Question 1

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

Accepted Answer

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

Question 2

Which of the following expressions is equivalent to   ? (x ≠ πn, y ≠ πn, where n is a whole number) ​

Accepted Answer

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

Question 3

Use the half-angle formulas to simplify the expression. ​   ​

Accepted Answer

A) ​- |cot x| 
B) ​- |3 tan x| 
C) ​- |3 tan 6x| 
D) ​- |3 cot 3x| 
E) ​- |cot 3x| 
A) ​- |cot x| 
B) ​- |3 tan x| 
C) ​- |3 tan 6x| 
D) ​- |3 cot 3x| 
E) ​- |cot 3x|

Question 4

Use the formula   , where     , to rewrite the trigonometric expression in the form   ​ 9   ​

Accepted Answer

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

Question 5

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

Accepted Answer

A) 16 cos θ 
B) 16 sin θ 
C) 4 sin θ 
D) - 4 sin θ 
E) 4 cos θ 
A) 16 cos θ 
B) 16 sin θ 
C) 4 sin θ 
D) - 4 sin θ 
E) 4 cos θ

Question 6

Which of the following is a solution to the given equation?

Accepted Answer

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

Question 7

Simplify the following expression algebraically. ​   ​

Accepted Answer

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

Question 8

Solve the following equation. ​   ​

Accepted Answer

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

Question 9

Use the product-to-sum formula to write the given product as a sum or difference. ​   ​

Accepted Answer

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

Question 10

Solve the following equation. ​   ​

Accepted Answer

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

Question 11

Evaluate the following expression.(x ≠ (π/8)n, where n is a whole number) ​   ​

Accepted Answer

A) 3 (tan 4x - cot 4x) 
B) -4 (tan 4x - cot 4x) 
C) 3 (tan 4x + cot 4x) 
D) - (tan 4x - cot 4x) 
E) - (tan 4x + cot 4x) 
A) 3 (tan 4x - cot 4x) 
B) -4 (tan 4x - cot 4x) 
C) 3 (tan 4x + cot 4x) 
D) - (tan 4x - cot 4x) 
E) - (tan 4x + cot 4x)

Question 12

Solve the following equation.

Accepted Answer

A) ​   , where n is an integer 
B)    , where n is an integer 
C) ​   , where n is an integer 
D)    , where n is an integer 
E) ​   , where n is an integer 
A) ​   , where n is an integer 
B)    , where n is an integer 
C) ​   , where n is an integer 
D)    , where n is an integer 
E) ​   , where n is an integer

Question 13

Convert the expression. ​   ​

Accepted Answer

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

Question 14

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 15

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

Accepted Answer

A) 1 
B) 2 
C) -1 
D) 0 
E)    
A) 1 
B) 2 
C) -1 
D) 0 
E)

Question 16

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

Accepted Answer

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

Question 17

Use the half-angle formulas to simplify the expression. ​
​   ​

Accepted Answer

A) |sin 5x| 
B) - |sin x| 
C) |sin 10x| 
D) - |sin 5x| 
E) |sin x| 
A) |sin 5x| 
B) - |sin x| 
C) |sin 10x| 
D) - |sin 5x| 
E) |sin x|

Question 18

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 19

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 20

​The equation   has four times the number of solutions in the interval [0, 2π) as the equation   .
​

Accepted Answer

A) True 
 B)False

Find the expression as the sine of an angle.

Which of the following expressions is equivalent to ? (x ≠ πn, y ≠ πn, where n is a whole number)

Use the half-angle formulas to simplify the expression.

Use the formula , where , to rewrite the trigonometric expression in the form 9

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

Which of the following is a solution to the given equation?

Simplify the following expression algebraically.

Solve the following equation.

Use the product-to-sum formula to write the given product as a sum or difference.

Solve the following equation.

Evaluate the following expression.(x ≠ (π/8)n, where n is a whole number)

Solve the following equation.

Convert the expression.

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

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

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

Use the half-angle formulas to simplify the expression.

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

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

The equation has four times the number of solutions in the interval [0, 2π) as the equation .

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

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

Which of the following expressions is equivalent to ? (x ≠ πn, y ≠ πn, where n is a whole number) ​

Use the half-angle formulas to simplify the expression. ​ ​

Use the formula , where , to rewrite the trigonometric expression in the form ​ 9 ​

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

Which of the following is a solution to the given equation?

Simplify the following expression algebraically. ​ ​

Solve the following equation. ​ ​

Use the product-to-sum formula to write the given product as a sum or difference. ​ ​

Solve the following equation. ​ ​

Evaluate the following expression.(x ≠ (π/8)n, where n is a whole number) ​ ​

Solve the following equation.

Convert the expression. ​ ​

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

Use the cofunction identities to evaluate the expression below without the aid of a calculator.

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

Use the half-angle formulas to simplify the expression. ​ ​ ​

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

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

​The equation has four times the number of solutions in the interval [0, 2π) as the equation . ​

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find the expression as the sine of an angle.

Which of the following expressions is equivalent to ? (x ≠ πn, y ≠ πn, where n is a whole number)

Use the half-angle formulas to simplify the expression.

Use the formula , where , to rewrite the trigonometric expression in the form 9

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

Simplify the following expression algebraically.

Solve the following equation.

Use the product-to-sum formula to write the given product as a sum or difference.

Solve the following equation.

Evaluate the following expression.(x ≠ (π/8)n, where n is a whole number)

Convert the expression.

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

Use the half-angle formulas to simplify the expression.

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

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

The equation has four times the number of solutions in the interval [0, 2π) as the equation .