Question 1

Simplify the following expression algebraically. ​   ​

Accepted Answer

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

Question 2

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

Accepted Answer

A) 5 sec 4θ 
B) - 5 csc 4θ 
C) 5 csc 4θ 
D) - 5 sec 4θ 
E) 5 cot 4θ 
A) 5 sec 4θ 
B) - 5 csc 4θ 
C) 5 csc 4θ 
D) - 5 sec 4θ 
E) 5 cot 4θ

Question 3

Solve the multiple-angle equation. ​   ​

Accepted Answer

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

Question 4

Use the fundamental identities to simplify the expression. ​   ​

Accepted Answer

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

Question 5

Find the exact value of the given expression. ​

Accepted Answer

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

Question 6

Find the exact value of the given expression.

Accepted Answer

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

Question 7

Evaluate the following expression. ​
4 tan x (arcsin x)
​

Accepted Answer

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

Question 8

Which of the following expressions is equivalent to 2 - 4 cos2x + 4 cos4x? ​

Accepted Answer

A) 2 sin2x + 2 cos2x 
B) 2 sin4x - 2 cos2x 
C) 2 sin2x + 2 cos4x 
D) 2 sin4x + 2 cos4x 
E) 2 sin4x - 2 cos4x 
A) 2 sin2x + 2 cos2x 
B) 2 sin4x - 2 cos2x 
C) 2 sin2x + 2 cos4x 
D) 2 sin4x + 2 cos4x 
E) 2 sin4x - 2 cos4x

Question 9

Use the given values to evaluate (if possible) three trigonometric functions csc x, tan x, cot x. ​   ​

Accepted Answer

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

Question 10

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x. ​

Accepted Answer

A) ​   tan x = -  
​ 
B) ​   tan x = - ​   
C) ​   ​tan x =  
​ 
D) ​   ​tan x =  
​ 
E) ​   ​tan x = -  
​ 
A) ​   tan x = -  
​ 
B) ​   tan x = - ​   
C) ​   ​tan x =  
​ 
D) ​   ​tan x =  
​ 
E) ​   ​tan x = -  
​

Question 11

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

Accepted Answer

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

Question 12

Which of the following expressions is equivalent to 3 sin2 α - 3 sin4 α? ​

Accepted Answer

A) 3 cos4 α + cos2 α 
B) -cos2 α - 3 cos4 α) 
C) 3 (cos2 α + cos4 α) 
D) 3 (cos2 α - cos4 α) 
E) -3 (cos2 α - cos4 α) 
A) 3 cos4 α + cos2 α 
B) -cos2 α - 3 cos4 α) 
C) 3 (cos2 α + cos4 α) 
D) 3 (cos2 α - cos4 α) 
E) -3 (cos2 α - cos4 α)

Question 13

A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by ​   ​
Where y is the distance from equilibrium (in feet) and t is the time (in seconds).
​
Use the identity   where   , to write the model in the form   .
​

Accepted Answer

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

Question 14

Use the cofunction identities to evaluate the expression without using a calculator. ​
Sin225° + sin265°
​

Accepted Answer

A) -1 
B) -2 
C) 1 
D) 2 
E) 3 
A) -1 
B) -2 
C) 1 
D) 2 
E) 3

Question 15

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where   .Then find sin θ and cos θ.

Accepted Answer

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

Question 16

Use the trigonometric substitution u = a csc θ, where 0  0 to simplify the expression   . ​

Accepted Answer

A) a tan θ 
B) - a cot θ 
C) a csc θ 
D) a cos θ 
E) a cot θ 
A) a tan θ 
B) - a cot θ 
C) a csc θ 
D) a cos θ 
E) a cot θ

Question 17

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where   .Then find sin θ and cos θ. ​

Accepted Answer

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

Question 18

Use the trigonometric substitution u = a tan θ, where 0 < θ < π/2 and to simplify the expression   . ​

Accepted Answer

A) ​- a sec θ 
B) ​a sec θ 
C) ​a tan θ 
D) ​a sin θ 
E) ​a csc θ 
A) ​- a sec θ 
B) ​a sec θ 
C) ​a tan θ 
D) ​a sin θ 
E) ​a csc θ

Question 19

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

Accepted Answer

A)      
B)      
C) 7   
D) 3   
E) 3   
A)      
B)      
C) 7   
D) 3   
E) 3

Question 20

Solve the following equation. ​
​   ​

Accepted Answer

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

Simplify the following expression algebraically.

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

Solve the multiple-angle equation.

Use the fundamental identities to simplify the expression.

Find the exact value of the given expression.

Find the exact value of the given expression.

Evaluate the following expression. 4 tan x (arcsin x)

Which of the following expressions is equivalent to 2 - 4 cos²x + 4 cos⁴x?

Use the given values to evaluate (if possible) three trigonometric functions csc x, tan x, cot x.

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x.

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

Which of the following expressions is equivalent to 3 sin² α - 3 sin⁴ α?

Use the cofunction identities to evaluate the expression without using a calculator. Sin²25° + sin²65°

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .Then find sin θ and cos θ.

Use the trigonometric substitution u = a csc θ, where 0 < θ < π/2 and a > 0 to simplify the expression .

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .Then find sin θ and cos θ.

Use the trigonometric substitution u = a tan θ, where 0 < θ < π/2 and to simplify the expression .

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

Solve the following equation.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Simplify the following expression algebraically. ​ ​

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

Solve the multiple-angle equation. ​ ​

Use the fundamental identities to simplify the expression. ​ ​

Find the exact value of the given expression. ​

Find the exact value of the given expression.

Evaluate the following expression. ​ 4 tan x (arcsin x) ​

Which of the following expressions is equivalent to 2 - 4 cos2x + 4 cos4x? ​

Use the given values to evaluate (if possible) three trigonometric functions csc x, tan x, cot x. ​ ​

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x. ​

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

Which of the following expressions is equivalent to 3 sin2 α - 3 sin4 α? ​

Use the cofunction identities to evaluate the expression without using a calculator. ​ Sin225° + sin265° ​

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .Then find sin θ and cos θ.

Use the trigonometric substitution u = a csc θ, where 0 < θ < π/2 and a > 0 to simplify the expression . ​

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .Then find sin θ and cos θ. ​

Use the trigonometric substitution u = a tan θ, where 0 < θ < π/2 and to simplify the expression . ​

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

Solve the following equation. ​ ​ ​

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Simplify the following expression algebraically.

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

Solve the multiple-angle equation.

Use the fundamental identities to simplify the expression.

Find the exact value of the given expression.

Evaluate the following expression. 4 tan x (arcsin x)

Which of the following expressions is equivalent to 2 - 4 cos²x + 4 cos⁴x?

Use the given values to evaluate (if possible) three trigonometric functions csc x, tan x, cot x.

Use the given values to evaluate (if possible) three trigonometric functions cos x, csc x, tan x.

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

Which of the following expressions is equivalent to 3 sin² α - 3 sin⁴ α?

Use the cofunction identities to evaluate the expression without using a calculator. Sin²25° + sin²65°

Use the trigonometric substitution u = a csc θ, where 0 < θ < π/2 and a > 0 to simplify the expression .

Use the trigonometric substitution to rewrite the algebraic expression as a trigonometric function of θ, where .Then find sin θ and cos θ.

Use the trigonometric substitution u = a tan θ, where 0 < θ < π/2 and to simplify the expression .

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

Solve the following equation.