Question 1

Convert the expression. ​   ​

Accepted Answer

A) 2 cos b 
B) ​cos 2b 
C) ​​cos b 
D) 2 ​cos 2b 
E) ​4 cos b 
A) 2 cos b 
B) ​cos 2b 
C) ​​cos b 
D) 2 ​cos 2b 
E) ​4 cos b

Question 2

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 3

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 4

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 5

Find the rate of change of the function   . ​

Accepted Answer

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

Question 6

Solve the following equation. ​   ​

Accepted Answer

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

Question 7

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

Accepted Answer

A) 6 sec θ 
B) sec 6θ 
C) - sec θ 
D) sec θ 
E) -6 sec θ 
A) 6 sec θ 
B) sec 6θ 
C) - sec θ 
D) sec θ 
E) -6 sec θ

Question 8

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 9

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

Accepted Answer

A)      
B) 9   
C) 9   
D)      
E) 2   
A)      
B) 9   
C) 9   
D)      
E) 2

Question 10

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 11

Solve the following equation. ​   ​

Accepted Answer

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

Question 12

Write the given expression as the tangent of an angle. ​

Accepted Answer

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

Question 13

Use a double-angle formula to rewrite the expression. ​
​   ​

Accepted Answer

A) ​sin x 
B) ​​2 sin x 
C) ​​​2 sin 2x 
D) ​ sin x 
E) ​ sin 2x 
A) ​sin x 
B) ​​2 sin x 
C) ​​​2 sin 2x 
D) ​ sin x 
E) ​ sin 2x

Question 14

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

Accepted Answer

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

Question 15

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 16

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure).The radius of each arc r (in feet) and the angle θ are related by ​   ​
Write a formula for x in terms of cos θ.
​   ​

Accepted Answer

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

Question 17

Which of the following is a solution to the given equation? ​
Cscx - 2 = 0

Accepted Answer

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

Question 18

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 19

Convert the expression. ​
​   ​

Accepted Answer

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

Question 20

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) ​

Convert the expression.

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

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

Use a graphing utility to graph the function.

Find the rate of change of the function .

Solve the following equation.

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

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.

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

Solve the following equation.

Write the given expression as the tangent of an angle.

Use a double-angle formula to rewrite the expression.

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

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

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure).The radius of each arc r (in feet) and the angle θ are related by Write a formula for x in terms of cos θ.

Which of the following is a solution to the given equation? Cscx - 2 = 0

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

Convert the expression.

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

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Convert the expression. ​ ​

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

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

Use a graphing utility to graph the function. ​ ​

Find the rate of change of the function . ​

Solve the following equation. ​ ​

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

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. ​ ​ ​

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

Solve the following equation. ​ ​

Write the given expression as the tangent of an angle. ​

Use a double-angle formula to rewrite the expression. ​ ​ ​

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

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

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure).The radius of each arc r (in feet) and the angle θ are related by ​ ​ Write a formula for x in terms of cos θ. ​ ​

Which of the following is a solution to the given equation? ​ Cscx - 2 = 0

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

Convert the expression. ​ ​ ​

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

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Convert the expression.

Use a graphing utility to graph the function.

Find the rate of change of the function .

Solve the following equation.

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

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.

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

Solve the following equation.

Write the given expression as the tangent of an angle.

Use a double-angle formula to rewrite the expression.

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

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

When two railroad tracks merge, the overlapping portions of the tracks are in the shapes of circular arcs (see figure).The radius of each arc r (in feet) and the angle θ are related by Write a formula for x in terms of cos θ.

Which of the following is a solution to the given equation? Cscx - 2 = 0

Convert the expression.