Question 1

Evaluate the following expression. ​
4 tan t cot t
​

Accepted Answer

A) 3 
B) 5 
C) 4 
D) 2 
E) 6 
A) 3 
B) 5 
C) 4 
D) 2 
E) 6

Question 2

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 3

Simplify the expression algebraically.   ​

Accepted Answer

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

Question 4

Factor; 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 5

Evaluate the following expression. ​   ​

Accepted Answer

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

Question 6

​Use the figure below to find the exact value of the given trigonometric expression.   ​ ​   10
24
(figure not necessarily to scale)
​

Accepted Answer

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

Question 7

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

Accepted Answer

A) 6   
B)      
C)      
D) 13   
E) 13   
A) 6   
B)      
C)      
D) 13   
E) 13

Question 8

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π). ​   ​

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Evaluate the expression. ​   ​

Accepted Answer

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

Question 11

Using the grid provided, sketch the graph of the given function in the interval (-5, 5) and then determine the x-intercepts, if any.

Accepted Answer

A) (-3,0) and (1,0) 
B) (-2,0) 
C) (-2,0) and (2,0) 
D) no x-intercepts 
E) (-4,0), (0,0), and (4,0) 
A) (-3,0) and (1,0) 
B) (-2,0) 
C) (-2,0) and (2,0) 
D) no x-intercepts 
E) (-4,0), (0,0), and (4,0)

Question 12

Use a graphing utility to select the correct graph of ​   and   in the same viewing window.Use the graphs to determine whether   .Explain your reasoning. ​   ​

Accepted Answer

A) ​   No,   because their graphs are different. 
B) ​   No,   because their graphs are Same. 
C) ​   Yes,   because their graphs are different. 
D) ​   Yes,   because their graphs are same. 
E) ​   No,   because their graphs are different. 
A) ​   No,   because their graphs are different. 
B) ​   No,   because their graphs are Same. 
C) ​   Yes,   because their graphs are different. 
D) ​   Yes,   because their graphs are same. 
E) ​   No,   because their graphs are different.

Question 13

Use the sum-to-product formulas to find the exact value of the given expression. ​
​   ​

Accepted Answer

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

Question 14

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

Accepted Answer

A) 5 sec2x 
B) - 5 cot2x 
C) 5 tan2x 
D) - 5 tan2x 
E) 5 cot2x 
A) 5 sec2x 
B) - 5 cot2x 
C) 5 tan2x 
D) - 5 tan2x 
E) 5 cot2x

Question 15

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

Accepted Answer

A) sin t (2 - 2 csc2t) 
B) cos t (2 csc2t - 2) 
C) cos t (2 - 2 csc2t) 
D) sin t (2 csc2t - 2) 
E) tan t (2 csc2t - 2) 
A) sin t (2 - 2 csc2t) 
B) cos t (2 csc2t - 2) 
C) cos t (2 - 2 csc2t) 
D) sin t (2 csc2t - 2) 
E) tan t (2 csc2t - 2)

Question 16

Find the exact solutions of the given equation in the interval [0, 2π). ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​x = 0 
E) ​   
A) ​   
B) ​   
C) ​   
D) ​x = 0 
E) ​

Question 17

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

Accepted Answer

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

Question 18

Rewrite   as a single logarithm and then simplify the result.

Accepted Answer

A) ​ln |sin θ| 
B) ​ln |tan θ| 
C) ​ln |cos θ| 
D) ​ln |sec θ| 
E) ​ln |csc θ| 
A) ​ln |sin θ| 
B) ​ln |tan θ| 
C) ​ln |cos θ| 
D) ​ln |sec θ| 
E) ​ln |csc θ|

Question 19

Use the figure to find the exact value of the trigonometric function. ​     ​
Sin 2α
​

Accepted Answer

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

Question 20

Use the half-angle formula to simplify the given expression. ​
​   ​

Accepted Answer

A) ​​cos |2x| 
B) ​​cos |8x| 
C) ​​cos |16x| 
D) ​​cos |32x| 
E) ​cos |4x| 
A) ​​cos |2x| 
B) ​​cos |8x| 
C) ​​cos |16x| 
D) ​​cos |32x| 
E) ​cos |4x|

Evaluate the following expression. 4 tan t cot t

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

Simplify the expression algebraically.

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

Evaluate the following expression.

Use the figure below to find the exact value of the given trigonometric expression. 10 24 (figure not necessarily to scale)

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

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).

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

Evaluate the expression.

Using the grid provided, sketch the graph of the given function in the interval (-5, 5) and then determine the x-intercepts, if any.

Use a graphing utility to select the correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning.

Use the sum-to-product formulas to find the exact value of the given expression.

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

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

Find the exact solutions of the given equation in the interval [0, 2π).

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

Rewrite as a single logarithm and then simplify the result.

Use the figure to find the exact value of the trigonometric function. Sin 2α

Use the half-angle formula to simplify the given expression.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Evaluate the following expression. ​ 4 tan t cot t ​

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

Simplify the expression algebraically. ​

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

Evaluate the following expression. ​ ​

​Use the figure below to find the exact value of the given trigonometric expression. ​ ​ 10 24 (figure not necessarily to scale) ​

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

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π). ​ ​

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

Evaluate the expression. ​ ​

Using the grid provided, sketch the graph of the given function in the interval (-5, 5) and then determine the x-intercepts, if any.

Use a graphing utility to select the correct graph of ​ and in the same viewing window.Use the graphs to determine whether .Explain your reasoning. ​ ​

Use the sum-to-product formulas to find the exact value of the given expression. ​ ​ ​

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

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

Find the exact solutions of the given equation in the interval [0, 2π). ​

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

Rewrite as a single logarithm and then simplify the result.

Use the figure to find the exact value of the trigonometric function. ​ ​ Sin 2α ​

Use the half-angle formula to simplify the given expression. ​ ​ ​

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Evaluate the following expression. 4 tan t cot t

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

Simplify the expression algebraically.

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

Evaluate the following expression.

Use the figure below to find the exact value of the given trigonometric expression. 10 24 (figure not necessarily to scale)

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

Use inverse functions where needed to find all solutions of the equation in the interval [0,2π).

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

Evaluate the expression.

Use a graphing utility to select the correct graph of and in the same viewing window.Use the graphs to determine whether .Explain your reasoning.

Use the sum-to-product formulas to find the exact value of the given expression.

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

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

Find the exact solutions of the given equation in the interval [0, 2π).

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

Use the figure to find the exact value of the trigonometric function. Sin 2α

Use the half-angle formula to simplify the given expression.