Question 1

Rewrite   as a single logarithm and then simplify the result.

Accepted Answer

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

Question 2

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Accepted Answer

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

Question 3

Write the given expression as the tangent of an angle.

Accepted Answer

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

Question 4

Multiply; 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 5

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by   where t is the time (in months), with   corresponding to January. Determine the months when sales exceed   units at any time during the month.

Accepted Answer

A)  March through September 
B)  April through August 
C)  March through August 
D)  August through April 
E)  May through September 
A)  March through September 
B)  April through August 
C)  March through August 
D)  August through April 
E)  May through September

Question 6

Find the exact value of the given expression.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Verify the identity shown below.

Accepted Answer

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

Question 9

Find all solutions of the given equation in the interval   .

Accepted Answer

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

Question 10

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 11

Use the Quadratic Formula to solve the given equation on the interval   ; then use a graphing utility to approximate the angle x. Round answers to three decimal places.

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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)

Question 14

Find all solutions of the given equation in the interval   .

Accepted Answer

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

Question 15

Use the product-to-sum formula to write the given product as a sum or difference.

Accepted Answer

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

Question 16

Solve the following equation.

Accepted Answer

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

Question 17

Use the half-angle formula to simplify the given expression.

Accepted Answer

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

Question 18

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 19

Verify the identity shown below.

Accepted Answer

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

Question 20

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

Accepted Answer

A)    
B)    
C)    
D)    3 
E)    
A)    
B)    
C)    
D)    3 
E)

Rewrite as a single logarithm and then simplify the result.

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Write the given expression as the tangent of an angle.

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

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months), with corresponding to January. Determine the months when sales exceed units at any time during the month.

Find the exact value of the given expression.

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

Verify the identity shown below.

Find all solutions of the given equation in the interval .

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

Use the Quadratic Formula to solve the given equation on the interval ; then use a graphing utility to approximate the angle x. Round answers to three decimal places.

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

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

Find all solutions of the given equation in the interval .

Use the product-to-sum formula to write the given product as a sum or difference.

Solve the following equation.

Use the half-angle formula to simplify the given expression.

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

Verify the identity shown below.

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

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

Rewrite as a single logarithm and then simplify the result.

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Write the given expression as the tangent of an angle.

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

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months), with corresponding to January. Determine the months when sales exceed units at any time during the month.

Find the exact value of the given expression.

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

Verify the identity shown below.

Find all solutions of the given equation in the interval .

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

Use the Quadratic Formula to solve the given equation on the interval ; then use a graphing utility to approximate the angle x. Round answers to three decimal places.

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

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

Find all solutions of the given equation in the interval .

Use the product-to-sum formula to write the given product as a sum or difference.

Solve the following equation.

Use the half-angle formula to simplify the given expression.

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

Verify the identity shown below.

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

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