Question 1

Use the cofunction identities to evaluate the expression without using a calculator. ​
Cos235° + cos250° + cos240° + cos255°
​

Accepted Answer

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

Question 2

Find the exact value of the given expression.

Accepted Answer

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

Question 3

Use a graphing utility to graph the function. ​   ​

Accepted Answer

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

Question 4

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​
Cos 3θ + cos 8θ
​

Accepted Answer

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

Question 5

Solve the following equation. ​
Secx - 2 = 0
​

Accepted Answer

A) ​   and   , where n is a integer 
B) ​   and   , where n is a integer 
C) ​   and   , where n is a integer 
D) ​   and   , where n is a integer 
E) ​   and   , where n is a integer 
A) ​   and   , where n is a integer 
B) ​   and   , where n is a integer 
C) ​   and   , where n is a integer 
D) ​   and   , where n is a integer 
E) ​   and   , where n is a integer

Question 6

A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by ​   where y is the distance from equilibrium (in feet) and t is the time (in seconds).
Find the amplitude of the oscillations of the weight.
​

Accepted Answer

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

Question 7

Use the figure to find the exact value of the trigonometric function. ​     ​
Cos 2β
​

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Evaluate the following expression. ​
​   ​

Accepted Answer

A) -6 
B) 6 
C) 4 
D) 5 
E) -5 
A) -6 
B) 6 
C) 4 
D) 5 
E) -5

Question 10

Use the trigonometric substitution u = a sin θ, where - π/2  0 to simplify the expression   . ​

Accepted Answer

A) ​a csc θ 
B) ​a sin θ 
C) ​a tan θ 
D) ​a cos θ 
E) ​- a cos θ 
A) ​a csc θ 
B) ​a sin θ 
C) ​a tan θ 
D) ​a cos θ 
E) ​- a cos θ

Question 11

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

Accepted Answer

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

Question 12

Use a calculator to demonstrate the identity for the value of θ. ​   ​

Accepted Answer

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

Question 13

If x = 5 sin θ, use trigonometric substitution to write   as a trigonometric function of θ, where   .

Accepted Answer

A) ​5 sin θ 
B) ​5 cos θ 
C) ​5 tan θ 
D) ​5 csc θ 
E) ​5 sec θ 
A) ​5 sin θ 
B) ​5 cos θ 
C) ​5 tan θ 
D) ​5 csc θ 
E) ​5 sec θ

Question 14

Multiply; 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 15

Simplify the expression algebraically.   ​

Accepted Answer

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

Question 16

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by   where t is the time (in months), with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.

Accepted Answer

A) April through August 
B) July through May 
C) June through August 
D) April through July 
E) May through July 
A) April through August 
B) July through May 
C) June through August 
D) April through July 
E) May through July

Question 17

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

Accepted Answer

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

Question 18

Solve the following 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 19

Solve the multiple-angle equation. ​   ​

Accepted Answer

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

Question 20

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

Accepted Answer

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

Use the cofunction identities to evaluate the expression without using a calculator. Cos²35° + cos²50° + cos²40° + cos²55°

Find the exact value of the given expression.

Use a graphing utility to graph the function.

Use the sum-to-product formulas to rewrite the sum or difference as a product. Cos 3θ + cos 8θ

Solve the following equation. Secx - 2 = 0

Use the figure to find the exact value of the trigonometric function. Cos 2β

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

Evaluate the following expression.

Use the trigonometric substitution u = a sin θ, where - π/2 < θ < π/2 and a > 0 to simplify the expression .

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

Use a calculator to demonstrate the identity for the value of θ.

If x = 5 sin θ, use trigonometric substitution to write as a trigonometric function of θ, where .

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

Simplify the expression algebraically.

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months), with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.

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

Solve the following equation.

Solve the multiple-angle equation.

Use the half-angle formulas to simplify the expression.

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Exam 2: Analytic-Trigonometry

Use the cofunction identities to evaluate the expression without using a calculator. ​ Cos235° + cos250° + cos240° + cos255° ​

Find the exact value of the given expression.

Use a graphing utility to graph the function. ​ ​

Use the sum-to-product formulas to rewrite the sum or difference as a product. ​ Cos 3θ + cos 8θ ​

Solve the following equation. ​ Secx - 2 = 0 ​

Use the figure to find the exact value of the trigonometric function. ​ ​ Cos 2β ​

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

Evaluate the following expression. ​ ​ ​

Use the trigonometric substitution u = a sin θ, where - π/2 < θ < π/2 and a > 0 to simplify the expression . ​

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

Use a calculator to demonstrate the identity for the value of θ. ​ ​

If x = 5 sin θ, use trigonometric substitution to write as a trigonometric function of θ, where .

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

Simplify the expression algebraically. ​

The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site are approximated by where t is the time (in months), with t = 1 corresponding to January.Determine the months when sales exceed 7700 units at any time during the month.

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

Solve the following equation. ​ ​

Solve the multiple-angle equation. ​ ​

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

Trigonometry

Additional-Topics-In-Trigonometry

Complex-Numbers

Exponential-And-Logarithmic-Functions

Topics-In-Analytic-Geometry

Prerequisites

Filters

Use the cofunction identities to evaluate the expression without using a calculator. Cos²35° + cos²50° + cos²40° + cos²55°

Use a graphing utility to graph the function.

Use the sum-to-product formulas to rewrite the sum or difference as a product. Cos 3θ + cos 8θ

Solve the following equation. Secx - 2 = 0

Use the figure to find the exact value of the trigonometric function. Cos 2β

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

Evaluate the following expression.

Use the trigonometric substitution u = a sin θ, where - π/2 < θ < π/2 and a > 0 to simplify the expression .

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

Use a calculator to demonstrate the identity for the value of θ.

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

Simplify the expression algebraically.

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

Solve the following equation.

Solve the multiple-angle equation.

Use the half-angle formulas to simplify the expression.