Question 1

Find all solutions of the following equation in the interval [0, 2π). ​   ​

Accepted Answer

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

Question 2

Simplify the expression algebraically. ​   ​

Accepted Answer

A)    
B) 0 
C)    
D) 1 
E) 6 
A)    
B) 0 
C)    
D) 1 
E) 6

Question 3

Use a graphing utility to graph the function. ​
​   ​

Accepted Answer

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

Question 4

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 5

Use a double-angle formula to rewrite the expression. ​
2 sin2 x - 1
​

Accepted Answer

A) cos x 
B) cos 2x ​ 
C) -2 cos x ​ 
D) 2 cos 2x ​ 
E) - cos 2x ​ 
A) cos x 
B) cos 2x ​ 
C) -2 cos x ​ 
D) 2 cos 2x ​ 
E) - cos 2x ​

Question 6

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

Accepted Answer

A) 3 (csc x - sin x) 
B) (csc x + sin x) 
C) - 3 (csc x - sin x) 
D) 3 (csc x + sin x) 
E) (csc x - sin x) 
A) 3 (csc x - sin x) 
B) (csc x + sin x) 
C) - 3 (csc x - sin x) 
D) 3 (csc x + sin x) 
E) (csc x - sin x)

Question 7

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

Accepted Answer

A) 25 tan θ 
B) 5 tan θ 
C) 25 sec θ 
D) 6 sec θ 
E) - 5 sec θ 
A) 25 tan θ 
B) 5 tan θ 
C) 25 sec θ 
D) 6 sec θ 
E) - 5 sec θ

Question 8

Find all solutions of the following equation in the interval [0, 2π). ​   ​

Accepted Answer

A)    
B) No solution 
C) ​   
D) ​   
E) ​   
A)    
B) No solution 
C) ​   
D) ​   
E) ​

Question 9

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

Accepted Answer

A) 2   
B)      
C)      
D) 2   
E) 8   
A) 2   
B)      
C)      
D) 2   
E) 8

Question 10

Find the rate of change of the function   . ​

Accepted Answer

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

Question 11

Evaluate the following expression.(x ≠ π/2 + πn, where n is a whole number) ​   ​

Accepted Answer

A) - 11 tan x 
B) 11 cot x 
C) 12 tan x 
D) - 11 cot x 
E) 11 tan x 
A) - 11 tan x 
B) 11 cot x 
C) 12 tan x 
D) - 11 cot x 
E) 11 tan x

Question 12

Find the expression as the sine of an angle. ​   ​

Accepted Answer

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

Question 13

Solve the multiple-angle equation. ​   ​

Accepted Answer

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

Question 14

Which of the following is equivalent to the given expression?

Accepted Answer

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

Question 15

Use the figure to find the exact value of the trigonometric function. ​
Sec 2θ
​   ​
A = 1, b = 8
​

Accepted Answer

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

Question 16

Evaluate the following expression. ​
(sin2x - sin4x) cos x
​

Accepted Answer

A) cos4x sin2x 
B) cos2x sin2x 
C) cos2x sin6x 
D) cos3x sin2x 
E) cos x sin x 
A) cos4x sin2x 
B) cos2x sin2x 
C) cos2x sin6x 
D) cos3x sin2x 
E) cos x sin x

Question 17

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 18

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). ​   ​

Accepted Answer

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

Question 19

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​
2 cos x + 2 sin x tan x
​

Accepted Answer

A) -2 sec x 
B) 2 sec x 
C) 4 cos x 
D) -4 cos x 
E) 3 sin x 
A) -2 sec x 
B) 2 sec x 
C) 4 cos x 
D) -4 cos x 
E) 3 sin x

Question 20

Simplify the expression algebraically. ​   ​

Accepted Answer

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

Find all solutions of the following equation in the interval [0, 2π).

Simplify the expression algebraically.

Use a graphing utility to graph the function.

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 expression. 2 sin²x - 1

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

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

Find all solutions of the following equation in the interval [0, 2π).

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

Find the rate of change of the function .

Evaluate the following expression.(x ≠ π/2 + πn, where n is a whole number)

Find the expression as the sine of an angle.

Solve the multiple-angle equation.

Which of the following is equivalent to the given expression?

Use the figure to find the exact value of the trigonometric function. Sec 2θ A = 1, b = 8

Evaluate the following expression. (sin²x - sin⁴x) cos x

Use a graphing utility to graph the function.

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π).

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) 2 cos x + 2 sin x tan x

Simplify the expression algebraically.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Find all solutions of the following equation in the interval [0, 2π). ​ ​

Simplify the expression algebraically. ​ ​

Use a graphing utility to graph the function. ​ ​ ​

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 expression. ​ 2 sin2 x - 1 ​

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

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

Find all solutions of the following equation in the interval [0, 2π). ​ ​

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

Find the rate of change of the function . ​

Evaluate the following expression.(x ≠ π/2 + πn, where n is a whole number) ​ ​

Find the expression as the sine of an angle. ​ ​

Solve the multiple-angle equation. ​ ​

Which of the following is equivalent to the given expression?

Use the figure to find the exact value of the trigonometric function. ​ Sec 2θ ​ ​ A = 1, b = 8 ​

Evaluate the following expression. ​ (sin2x - sin4x) cos x ​

Use a graphing utility to graph the function. ​ ​

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π). ​ ​

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​ 2 cos x + 2 sin x tan x ​

Simplify the expression algebraically. ​ ​

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find all solutions of the following equation in the interval [0, 2π).

Simplify the expression algebraically.

Use a graphing utility to graph the function.

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 expression. 2 sin²x - 1

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

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

Find all solutions of the following equation in the interval [0, 2π).

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

Find the rate of change of the function .

Evaluate the following expression.(x ≠ π/2 + πn, where n is a whole number)

Find the expression as the sine of an angle.

Solve the multiple-angle equation.

Use the figure to find the exact value of the trigonometric function. Sec 2θ A = 1, b = 8

Evaluate the following expression. (sin²x - sin⁴x) cos x

Use a graphing utility to graph the function.

Use inverse functions where needed to find all solutions of the equation in the interval [0, 2π).

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) 2 cos x + 2 sin x tan x

Simplify the expression algebraically.