Question 1

Use a calculator to evaluate the trigonometric function   to four decimal places. ​

Accepted Answer

A)  -1.6266 
B)  -1.4281 
C)  -0.6148 
D)  0.8192 
E)  -0.7002 
A)  -1.6266 
B)  -1.4281 
C)  -0.6148 
D)  0.8192 
E)  -0.7002

Question 2

Find the derivative of the function. ​   ​

Accepted Answer

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

Question 3

Solve the equation for θ   For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results. ​   ​

Accepted Answer

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

Question 4

Solve the equation below for θ   For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results. ​   ​

Accepted Answer

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

Question 5

Find two values of θ that satisfy the equation below.Give values of θ in radians   Do not use a calculator. ​   ​

Accepted Answer

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

Question 6

Find the derivative of the function   and simplify your answer by using the trigonometric identities. ​

Accepted Answer

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

Question 7

Determine two coterminal angles (one positive and one negative)for each angle.Give the answers in radians. ​     ​

Accepted Answer

A)  ​​positive:  
Negative:   
B)  ​​positive:  
Negative:   
C)  positive:   ​​
Negative:   
D)  ​​positive:  
Negative:   
E)  ​​positive:  
Negative:   
A)  ​​positive:  
Negative:   
B)  ​​positive:  
Negative:   
C)  positive:   ​​
Negative:   
D)  ​​positive:  
Negative:   
E)  ​​positive:  
Negative:

Question 8

Find   from the given graph. ​   ​   ​
​

Accepted Answer

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

Question 9

Solve the triangle for the indicated side and angle. ​   a = 5,b = 5,   ​

Accepted Answer

A)  angle θ: 45°
Side c:   
B)  angle θ: 45°
Side c:   
C)  angle θ: 45°
Side c: 20 
D)  angle θ: 30°
Side c: 10 
E)  angle θ: 30°
Side c:20 
A)  angle θ: 45°
Side c:   
B)  angle θ: 45°
Side c:   
C)  angle θ: 45°
Side c: 20 
D)  angle θ: 30°
Side c: 10 
E)  angle θ: 30°
Side c:20

Question 10

A 22-foot ladder leaning against the side of a house makes a 77° angle with the ground (see figure).How far up the side of the house does the ladder reach? Round your answer to four decimal places. ​   ​   ​

Accepted Answer

A)  21.4361 feet 
B)  22.5787 feet 
C)  4.9489 feet 
D)  5.0791 feet 
E)  97.7991 feet 
A)  21.4361 feet 
B)  22.5787 feet 
C)  4.9489 feet 
D)  5.0791 feet 
E)  97.7991 feet

Question 11

Find the period of the trigonometric function. ​   ​

Accepted Answer

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

Question 12

Use integration by parts to find the indefinite integral. ​   ​

Accepted Answer

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

Question 13

For a person at rest,the velocity v (in liters per second)of air flow into and out of the lungs during a respiratory cycle is given by   ,where t is the time in seconds.Inhalation occurs when   and exhalation occurs when   Find the time for one full respiratory cycle. ​

Accepted Answer

A)    seconds 
B)    seconds 
C)  6 seconds 
D)    seconds 
E)  3 seconds 
A)    seconds 
B)    seconds 
C)  6 seconds 
D)    seconds 
E)  3 seconds

Question 14

Find the derivative of the trigonometric function. ​   ​

Accepted Answer

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

Question 15

Solve the equation below for   For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results. ​   ​

Accepted Answer

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

Question 16

Sketch the graph of the function   ​

Accepted Answer

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

Question 17

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive 13 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.Round your answer to two decimal places. ​   ​   ​

Accepted Answer

A)  51.64 miles 
B)  8.18 miles 
C)  1.58 miles 
D)  1.30 miles 
E)  16.36 miles 
A)  51.64 miles 
B)  8.18 miles 
C)  1.58 miles 
D)  1.30 miles 
E)  16.36 miles

Question 18

Find the derivative of the function and simplify your answer by using the trigonometric identities ​   ​

Accepted Answer

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

Question 19

Approximate using a calculator (set for radians).Round answers to two decimal places. ​   ​

Accepted Answer

A)  -0.65 
B)  -0.76 
C)  -0.99 
D)  0.15 
E)  0.35 
A)  -0.65 
B)  -0.76 
C)  -0.99 
D)  0.15 
E)  0.35

Question 20

Find the area of the equilateral triangle with sides of length   in.Round your answer to two decimal places. ​

Accepted Answer

A)  55.43 square inches 
B)  16.00 square inches 
C)  27.71 square inches 
D)  32.00 square inches 
E)  45.25 square inches 
A)  55.43 square inches 
B)  16.00 square inches 
C)  27.71 square inches 
D)  32.00 square inches 
E)  45.25 square inches

Use a calculator to evaluate the trigonometric function to four decimal places.

Find the derivative of the function.

Solve the equation for θ For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results.

Solve the equation below for θ For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results.

Find two values of θ that satisfy the equation below.Give values of θ in radians Do not use a calculator.

Find the derivative of the function and simplify your answer by using the trigonometric identities.

Determine two coterminal angles (one positive and one negative)for each angle.Give the answers in radians.

Find from the given graph.

Solve the triangle for the indicated side and angle. a = 5,b = 5,

A 22-foot ladder leaning against the side of a house makes a 77° angle with the ground (see figure).How far up the side of the house does the ladder reach? Round your answer to four decimal places.

Find the period of the trigonometric function.

Use integration by parts to find the indefinite integral.

For a person at rest,the velocity v (in liters per second)of air flow into and out of the lungs during a respiratory cycle is given by ,where t is the time in seconds.Inhalation occurs when and exhalation occurs when Find the time for one full respiratory cycle.

Find the derivative of the trigonometric function.

Solve the equation below for For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results.

Sketch the graph of the function

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive 13 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.Round your answer to two decimal places.

Find the derivative of the function and simplify your answer by using the trigonometric identities

Approximate using a calculator (set for radians).Round answers to two decimal places.

Find the area of the equilateral triangle with sides of length in.Round your answer to two decimal places.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 8: Trigonometric Functions

Use a calculator to evaluate the trigonometric function to four decimal places. ​

Find the derivative of the function. ​ ​

Solve the equation for θ For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results. ​ ​

Solve the equation below for θ For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results. ​ ​

Find two values of θ that satisfy the equation below.Give values of θ in radians Do not use a calculator. ​ ​

Find the derivative of the function and simplify your answer by using the trigonometric identities. ​

Determine two coterminal angles (one positive and one negative)for each angle.Give the answers in radians. ​ ​

Find from the given graph. ​ ​ ​ ​

Solve the triangle for the indicated side and angle. ​ a = 5,b = 5, ​

A 22-foot ladder leaning against the side of a house makes a 77° angle with the ground (see figure).How far up the side of the house does the ladder reach? Round your answer to four decimal places. ​ ​ ​

Find the period of the trigonometric function. ​ ​

Use integration by parts to find the indefinite integral. ​ ​

For a person at rest,the velocity v (in liters per second)of air flow into and out of the lungs during a respiratory cycle is given by ,where t is the time in seconds.Inhalation occurs when and exhalation occurs when Find the time for one full respiratory cycle. ​

Find the derivative of the trigonometric function. ​ ​

Solve the equation below for For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results. ​ ​

Sketch the graph of the function ​

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive 13 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.Round your answer to two decimal places. ​ ​ ​

Find the derivative of the function and simplify your answer by using the trigonometric identities ​ ​

Approximate using a calculator (set for radians).Round answers to two decimal places. ​ ​

Find the area of the equilateral triangle with sides of length in.Round your answer to two decimal places. ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Use a calculator to evaluate the trigonometric function to four decimal places.

Find the derivative of the function.

Solve the equation for θ For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results.

Solve the equation below for θ For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results.

Find two values of θ that satisfy the equation below.Give values of θ in radians Do not use a calculator.

Find the derivative of the function and simplify your answer by using the trigonometric identities.

Determine two coterminal angles (one positive and one negative)for each angle.Give the answers in radians.

Find from the given graph.

Solve the triangle for the indicated side and angle. a = 5,b = 5,

A 22-foot ladder leaning against the side of a house makes a 77° angle with the ground (see figure).How far up the side of the house does the ladder reach? Round your answer to four decimal places.

Find the period of the trigonometric function.

Use integration by parts to find the indefinite integral.

For a person at rest,the velocity v (in liters per second)of air flow into and out of the lungs during a respiratory cycle is given by ,where t is the time in seconds.Inhalation occurs when and exhalation occurs when Find the time for one full respiratory cycle.

Find the derivative of the trigonometric function.

Solve the equation below for For some of the equations you should use the trigonometric identities listed in this section.Use the trace feature of a graphing utility to verify your results.

Sketch the graph of the function

In traveling across flat land,you notice a mountain directly in front of you.Its angle of elevation (to the peak)is 3.5°.After you drive 13 miles closer to the mountain,the angle of elevation is 9°.Approximate the height of the mountain.Round your answer to two decimal places.

Find the derivative of the function and simplify your answer by using the trigonometric identities

Approximate using a calculator (set for radians).Round answers to two decimal places.

Find the area of the equilateral triangle with sides of length in.Round your answer to two decimal places.