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 given expression algebraically. ​

Accepted Answer

A)    
B)    
C)    
D)    
E) 1 
A)    
B)    
C)    
D)    
E) 1

Question 3

If   , evaluate the following function. ​cot x
​

Accepted Answer

A) ​cot x =     
B) ​cot x =     
C) ​cot x = 2 
D) ​cot x =   
E) ​cot x =   
A) ​cot x =     
B) ​cot x =     
C) ​cot x = 2 
D) ​cot x =   
E) ​cot x =

Question 4

Use a double-angle formula to rewrite the expression. ​
3 - 6 sin2 x
​

Accepted Answer

A) 6 cos x 
B) ​3 sin 2x 
C) ​3 sin x 
D) ​3 cos 2x 
E) ​6 cos 2x 
A) 6 cos x 
B) ​3 sin 2x 
C) ​3 sin x 
D) ​3 cos 2x 
E) ​6 cos 2x

Question 5

Solve the multiple-angle equation. ​   ​

Accepted Answer

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

Question 6

Use a double angle formula to rewrite the given expression.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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 9

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 10

Use the cofunction identities to evaluate the expression below without using calculator. sin220° + sin227° + sin270° + sin263°

Accepted Answer

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

Question 11

Multiply; 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 12

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​
(tan5x + tan7x) sec2x
​

Accepted Answer

A) sec4x tan12x 
B) sec4x tan5x 
C) 7 sec4x tan5x 
D) 5 sec4x tan5x 
E) sec12x tan5x 
A) sec4x tan12x 
B) sec4x tan5x 
C) 7 sec4x tan5x 
D) 5 sec4x tan5x 
E) sec12x tan5x

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

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

Question 15

Evaluate the following expression. ​
4 sec y cos y
​

Accepted Answer

A) 5 
B) 3 
C) 6 
D) 7 
E) 4 
A) 5 
B) 3 
C) 6 
D) 7 
E) 4

Question 16

Write the given expression as an algebraic expression. cos(arccos x - arcsin x)

Accepted Answer

A)    
B)    
C)    
D) 1 
E)    
A)    
B)    
C)    
D) 1 
E)

Question 17

Evaluate the following expression. ​
Cos2 β - sin2 β
​

Accepted Answer

A) 1 + 2 sin2 β 
B) 1 + 2 cos2 β 
C) 2 cos2 β - 1 
D) 2 sin2 β - 1 
E) 1 - 2 cos2 β 
A) 1 + 2 sin2 β 
B) 1 + 2 cos2 β 
C) 2 cos2 β - 1 
D) 2 sin2 β - 1 
E) 1 - 2 cos2 β

Question 18

Solve the multiple-angle equation.

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Which of the following expressions is equivalent to   ? (β ≠ π/2+πn, where n is a whole number) ​

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 given expression algebraically.

If , evaluate the following function. cot x

Use a double-angle formula to rewrite the expression. 3 - 6 sin²x

Solve the multiple-angle equation.

Use a double angle formula to rewrite the given expression.

Find the expression as the tangent of an angle.

Solve the following equation.

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 cofunction identities to evaluate the expression below without using calculator. sin²20° + sin²27° + sin²70° + sin²63°

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

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) (tan⁵x + tan⁷x) sec²x

Write the given expression as the cosine of an angle.

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

Evaluate the following expression. 4 sec y cos y

Write the given expression as an algebraic expression. cos(arccos x - arcsin x)

Evaluate the following expression. Cos² β - sin² β

Solve the multiple-angle equation.

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

Which of the following expressions is equivalent to ? (β ≠ π/2+πn, where n is a whole number)

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 given expression algebraically. ​

If , evaluate the following function. ​cot x ​

Use a double-angle formula to rewrite the expression. ​ 3 - 6 sin2 x ​

Solve the multiple-angle equation. ​ ​

Use a double angle formula to rewrite the given expression.

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

Solve the following equation. ​

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 cofunction identities to evaluate the expression below without using calculator. sin220° + sin227° + sin270° + sin263°

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

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​ (tan5x + tan7x) sec2x ​

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

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

Evaluate the following expression. ​ 4 sec y cos y ​

Write the given expression as an algebraic expression. cos(arccos x - arcsin x)

Evaluate the following expression. ​ Cos2 β - sin2 β ​

Solve the multiple-angle equation.

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

Which of the following expressions is equivalent to ? (β ≠ π/2+πn, where n is a whole number) ​

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 given expression algebraically.

If , evaluate the following function. cot x

Use a double-angle formula to rewrite the expression. 3 - 6 sin²x

Solve the multiple-angle equation.

Find the expression as the tangent of an angle.

Solve the following equation.

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 cofunction identities to evaluate the expression below without using calculator. sin²20° + sin²27° + sin²70° + sin²63°

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

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) (tan⁵x + tan⁷x) sec²x

Write the given expression as the cosine of an angle.

Evaluate the following expression. 4 sec y cos y

Evaluate the following expression. Cos² β - sin² β

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

Which of the following expressions is equivalent to ? (β ≠ π/2+πn, where n is a whole number)