Deck 12: Trigonometric Functions

Question 1

Evaluate the given integral.
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Answer 1

Question 2

Evaluate the given integral.
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Answer 2

Question 3

Evaluate the given integral.
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Answer 3

Question 4

Use the sixth Taylor polynomial approximation of ​ ​to obtain an approximation of the given integral. Round your answer to the nearest tenth, if necessary.
​ __________

Question 5

The revenue of McMenamy's Fish Shanty located at a popular summer resort is approximately
​ ​
during the t ^th week ( , which corresponds to the first week of June), where is measured in thousands of dollars. On what week does the restaurant realize the greatest revenue?
​ week number __________

Question 6

Evaluate the given integral.
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Question 7

Evaluate the given integral.
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Question 8

Suppose that the rate of air flow in and out of a person's lungs during respiration is
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liters per second, where is the time in seconds. Find an expression for the volume of air in the person's lungs at any time . Suppose that at the initial moment the volume of air in the person's lungs is 0.

Question 9

Evaluate the given integral.
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Question 10

Evaluate the given integral.
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Question 11

Evaluate the given integral.
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Question 12

Find the area of the region bounded above by the graph of and below by the graph of from to .

Question 13

Evaluate the given integral.
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Question 14

Evaluate the integral.
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Question 15

Evaluate the given integral.
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Question 16

Evaluate the given integral.
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Question 17

The revenue of a certain Fish Shanty, located at a popular summer resort, is approximately
​ ​
during the ^th week ( , which corresponds to the first week of June), where is measured in thousands of dollars. What is the total revenue realized by the restaurant over the 10-wk period starting June 1? $__________

Question 18

Find the area of the region under the graph of the function from to .

Question 19

Suppose that the rate of air flow in and out of a person's lungs during respiration is
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liters per second, where is the time in seconds. What is the average volume of inspired air in the person's lungs during one respiratory cycle?
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Question 20

Evaluate the given integral.
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Question 21

Find the derivative of the function.
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Question 22

Evaluate the trigonometric function.
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Question 23

Find the derivative of the function.
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Question 24

A police cruiser hunting for a suspect pulls over and stops at a point a = 10 ft from a straight wall. The flasher on top of the cruiser revolves at a constant rate of 75°/second, and the light beam casts a spot of light as it strikes the wall. How fast is the spot of light moving along the wall at a point 50 ft from the point on the wall closest to the cruiser?
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Round the answer to the nearest tenth, if necessary.
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__________ ft/sec

Question 25

Find the derivative of the function.
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Question 26

Find the derivative of the function.
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Question 27

Find the derivative of the function.
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Question 28

Find the derivative of the function.
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Question 29

Find all values of θ that satisfy the equation over the interval [0, 2π].
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Question 30

Evaluate the trigonometric function.
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Question 31

Find the derivative of the function.
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Question 32

The wolf population in a certain northern region is estimated to be
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in month , and the caribou population in the same region is given by
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Find the rate of change of each population when . Round your answers to the nearest integer.
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__________ wolves/mo
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__________ caribou/mo

Question 33

Find the equation of the tangent line to the graph of the function at the point .

Question 34

Find the derivative of the function.
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Question 35

Find the derivative of the function.
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Question 36

Find all values of θ that satisfy the equation over the interval [0, 2π].
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Question 37

Find the derivative of the function.
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Question 38

Find the derivative of the function.
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Question 39

The cross section of a drain is a trapezoid, as shown in the figure. The sides and the bottom of the trapezoid are each ​a = 9 ft long. Determine the angle so that the drain will have a maximal cross-sectional area.
​ ​ __________°

Question 40

Find the derivative of the function.
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Question 41

Convert the given angle to degree measure.
​ radians = __________°

Question 42

Convert the given angle to radian measure.
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-470°

Question 43

Find all values of θ that satisfy the equation over the interval [0, 2π].
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Question 44

Determine a positive angle and a negative angle that are coterminal angles of the angle θ. Use degree measure.
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​ ​ ​
Positive angle: __________°
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Negative angle: __________°

Question 45

Convert the given angle to degree measure.
​ radians = __________°

Question 46

Identify the quadrant in which each of the angles lies. Answer 1, 2, 3 or 4.
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220° lies in quadrant __________.
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-100° lies in quadrant __________.
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430° lies in quadrant __________.
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-330° lies in quadrant __________.

Question 47

Verify the identity.
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Question 48

Convert the given angle to radian measure.
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640°

Question 49

Convert the given angle to radian measure.
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​305°

Question 50

Convert the given angle to radian measure.
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80°

Question 51

Identify the quadrant in which each of the angles lies. Answer 1, 2, 3 or 4.
​ radians lies in quadrant __________.
​ radians lies in quadrant __________.
​ radians lies in quadrant __________.
​ radians lies in quadrant __________.

Question 52

Express the angle shown in the diagram in radian measure.
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Question 53

Convert the given angle to degree measure.
​ radians = __________°
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Question 54

Find all values of θ that satisfy the equation over the interval [0, 2π].
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Question 55

Convert the given angle to degree measure.
​ radians = __________°

Question 56

Convert the given angle to degree measure.
​ radians = __________°

Question 57

Verify the identity.
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Question 58

Convert the given angle to radian measure.
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115°

Question 59

Express the angle shown in the diagram in radian measure.
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Question 60

Verify the identity.
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Question 61

Determine a positive angle and a negative angle that are coterminal angles of the angle θ. Use degree measure.
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Positive angle: __________°
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Negative angle: __________°

Question 62

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
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The angle radians lies in the second quadrant.

Question 63

Determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.
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The angle 5,093° lies in the first quadrant.

Question 64

Determine a positive angle and a negative angle that are coterminal angles of the angle θ. Use degree measure.
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Positive angle: __________°
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Negative angle: __________°