Question 1

Find the exact values of   for the given values of   .

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Tell whether the reduction formula is correct or incorrect.

Accepted Answer

A) incorrect 
B) correct 
A) incorrect 
B) correct

Question 4

Verify the identity.

Accepted Answer

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

Question 5

Verify the identity.

Accepted Answer

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

Question 6

Express as a product.

Accepted Answer

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

Question 7

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 4 meters and D was 3.08 kilometers. Approximate M for d = 6 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 8

Find the exact values of   for the given values of   .

Accepted Answer

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

Question 9

Verify the identity.

Accepted Answer

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

Question 10

Express as a sum or difference.

Accepted Answer

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

Question 11

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. Approximate the depth D of the focal point of an earthquake with S = 3 m if a point on the surface of Earth 3 kilometers from the fault line moved 0.75 meters horizontally. Round the answer to the nearest hundredth.

Accepted Answer

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

Question 12

Verify the identity.

Accepted Answer

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

Question 13

Verify the identity.

Accepted Answer

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

Question 14

Express as a product.

Accepted Answer

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

Question 15

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  = 2 and   = 2, find the initial velocities that result in an amplitude of 4 feet.

Accepted Answer

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

Question 16

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 17

Verify the identity.

Accepted Answer

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

Question 18

Verify the identity.

Accepted Answer

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

Question 19

Tell whether the reduction formula is correct or incorrect.

Accepted Answer

A) correct 
B) incorrect 
A) correct 
B) incorrect

Question 20

Find an identical expression.

Accepted Answer

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

Find the exact values of for the given values of .

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

Tell whether the reduction formula is correct or incorrect.

Verify the identity.

Verify the identity.

Express as a product.

Find the exact values of for the given values of .

Verify the identity.

Express as a sum or difference.

Verify the identity.

Verify the identity.

Express as a product.

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

Verify the identity.

Verify the identity.

Tell whether the reduction formula is correct or incorrect.

Find an identical expression.

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

Exam 7: Analytic Trigonometry

Find the exact values of for the given values of .

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

Tell whether the reduction formula is correct or incorrect.

Verify the identity.

Verify the identity.

Express as a product.

Find the exact values of for the given values of .

Verify the identity.

Express as a sum or difference.

Verify the identity.

Verify the identity.

Express as a product.

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

Verify the identity.

Verify the identity.

Tell whether the reduction formula is correct or incorrect.

Find an identical expression.

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