Question 1

Find the exact solutions of the given equation in the interval   .

Accepted Answer

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

Question 2

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

Accepted Answer

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

Question 3

If   , use trigonometric substitution to write   as a trigonometric function of q, where   .

Accepted Answer

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

Question 4

Verify the identity shown below.

Accepted Answer

The answer of Verify the identity shown below.  ...

Question 5

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval   .

Accepted Answer

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

Question 6

Using the grid provided, sketch the graph of the given function in the interval   and then determine the x-intercepts, if any.

Accepted Answer

A)  no x-intercepts 
B)  (-2,0) and (2,0) 
C)  (-4,0), (-2,0), (2,0), and (4,0) 
D)  (-2,0) 
E)  (-3,0), (-1,0), (1,0), and (3,0) 
A)  no x-intercepts 
B)  (-2,0) and (2,0) 
C)  (-4,0), (-2,0), (2,0), and (4,0) 
D)  (-2,0) 
E)  (-3,0), (-1,0), (1,0), and (3,0)

Question 7

Find the exact value of the given expression using a sum or difference formula.

Accepted Answer

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

Question 8

Which of the following is a solution to the given equation?

Accepted Answer

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

Question 9

Simplify the given expression algebraically.

Accepted Answer

A)    
B)    
C)    
D)    
E)  1 
A)    
B)    
C)    
D)    
E)  1

Question 10

Find all solutions of the following equation in the interval   .

Accepted Answer

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

Question 11

Verify the identity shown below.

Accepted Answer

The answer of Verify the identity shown below.  ...

Question 12

Solve the following equation.

Accepted Answer

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

Question 13

Write the given expression as an algebraic expression.

Accepted Answer

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

Question 14

The horizontal distance d (in feet) traveled by a projectile with an initial speed of v feet per second is modeled by   , where q is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 50 feet per second when the ball is hit at an angle of   . Round to the nearest foot.

Accepted Answer

A)  115 
B)  154 
C)  77 
D)  135 
E)  38 
A)  115 
B)  154 
C)  77 
D)  135 
E)  38

Question 15

Use the figure below to find the exact value of the given trigonometric expression.     15 36
(figure not necessarily to scale)

Accepted Answer

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

Question 16

A Ferris wheel is built such that the height h (in feet) above the ground of a seat on the wheel at time t (in seconds) can be modeled by   . The wheel makes one revolution every 36 seconds and the ride begins when   . During the first 36 seconds of the ride, when will a person, who starts at the bottom of the Ferris wheel, be   feet above the ground?

Accepted Answer

A)  10 seconds and 22 seconds 
B)  10 seconds and 17 seconds 
C)  9 seconds and 27 seconds 
D)  9 seconds and 22 seconds 
E)  9 seconds and 17 seconds 
A)  10 seconds and 22 seconds 
B)  10 seconds and 17 seconds 
C)  9 seconds and 27 seconds 
D)  9 seconds and 22 seconds 
E)  9 seconds and 17 seconds

Question 17

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

Accepted Answer

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

Question 18

Use a double angle formula to rewrite the given expression.

Accepted Answer

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

Question 19

Find the exact value of the given expression.

Accepted Answer

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

Question 20

Find the exact value of   given that   and   . (Both u and v are in Quadrant II.)

Accepted Answer

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

Find the exact solutions of the given equation in the interval .

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

If , use trigonometric substitution to write as a trigonometric function of q, where .

Verify the identity shown below.

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

Using the grid provided, sketch the graph of the given function in the interval and then determine the x-intercepts, if any.

Find the exact value of the given expression using a sum or difference formula.

Which of the following is a solution to the given equation?

Simplify the given expression algebraically.

Find all solutions of the following equation in the interval .

Verify the identity shown below.

Solve the following equation.

Write the given expression as an algebraic expression.

Use the figure below to find the exact value of the given trigonometric expression. 15 36 (figure not necessarily to scale)

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

Use a double angle formula to rewrite the given expression.

Find the exact value of the given expression.

Find the exact value of given that and . (Both u and v are in Quadrant II.)

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters

Exam 7: Analytic Trigonometry

Find the exact solutions of the given equation in the interval .

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

If , use trigonometric substitution to write as a trigonometric function of q, where .

Verify the identity shown below.

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval .

Using the grid provided, sketch the graph of the given function in the interval and then determine the x-intercepts, if any.

Find the exact value of the given expression using a sum or difference formula.

Which of the following is a solution to the given equation?

Simplify the given expression algebraically.

Find all solutions of the following equation in the interval .

Verify the identity shown below.

Solve the following equation.

Write the given expression as an algebraic expression.

Use the figure below to find the exact value of the given trigonometric expression. 15 36 (figure not necessarily to scale)

Factor; then use fundamental identities to simplify the expression below and determine which of the following is not equivalent.

Use a double angle formula to rewrite the given expression.

Find the exact value of the given expression.

Find the exact value of given that and . (Both u and v are in Quadrant II.)

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Rational Functions and Conics

Exponential and Logarithmic Functions

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters