Question 1

Evaluate the following expression.(θ ≠ (π+2πn)/6, where n is a whole number) ​   ​

Accepted Answer

A) - cos 3θ 
B) cos 3θ 
C) sec 3θ 
D) - sec 3θ 
E) sec 3θ​ - cos 3θ 
A) - cos 3θ 
B) cos 3θ 
C) sec 3θ 
D) - sec 3θ 
E) sec 3θ​ - cos 3θ

Question 2

Convert the expression. ​
​   ​

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

A) ​x = 0.398 
B) ​​x = 1.336 
C) ​​x = 0.094 
D) ​​x = 0.73 
E) ​​x = 0.139 
A) ​x = 0.398 
B) ​​x = 1.336 
C) ​​x = 0.094 
D) ​​x = 0.73 
E) ​​x = 0.139

Question 5

If x = 6 sin θ, use trigonometric substitution to write   as a trigonometric function of θ, where   .

Accepted Answer

A) ​6 csc θ 
B) ​6 sec θ 
C) ​6 sin θ 
D) ​6 cos θ 
E) ​6 tan θ 
A) ​6 csc θ 
B) ​6 sec θ 
C) ​6 sin θ 
D) ​6 cos θ 
E) ​6 tan θ

Question 6

Solve the following equation. ​   ​

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Find the exact solutions of the given equation in the interval   . sin 4x= -2sin 2x

Accepted Answer

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

Question 9

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2π). ​   ​

Accepted Answer

A) x = 1.624, 1.932, 5.776, 5.997 
B) ​x = 1.101, 2.118, 3.982, 5.104 
C) ​x = 1.571, 3.990, 4.712, 5.435 
D) ​x = 1.055, 3.785, 4.652, 5.721 
E) ​x = 1.484, 3.799, 4.626, 5.490 
A) x = 1.624, 1.932, 5.776, 5.997 
B) ​x = 1.101, 2.118, 3.982, 5.104 
C) ​x = 1.571, 3.990, 4.712, 5.435 
D) ​x = 1.055, 3.785, 4.652, 5.721 
E) ​x = 1.484, 3.799, 4.626, 5.490

Question 10

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​
Sec5x (sec x tan x) - ​sec3x (sec x tan x)
​

Accepted Answer

A) ​sec4x tan x 
B) ​4 sec x tan4 x 
C) ​sec3x tan5x 
D) ​sec4x tan3 x 
E) ​sec3x tan3x 
A) ​sec4x tan x 
B) ​4 sec x tan4 x 
C) ​sec3x tan5x 
D) ​sec4x tan3 x 
E) ​sec3x tan3x

Question 11

The mach number M of an airplane is the ratio of its speed to the speed of sound.When an airplane travels faster than the speed of sound, the sound waves form a cone behind the airplane (see figure).The mach number is related to the apex angle θ of the cone by   . ​   ​
Rewrite the equation in terms of θ.
​

Accepted Answer

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

Question 12

Use the given values to evaluate (if possible) three trigonometric functions   . ​   ​

Accepted Answer

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

Question 13

Evaluate the following expression. ​
(1 + sin 5y)(1 + sin (- 5y))
​

Accepted Answer

A) sin25y 
B) cos22y 
C) - sin25y 
D) - cos25y 
E) cos25y 
A) sin25y 
B) cos22y 
C) - sin25y 
D) - cos25y 
E) cos25y

Question 14

Use a graphing utility to select correct graph of   and   in the same viewing window.Use the graphs to determine whether   .Explain your reasoning. ​   ​

Accepted Answer

A) ​   No,   because their graphs are different. 
B) ​   Yes,   because their graphs are different. 
C) ​   Yes,   because their graphs are same. 
D) ​   No,   because their graphs are Same. 
E) ​   No,   because their graphs are different. 
A) ​   No,   because their graphs are different. 
B) ​   Yes,   because their graphs are different. 
C) ​   Yes,   because their graphs are same. 
D) ​   No,   because their graphs are Same. 
E) ​   No,   because their graphs are different.

Question 15

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) x = 1.229, 1.433 
B) ​x = 1.227, 1.422 
C) ​x = 1.233, 1.469 
D) ​x = 1.231, 1.451 
E) ​x = 1.235, 1.480 
A) x = 1.229, 1.433 
B) ​x = 1.227, 1.422 
C) ​x = 1.233, 1.469 
D) ​x = 1.231, 1.451 
E) ​x = 1.235, 1.480

Question 16

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

Accepted Answer

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

Question 17

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 18

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

Accepted Answer

A) ​-1 
B) ​   
C) ​cot x 
D) ​1/ tan x 
E) ​cos x csc x 
A) ​-1 
B) ​   
C) ​cot x 
D) ​1/ tan x 
E) ​cos x csc x

Question 19

Simplify the following expression algebraically. ​   ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

Evaluate the following expression.(θ ≠ (π+2πn)/6, where n is a whole number)

Convert the expression.

Find the expression as the sine or cosine of an angle.

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

If x = 6 sin θ, use trigonometric substitution to write as a trigonometric function of θ, where .

Solve the following equation.

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

Find the exact solutions of the given equation in the interval . sin 4x= -2sin 2x

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2π).

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) Sec⁵x (sec x tan x) - sec³x (sec x tan x)

The mach number M of an airplane is the ratio of its speed to the speed of sound.When an airplane travels faster than the speed of sound, the sound waves form a cone behind the airplane (see figure).The mach number is related to the apex angle θ of the cone by . Rewrite the equation in terms of θ.

Use the given values to evaluate (if possible) three trigonometric functions .

Evaluate the following expression. (1 + sin 5y)(1 + sin (- 5y))

Use a graphing utility to select correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning.

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.

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

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

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

Simplify the following expression algebraically.

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

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Evaluate the following expression.(θ ≠ (π+2πn)/6, where n is a whole number) ​ ​

Convert the expression. ​ ​ ​

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

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

If x = 6 sin θ, use trigonometric substitution to write as a trigonometric function of θ, where .

Solve the following equation. ​ ​

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

Find the exact solutions of the given equation in the interval . sin 4x= -2sin 2x

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2π). ​ ​

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​ Sec5x (sec x tan x) - ​sec3x (sec x tan x) ​

Use the given values to evaluate (if possible) three trigonometric functions . ​ ​

Evaluate the following expression. ​ (1 + sin 5y)(1 + sin (- 5y)) ​

Use a graphing utility to select correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning. ​ ​

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. ​ ​

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

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

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

Simplify the following expression algebraically. ​ ​

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

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Evaluate the following expression.(θ ≠ (π+2πn)/6, where n is a whole number)

Convert the expression.

Find the expression as the sine or cosine of an angle.

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

Solve the following equation.

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

Use a graphing utility to approximate the solutions (to three decimal places) of the given equation in the interval [0, 2π).

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) Sec⁵x (sec x tan x) - sec³x (sec x tan x)

Use the given values to evaluate (if possible) three trigonometric functions .

Evaluate the following expression. (1 + sin 5y)(1 + sin (- 5y))

Use a graphing utility to select correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning.

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.

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

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

Simplify the following expression algebraically.

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