 
C)    for every integer n. 
D)    for every integer n. 
E)    for every integer n. 
A)    for every integer n. 
B)    for every integer n. 
C)    for every integer n. 
D)    for every integer n. 
E)    for every integer n.

Question 13

Find the exact value of the expression.

Accepted Answer

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

Question 14

A graph of   for   is shown in the figure. Find the exact values of the x-intercepts.

Accepted Answer

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

Question 15

If   and   for a second-quadrant angle   and a third-quadrant angle   , find

Accepted Answer

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

Question 16

Express as a cofunction of a complementary angle.

Accepted Answer

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

Question 17

Verify the identity.

Accepted Answer

A) valid 
B) invalid 
A) valid 
B) invalid

Question 18

Find an identical expression.

Accepted Answer

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

Question 19

Verify the identity.

Accepted Answer

A) invalid 
B) valid 
A) invalid 
B) valid

Question 20

If a mass that is attached to a spring is raised y 0  feet and released with an initial vertical velocity of v 0  ft / sec, then the subsequent position y of the mass is given by   where t is time in seconds and   is a positive constant. If y 0  = 1 and   = 4, find the initial velocities that result in an amplitude of 5 feet.

Accepted Answer

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

Verify the identity.

Verify the identity.

Use the formula to determine the period of f (x).

Express as a sum or difference.

Verify the identity.

A graph of for is shown in the figure. Find the exact values of the x-intercepts.

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.

Find all solutions of the equation.

Find the solutions of the equation that are in the interval

Find all solutions of the equation.

Find the exact value of the expression.

A graph of for is shown in the figure. Find the exact values of the x-intercepts.

If and for a second-quadrant angle and a third-quadrant angle , find

Express as a cofunction of a complementary angle.

Verify the identity.

Find an identical expression.

Verify the identity.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

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Exam 7: Analytic Trigonometry

Verify the identity.

Verify the identity.

Use the formula to determine the period of f (x).

Express as a sum or difference.

Verify the identity.

A graph of for is shown in the figure. Find the exact values of the x-intercepts.

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.

Use the graph of f to find the simplest expression g(x) such that the equation is an identity.

Find all solutions of the equation.

Find the solutions of the equation that are in the interval

Find all solutions of the equation.

Find the exact value of the expression.

A graph of for is shown in the figure. Find the exact values of the x-intercepts.

If and for a second-quadrant angle and a third-quadrant angle , find

Express as a cofunction of a complementary angle.

Verify the identity.

Find an identical expression.

Verify the identity.

Fundamental Concepts of Algebra

Equations and Inequalities

Functions and Graphs

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

The Trigonometric Functions

Applications of Trigonometry

Systems of Equations and Inequalities

Sequences, Series and Probability

Topics From Analytic Geometry

Filters