Question 1

Use a double-angle formula to rewrite the expression. ​
10 cos2 x - 5
​

Accepted Answer

A) 5 cos x 
B) ​cos 5x 
C) ​10 cos 2x 
D) ​10 cos x 
E) ​5 cos 2x 
A) 5 cos x 
B) ​cos 5x 
C) ​10 cos 2x 
D) ​10 cos x 
E) ​5 cos 2x

Question 2

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​   ​

Accepted Answer

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

Question 3

Convert the expression. ​   ​

Accepted Answer

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

Question 4

Which of the following is equivalent to the given expression?   ​

Accepted Answer

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

Question 5

Write the given expression as the sine of an angle.

Accepted Answer

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

Question 6

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 t = 0.During the first 36 seconds of the ride, when will a person, who starts at the bottom of the Ferris wheel, be 67 feet above the ground? ​

Accepted Answer

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

Question 7

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​   ​

Accepted Answer

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

Question 8

Use the figure to find the exact value of the trigonometric function. ​
Tan 2θ
​   ​
A = 1, b = 6
​

Accepted Answer

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

Question 9

If x = 2 tan θ, use trigonometric substitution to write   as a trigonometric function of θ, where   . ​

Accepted Answer

A) ​2 cos θ 
B) ​2 tan θ 
C) ​2 sin θ 
D) ​2 sec θ 
E) ​2 csc θ 
A) ​2 cos θ 
B) ​2 tan θ 
C) ​2 sin θ 
D) ​2 sec θ 
E) ​2 csc θ

Question 10

Evaluate the following expression.(x ≠ π/10 + πn, where n is a whole number) ​   ​

Accepted Answer

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

Question 11

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where   .   ​

Accepted Answer

A) - 5 sec θ 
B) 5 tan θ 
C) 25 sec θ 
D) 25 tan θ 
E) 5 sec θ 
A) - 5 sec θ 
B) 5 tan θ 
C) 25 sec θ 
D) 25 tan θ 
E) 5 sec θ

Question 12

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 13

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 14

Use the formula   , where   , to rewrite the trigonometric expression in the following form. ​   ​   ​

Accepted Answer

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

Question 15

The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v0 feet per second is   where r is measured in feet.A golfer strikes a golf ball at 90 feet per second.Ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 150 feet? (Round your answer to the nearest degree.)

Accepted Answer

A) 14° 
B) 36° 
C) 18° 
D) 27° 
E) 41° 
A) 14° 
B) 36° 
C) 18° 
D) 27° 
E) 41°

Question 16

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 17

Simplify the expression algebraically. ​   ​

Accepted Answer

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

Question 18

If x = 4 cot θ, use trigonometric substitution to write   as a trigonometric function of θ, where 0 < θ < π.

Accepted Answer

A) ​4 cos θ 
B) ​4 csc θ 
C) ​4 cot θ 
D) ​4 sec θ 
E) ​4 sin θ 
A) ​4 cos θ 
B) ​4 csc θ 
C) ​4 cot θ 
D) ​4 sec θ 
E) ​4 sin θ

Question 19

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval [0, 2π). ​   ​

Accepted Answer

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

Question 20

Find the exact value of the given expression.

Accepted Answer

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

Use a double-angle formula to rewrite the expression. 10 cos²x - 5

Use the sum-to-product formulas to rewrite the sum or difference as a product.

Convert the expression.

Which of the following is equivalent to the given expression?

Write the given expression as the sine of an angle.

Use the sum-to-product formulas to rewrite the sum or difference as a product.

Use the figure to find the exact value of the trigonometric function. Tan 2θ A = 1, b = 6

If x = 2 tan θ, use trigonometric substitution to write as a trigonometric function of θ, where .

Evaluate the following expression.(x ≠ π/10 + πn, where n is a whole number)

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .

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

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

Use the formula , where , to rewrite the trigonometric expression in the following form.

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

Simplify the expression algebraically.

If x = 4 cot θ, use trigonometric substitution to write as a trigonometric function of θ, where 0 < θ < π.

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval [0, 2π).

Find the exact value of the given expression.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Use a double-angle formula to rewrite the expression. ​ 10 cos2 x - 5 ​

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​ ​

Convert the expression. ​ ​

Which of the following is equivalent to the given expression? ​

Write the given expression as the sine of an angle.

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​ ​

Use the figure to find the exact value of the trigonometric function. ​ Tan 2θ ​ ​ A = 1, b = 6 ​

If x = 2 tan θ, use trigonometric substitution to write as a trigonometric function of θ, where . ​

Evaluate the following expression.(x ≠ π/10 + πn, where n is a whole number) ​ ​

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where . ​

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

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

Use the formula , where , to rewrite the trigonometric expression in the following form. ​ ​ ​

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

Simplify the expression algebraically. ​ ​

If x = 4 cot θ, use trigonometric substitution to write as a trigonometric function of θ, where 0 < θ < π.

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval [0, 2π). ​ ​

Find the exact value of the given expression.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Use a double-angle formula to rewrite the expression. 10 cos²x - 5

Use the sum-to-product formulas to rewrite the sum or difference as a product.

Convert the expression.

Which of the following is equivalent to the given expression?

Use the sum-to-product formulas to rewrite the sum or difference as a product.

Use the figure to find the exact value of the trigonometric function. Tan 2θ A = 1, b = 6

If x = 2 tan θ, use trigonometric substitution to write as a trigonometric function of θ, where .

Evaluate the following expression.(x ≠ π/10 + πn, where n is a whole number)

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .

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

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

Use the formula , where , to rewrite the trigonometric expression in the following form.

Simplify the expression algebraically.

Use inverse functions where needed to find all solutions (if they exist) of the given equation on the interval [0, 2π).