Question 1

Solve the following equation. ​   ​

Accepted Answer

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

Question 2

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​
Tan7x sec2x - tan7x
​

Accepted Answer

A) 9 tan9x 
B) tan2x 
C) tan9x 
D) 7 tan7x 
E) tan7x 
A) 9 tan9x 
B) tan2x 
C) tan9x 
D) 7 tan7x 
E) tan7x

Question 3

Find the exact value of the given expression.

Accepted Answer

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

Question 4

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 5

Evaluate the expression. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) 0 
A)    
B)    
C)    
D)    
E) 0

Question 6

Simplify the expression algebraically. ​   ​

Accepted Answer

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

Question 7

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 8

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

Accepted Answer

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

Question 9

Perform the multiplication and use the fundamental identities to simplify. ​   ​

Accepted Answer

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

Question 10

Write the given expression as the sine of an angle.

Accepted Answer

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

Question 11

Evaluate the following expression.(x ≠ (π/5)n, where n is a whole number) ​
Csc 5x - sin 5x
​

Accepted Answer

A) cos 5x cot 5x 
B) - 5 sin 5x cot 5x 
C) - 5 cos 5x cot 5x 
D) sin 5x csc 5x 
E) 5 sin x cot x 
A) cos 5x cot 5x 
B) - 5 sin 5x cot 5x 
C) - 5 cos 5x cot 5x 
D) sin 5x csc 5x 
E) 5 sin x cot x

Question 12

Use the fundamental identities to simplify the expression. ​
Cot θ sec θ
​

Accepted Answer

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

Question 13

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

Accepted Answer

A) - 2 tan t 
B) 2 tan t 
C) 2 sin t 
D) - 2 cot t 
E) 2 cot t 
A) - 2 tan t 
B) 2 tan t 
C) 2 sin t 
D) - 2 cot t 
E) 2 cot t

Question 14

Solve the following equation. ​   ​

Accepted Answer

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

Question 15

Solve the multiple-angle 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 16

If x = 3 cot θ, use trigonometric substitution to write   as a trigonometric function of θ, where   . ​

Accepted Answer

A) ​3 sec θ 
B) ​3 csc θ 
C) ​3 cos θ 
D) ​3 sin θ 
E) ​3 cot θ 
A) ​3 sec θ 
B) ​3 csc θ 
C) ​3 cos θ 
D) ​3 sin θ 
E) ​3 cot θ

Question 17

Convert the expression. ​   ​

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

Question 19

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

Accepted Answer

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

Question 20

The forces acting on an object weighing W units on an inclined plane positioned at an angle of θ with the horizontal (see figure) are modeled by ​   ​
Where μ is the coefficient of friction.Solve the equation for μ and simplify the result.
​   ​

Accepted Answer

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

Solve the following equation.

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) Tan⁷x sec²x - tan⁷x

Find the exact value of the given expression.

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

Evaluate the expression.

Simplify the expression algebraically.

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

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

Perform the multiplication and use the fundamental identities to simplify.

Write the given expression as the sine of an angle.

Evaluate the following expression.(x ≠ (π/5)n, where n is a whole number) Csc 5x - sin 5x

Use the fundamental identities to simplify the expression. Cot θ sec θ

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

Solve the following equation.

Solve the multiple-angle equation.

If x = 3 cot θ, use trigonometric substitution to write as a trigonometric function of θ, where .

Convert the expression.

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

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

The forces acting on an object weighing W units on an inclined plane positioned at an angle of θ with the horizontal (see figure) are modeled by Where μ is the coefficient of friction.Solve the equation for μ and simplify the result.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Solve the following equation. ​ ​

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) ​ Tan7x sec2x - tan7x ​

Find the exact value of the given expression.

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

Evaluate the expression. ​ ​

Simplify the expression algebraically. ​ ​

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

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

Perform the multiplication and use the fundamental identities to simplify. ​ ​

Write the given expression as the sine of an angle.

Evaluate the following expression.(x ≠ (π/5)n, where n is a whole number) ​ Csc 5x - sin 5x ​

Use the fundamental identities to simplify the expression. ​ Cot θ sec θ ​

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

Solve the following equation. ​ ​

Solve the multiple-angle equation. ​

If x = 3 cot θ, use trigonometric substitution to write as a trigonometric function of θ, where . ​

Convert the expression. ​ ​

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

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

The forces acting on an object weighing W units on an inclined plane positioned at an angle of θ with the horizontal (see figure) are modeled by ​ ​ Where μ is the coefficient of friction.Solve the equation for μ and simplify the result. ​ ​

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Solve the following equation.

Evaluate the following expression.(x ≠ π/2+πn, where n is a whole number) Tan⁷x sec²x - tan⁷x

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

Evaluate the expression.

Simplify the expression algebraically.

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

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

Perform the multiplication and use the fundamental identities to simplify.

Evaluate the following expression.(x ≠ (π/5)n, where n is a whole number) Csc 5x - sin 5x

Use the fundamental identities to simplify the expression. Cot θ sec θ

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

Solve the following equation.

Solve the multiple-angle equation.

If x = 3 cot θ, use trigonometric substitution to write as a trigonometric function of θ, where .

Convert the expression.

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

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

The forces acting on an object weighing W units on an inclined plane positioned at an angle of θ with the horizontal (see figure) are modeled by Where μ is the coefficient of friction.Solve the equation for μ and simplify the result.