Question 1

Find the exact values of   for the given conditions.

Accepted Answer

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

Question 2

Find the solutions of the equation that are in the interval

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Question 3

Use an addition or subtraction formula to find the solutions of the equation that are in the interval   .

Accepted Answer

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

Question 4

Find the exact values of   for the given values of   .

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

Verify the identity.

Accepted Answer

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

Question 7

Find the solutions of the equation that are in the interval

Accepted Answer

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

Question 8

Verify the identity.

Accepted Answer

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

Question 9

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 10

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 0.77 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 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. For the San Francisco earthquake of 1906, S was 5 meters and D was 3.07 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 12

Shown in the figure is a graph of the function f for   . Use a sum-to-product formula to help find the first two x-intercepts.

Accepted Answer

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

Question 13

Use sum-to-product formulas to find the solutions of the equation.

Accepted Answer

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

Question 14

Express as a sum or difference.

Accepted Answer

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

Question 15

Find the exact value of the expression.

Accepted Answer

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

Question 16

Verify the identity.

Accepted Answer

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

Question 17

Express as a product.

Accepted Answer

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

Question 18

Express as a product.

Accepted Answer

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

Question 19

Use an addition or subtraction formula to find the solutions of the equation that are in the interval   .

Accepted Answer

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

Question 20

Find the solutions of the equation that are in the interval

Accepted Answer

A)    
B)    
C)    
D)    
E) no solution 
A)    
B)    
C)    
D)    
E) no solution

Find the exact values of for the given conditions.

Find the solutions of the equation that are in the interval

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .

Find the exact values of for the given values of .

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

Verify the identity.

Find the solutions of the equation that are in the interval

Verify the identity.

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

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.

Use sum-to-product formulas to find the solutions of the equation.

Express as a sum or difference.

Find the exact value of the expression.

Verify the identity.

Express as a product.

Express as a product.

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .

Find the solutions of the equation that are in the interval

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 conditions.

Find the solutions of the equation that are in the interval

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .

Find the exact values of for the given values of .

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

Verify the identity.

Find the solutions of the equation that are in the interval

Verify the identity.

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

Shown in the figure is a graph of the function f for . Use a sum-to-product formula to help find the first two x-intercepts.

Use sum-to-product formulas to find the solutions of the equation.

Express as a sum or difference.

Find the exact value of the expression.

Verify the identity.

Express as a product.

Express as a product.

Use an addition or subtraction formula to find the solutions of the equation that are in the interval .

Find the solutions of the equation that are in the interval

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