Question 1

Use a double-angle formula to find the exact value of   when   .

Accepted Answer

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

Question 2

Write the given expression as the sine of an angle.

Accepted Answer

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

Question 3

Write the given expression as the cosine of an angle.

Accepted Answer

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

Question 4

Verify the given identity.

Accepted Answer

The answer of Verify the given identity.   ...

Question 5

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

Accepted Answer

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

Question 6

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 7

Use the sum-to-product formulas to write the given expression as a product.

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

The range of a projectile fired at an angle q with the horizontal and with an initial velocity of   feet per second is   where r is measured in feet. A golfer strikes a golf ball at 120 feet per second. Ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (Round answer to nearest angle.)

Accepted Answer

A)  18$\degree$ 
B)  14$\degree$ 
C)  20$\degree$ 
D)  5$\degree$ 
E)  9$\degree$ 
A)  18$\degree$ 
B)  14$\degree$ 
C)  20$\degree$ 
D)  5$\degree$ 
E)  9$\degree$

Question 10

Use the figure below to determine the exact value of the given function.

Accepted Answer

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

Question 11

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

Accepted Answer

A)  0 
B)    
C)  -1 
D)  2 
E)  1 
A)  0 
B)    
C)  -1 
D)  2 
E)  1

Question 12

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval   .

Accepted Answer

A)    
B)    
C)    
D)  solution does not exist 
E)    
A)    
B)    
C)    
D)  solution does not exist 
E)

Question 13

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 14

Use the sum-to-product formulas to find the exact value of the given expression.

Accepted Answer

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

Question 15

Solve the multiple-angle equation.

Accepted Answer

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

Question 16

Use the figure below to find the exact value of the given trigonometric expression.

Accepted Answer

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

Question 17

Simplify the given expression algebraically.

Accepted Answer

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

Question 18

Which of the following is equivalent to the given expression?

Accepted Answer

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

Question 19

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 20

Find the exact value of the given expression.

Accepted Answer

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

Use a double-angle formula to find the exact value of when .

Write the given expression as the sine of an angle.

Write the given expression as the cosine of an angle.

Verify the given identity.

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

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

Use the sum-to-product formulas to write the given expression as a product.

Verify the identity shown below.

Use the figure below to determine the exact value of the given function.

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval .

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

Use the sum-to-product formulas to find the exact value of the given expression.

Solve the multiple-angle equation.

Use the figure below to find the exact value of the given trigonometric expression.

Simplify the given expression algebraically.

Which of the following is equivalent to the given expression?

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

Find the exact value of the given 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

Use a double-angle formula to find the exact value of when .

Write the given expression as the sine of an angle.

Write the given expression as the cosine of an angle.

Verify the given identity.

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

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

Use the sum-to-product formulas to write the given expression as a product.

Verify the identity shown below.

Use the figure below to determine the exact value of the given function.

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval .

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

Use the sum-to-product formulas to find the exact value of the given expression.

Solve the multiple-angle equation.

Use the figure below to find the exact value of the given trigonometric expression.

Simplify the given expression algebraically.

Which of the following is equivalent to the given expression?

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

Find the exact value of the given 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