Question 1

Convert the expression. ​   ​
​

Accepted Answer

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

Question 2

Solve the following equation. ​   ​

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

Use the cofunction identities to evaluate the expression without using a calculator. ​
Cos265° + cos225°
​

Accepted Answer

A) 3 
B) 4 
C) -3 
D) -1 
E) 1 
A) 3 
B) 4 
C) -3 
D) -1 
E) 1

Question 5

Rewrite   as a single logarithm and then simplify the result. ​

Accepted Answer

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

Question 6

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

Accepted Answer

A) - 6 tan x 
B) 6 sec x 
C) 6 tan x 
D) - 6 sec x 
E) 6 cot x 
A) - 6 tan x 
B) 6 sec x 
C) 6 tan x 
D) - 6 sec x 
E) 6 cot x

Question 7

The horizontal distance d (in feet) traveled by a projectile with an initial speed of v feet per second is modeled by   , where θ is the angle at which the projectile is launched.
Find the horizontal distance traveled by a golf ball that is hit with an initial speed of 80 feet per second when the ball is hit at an angle of   .Round to the nearest foot.

Accepted Answer

A) 260 
B) 346 
C) 173 
D) 303 
E) 87 
A) 260 
B) 346 
C) 173 
D) 303 
E) 87

Question 8

Solve the following equation. ​   ​

Accepted Answer

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

Question 9

Write the given expression as the tangent of an angle.

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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

Accepted Answer

A) 2 cos θ 
B) 36 sin θ 
C) - 2 sin θ 
D) 36 cos θ 
E) 6 sin θ 
A) 2 cos θ 
B) 36 sin θ 
C) - 2 sin θ 
D) 36 cos θ 
E) 6 sin θ

Question 12

Solve the following equation. ​   ​

Accepted Answer

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

Question 13

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

Accepted Answer

A) ​ y = cos x
2
- 2π  
2 π  
- 2
​ 
B) ​ y = sin x
2
- 2π  
2π  
- 2 
C) ​ y = csc x
4
- 2π  
2π  
- 4 
D) ​ y = cot x
4
- 2π  
2π  
- 4 
E) ​ y = tan x
4
- 2π  
2π  
- 4 
A) ​ y = cos x
2
- 2π  
2 π  
- 2
​ 
B) ​ y = sin x
2
- 2π  
2π  
- 2 
C) ​ y = csc x
4
- 2π  
2π  
- 4 
D) ​ y = cot x
4
- 2π  
2π  
- 4 
E) ​ y = tan x
4
- 2π  
2π  
- 4

Question 14

Evaluate the following expression.(x ≠ πn, y ≠ π/12 + πn, where n is a whole number) ​   ​

Accepted Answer

A) 7 tan 6x + 7 cot 6y 
B) 7 tan 6y - 7 cot 6x 
C) 7 tan 6y + 7 cot 6x 
D) - (7 tan 6y + 7 cot 6x) 
E) 7 tan 6x - 7 cot 6y 
A) 7 tan 6x + 7 cot 6y 
B) 7 tan 6y - 7 cot 6x 
C) 7 tan 6y + 7 cot 6x 
D) - (7 tan 6y + 7 cot 6x) 
E) 7 tan 6x - 7 cot 6y

Question 15

Simplify the expression algebraically. ​   ​

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

Use the half-angle formulas to determine the exact value of the given trigonometric expression. ​
​   ​

Accepted Answer

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

Question 18

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 19

Evaluate the following expression.(x ≠ (π + 2πn)/10, where n is a whole number) ​
Sec 5x - cos 5x
​

Accepted Answer

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

Question 20

Simplify the given expression algebraically.

Accepted Answer

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

Convert the expression.

Solve the following equation.

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

Use the cofunction identities to evaluate the expression without using a calculator. Cos²65° + cos²25°

Rewrite as a single logarithm and then simplify the result.

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

Solve the following equation.

Write the given expression as the tangent of an angle.

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

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

Solve the following equation.

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

Evaluate the following expression.(x ≠ πn, y ≠ π/12 + πn, where n is a whole number)

Simplify the expression algebraically.

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

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Use a graphing utility to graph the function.

Evaluate the following expression.(x ≠ (π + 2πn)/10, where n is a whole number) Sec 5x - cos 5x

Simplify the given expression algebraically.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Convert the expression. ​ ​ ​

Solve the following equation. ​ ​

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

Use the cofunction identities to evaluate the expression without using a calculator. ​ Cos265° + cos225° ​

Rewrite as a single logarithm and then simplify the result. ​

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

Solve the following equation. ​ ​

Write the given expression as the tangent of an angle.

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

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

Solve the following equation. ​ ​

Use a graphing utility to determine which of the trigonometric functions is equal to the following expression.

Evaluate the following expression.(x ≠ πn, y ≠ π/12 + πn, where n is a whole number) ​ ​

Simplify the expression algebraically. ​ ​

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

Use the half-angle formulas to determine the exact value of the given trigonometric expression. ​ ​ ​

Use a graphing utility to graph the function. ​ ​

Evaluate the following expression.(x ≠ (π + 2πn)/10, where n is a whole number) ​ Sec 5x - cos 5x ​

Simplify the given expression algebraically.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Convert the expression.

Solve the following equation.

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

Use the cofunction identities to evaluate the expression without using a calculator. Cos²65° + cos²25°

Rewrite as a single logarithm and then simplify the result.

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

Solve the following equation.

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

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

Solve the following equation.

Evaluate the following expression.(x ≠ πn, y ≠ π/12 + πn, where n is a whole number)

Simplify the expression algebraically.

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

Use the half-angle formulas to determine the exact value of the given trigonometric expression.

Use a graphing utility to graph the function.

Evaluate the following expression.(x ≠ (π + 2πn)/10, where n is a whole number) Sec 5x - cos 5x