Question 1

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

Accepted Answer

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

Question 2

Evaluate the following expression. ​
2(1 + sin α)(1 - sin α)
​

Accepted Answer

A) -3 sin2 α 
B) 3 cos2 α 
C) -2 cos2 α 
D) 2 sin2 α 
E) 2 cos2 α 
A) -3 sin2 α 
B) 3 cos2 α 
C) -2 cos2 α 
D) 2 sin2 α 
E) 2 cos2 α E

Question 3

Convert the expression. ​   ​

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

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 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

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   . ​   ​

Accepted Answer

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

Question 11

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

Accepted Answer

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

Question 12

Use the sum-to-product formulas to write the given expression as a product. ​
​   ​

Accepted Answer

A) ​​2 sin 4θ cos θ 
B) ​-2 sin 4θ sin θ 
C) -​2 cos 4θ cos θ 
D) ​2 cos 4θ sin θ 
E) ​​2 cos 4θ cos θ 
A) ​​2 sin 4θ cos θ 
B) ​-2 sin 4θ sin θ 
C) -​2 cos 4θ cos θ 
D) ​2 cos 4θ sin θ 
E) ​​2 cos 4θ cos θ

Question 13

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 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

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by   , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for   . ​   ​
​

Accepted Answer

A) 0.05sec, 0.49sec, 0.94sec 
B) 0.05sec, 0.05sec, 0.94sec 
C) -0.40sec, 0.49sec, 0.94sec 
D) -0.40sec, 0.49sec, -0.40sec 
E) 0.05sec, -0.40sec, 0.94sec 
A) 0.05sec, 0.49sec, 0.94sec 
B) 0.05sec, 0.05sec, 0.94sec 
C) -0.40sec, 0.49sec, 0.94sec 
D) -0.40sec, 0.49sec, -0.40sec 
E) 0.05sec, -0.40sec, 0.94sec

Question 16

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

Accepted Answer

A) ​- ​|cos x| 
B) ​|cos x| 
C) ​​|cos 4x| 
D) ​​- |cos 4x| 
E) ​- ​|cos 8x| 
A) ​- ​|cos x| 
B) ​|cos x| 
C) ​​|cos 4x| 
D) ​​- |cos 4x| 
E) ​- ​|cos 8x|

Question 17

Which of the following is a solution to the given equation? ​
Cscx + 2 = 0
​

Accepted Answer

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

Question 18

Use the figure to find the exact value of the trigonometric function. ​
Cot 2θ
​   ​
A = 1, b = 6
​

Accepted Answer

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

Question 19

Simplify the expression algebraically. ​   ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

Find the expression as the tangent of an angle.

Evaluate the following expression. 2(1 + sin α)(1 - sin α)

Convert the expression.

Find the expression as the tangent of an angle.

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

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

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

Find the expression as the cosine of an angle.

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

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

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

Use the sum-to-product formulas to write the given expression as a product.

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

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

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for .

Use the half-angle formulas to simplify the expression.

Which of the following is a solution to the given equation? Cscx + 2 = 0

Use the figure to find the exact value of the trigonometric function. Cot 2θ A = 1, b = 6

Simplify the expression algebraically.

Rewrite the expression as a single logarithm 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

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

Evaluate the following expression. ​ 2(1 + sin α)(1 - sin α) ​

Convert the expression. ​ ​

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

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

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

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

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

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

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

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

Use the sum-to-product formulas to write the given expression as a product. ​ ​ ​

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

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

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for . ​ ​ ​

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

Which of the following is a solution to the given equation? ​ Cscx + 2 = 0 ​

Use the figure to find the exact value of the trigonometric function. ​ Cot 2θ ​ ​ A = 1, b = 6 ​

Simplify the expression algebraically. ​ ​

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

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Find the expression as the tangent of an angle.

Evaluate the following expression. 2(1 + sin α)(1 - sin α)

Convert the expression.

Find the expression as the tangent of an angle.

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

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

Find the expression as the cosine of an angle.

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

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

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

Use the sum-to-product formulas to write the given expression as a product.

A weight is oscillating on the end of a spring (see figure).The position of the weight relative to the point of equilibrium is given by , where y is the displacement (in meters) and t is the time (in seconds).Find the times when the weight is at the point of equilibrium (y = 0) for .

Use the half-angle formulas to simplify the expression.

Which of the following is a solution to the given equation? Cscx + 2 = 0

Use the figure to find the exact value of the trigonometric function. Cot 2θ A = 1, b = 6

Simplify the expression algebraically.

Rewrite the expression as a single logarithm and simplify the result.