Question 1

Simplify the following expression algebraically. ​   ​

Accepted Answer

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

Question 2

Use a double-angle formula to find the exact value of cos2u when ​

Accepted Answer

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

Question 3

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 4

Simplify the expression algebraically. ​   ​

Accepted Answer

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

Question 5

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 6

Which of the following expressions is equivalent to   ? (x ≠ (π/3)n, where n is a whole number) ​

Accepted Answer

A) -3 sec x - sin x 
B) csc 3x - sin 3x 
C) csc 3x + sin 3x 
D) -3 csc x + sin x 
E) - csc x -3 sin x 
A) -3 sec x - sin x 
B) csc 3x - sin 3x 
C) csc 3x + sin 3x 
D) -3 csc x + sin x 
E) - csc x -3 sin x

Question 7

Find the rate of change of the function   . ​

Accepted Answer

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

Question 8

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

Accepted Answer

A) 6 sin θ 
B)    
C)    
D)    
E) 6 cos θ 
A) 6 sin θ 
B)    
C)    
D)    
E) 6 cos θ

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

A) 4 tan θ 
B) 16 sec θ 
C) - 4 tan θ 
D) 4 sec θ 
E) 16 tan θ 
A) 4 tan θ 
B) 16 sec θ 
C) - 4 tan θ 
D) 4 sec θ 
E) 16 tan θ

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

Accepted Answer

A) 4 sin θ 
B) - 4 cos θ 
C) 4 cos θ 
D) 16 sin θ 
E) 16 cos θ 
A) 4 sin θ 
B) - 4 cos θ 
C) 4 cos θ 
D) 16 sin θ 
E) 16 cos θ

Question 13

Use the cofunction identities to evaluate the expression without using a calculator. ​
Tan273° + cot214° - sec276° - csc217°
​

Accepted Answer

A) 3 
B) 1 
C) -1 
D) -2 
E) 2 
A) 3 
B) 1 
C) -1 
D) -2 
E) 2

Question 14

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

Accepted Answer

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

Question 15

Solve the following equation. ​   ​

Accepted Answer

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

Question 16

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 17

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

Accepted Answer

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

Question 18

Evaluate the following expression. ​   ​

Accepted Answer

A) 3 
B) - 2 
C) 2 
D) -3 
E) 0 
A) 3 
B) - 2 
C) 2 
D) -3 
E) 0

Question 19

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

Accepted Answer

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

Question 20

Evaluate the following expression. ​
Cot2t (2 sec2t - 2)
​

Accepted Answer

A) 2 
B) 0 
C) 3 
D) 4 
E) 1 
A) 2 
B) 0 
C) 3 
D) 4 
E) 1

Simplify the following expression algebraically.

Use a double-angle formula to find the exact value of cos2u when

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

Simplify the expression algebraically.

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

Which of the following expressions is equivalent to ? (x ≠ (π/3)n, where n is a whole number)

Find the rate of change of the function .

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

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

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

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

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

Use the cofunction identities to evaluate the expression without using a calculator. Tan²73° + cot²14° - sec²76° - csc²17°

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

Solve the following equation.

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

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

Evaluate the following expression.

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

Evaluate the following expression. Cot²t (2 sec²t - 2)

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Simplify the following expression algebraically. ​ ​

Use a double-angle formula to find the exact value of cos2u when ​

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

Simplify the expression algebraically. ​ ​

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

Which of the following expressions is equivalent to ? (x ≠ (π/3)n, where n is a whole number) ​

Find the rate of change of the function . ​

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

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

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

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

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

Use the cofunction identities to evaluate the expression without using a calculator. ​ Tan273° + cot214° - sec276° - csc217° ​

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

Solve the following equation. ​ ​

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

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

Evaluate the following expression. ​ ​

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

Evaluate the following expression. ​ Cot2t (2 sec2t - 2) ​

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Simplify the following expression algebraically.

Use a double-angle formula to find the exact value of cos2u when

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

Simplify the expression algebraically.

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

Which of the following expressions is equivalent to ? (x ≠ (π/3)n, where n is a whole number)

Find the rate of change of the function .

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

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

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

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

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

Use the cofunction identities to evaluate the expression without using a calculator. Tan²73° + cot²14° - sec²76° - csc²17°

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

Solve the following equation.

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

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

Evaluate the following expression.

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

Evaluate the following expression. Cot²t (2 sec²t - 2)