Deck 8: Trigonometric Functions

Question 1

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

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

Answer 1

angle θ: 45°
Side c:

Question 2

Solve the triangle for the indicated side. ​ ​ ​

A) ​​side h​:
B) ​ ​​​side h​:
C) ​side h​:
D) ​​side h​: ​
E) ​​​​side h​:

Answer 2

​side h​:

Question 3

Find the radian measure of the given angle. ​ ​

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the cosine of θ. ​ ​
​ ​

A) ​
B)
C) ​
D) ​
E) ​

Question 5

Evaluate without using a calculator. ​ ​

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

Question 6

Find the degree measure of the given angle.Round to the nearest tenth. ​ ​​

A) ​80.0°
B) 160.0​°
C) 165.0°​
D) 202.5°
E) 170.0​°

Question 7

A guy wire is stretched from a broadcasting tower at a point 250 feet above the ground to an anchor 150 feet from the base (see figure).How long is the wire? ​ ​ ​

A) 291.55 feet
B) 193.65 feet
C) 150.83 feet
D) 412.31 feet
E) 244.95 feet

Question 8

Determine the quadrant in which lies if sinθ<0 and cosθ>0. ​

A) fourth quadrant
B) third quadrant
C) first quadrant
D) second quadrant
E) second or third quadrants

Question 9

A sector of a circle is the region bounded by two radii of the circle and their intercepted arc (see figure). ​ ​
For a circle of radius r the area A of a sector of the circle with central angle θ (measured in radians)is given by A sprinkler system on a farm is set to spray water over a distance of 70 feet and rotates through an angle of 90°.Use the above given information to find the area of the region.Round your answer to two decimal places.
​

A) 3,848.45
B) 1,225.00
C) 2,348.45
D) 5,348.45
E) 7,696.90

Question 10

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

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

Question 11

Find the cosine of θ. ​ ​ ​

A) ​
B) ​
C)
D) ​
E) ​

Question 12

Evaluate without using a calculator,leaving the answers in exact form. ​ ​

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

Question 13

A compact disc can have an angular speed up to 3,154 radians per minute.At this angular speed,how many revolutions per minute would the CD make? Round your answer to the nearest integer. ​

A) 1,004
B) 1,577
C) 402
D) 502
E) 251

Question 14

From the given function ,find the following trigonometric function. ​ ​

A)
B)
C)
D)
E)

Question 15

Find given that and ​

A)
B)
C)
D)
E)

Question 16

Find from the given graph. ​ ​ ​
​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 17

Find the radian measure of the given angle. ​ ​

A)
B)
C)
D)
E)

Question 18

Solve the triangle for the indicated angle. ​ ​
​ ​

A) ​angle θ: 53​°
B) ​​angle θ: 42°
C) ​​angle θ:​ 56°
D) ​​angle θ:​ 37°
E) ​​angle θ:​ 27°

Question 19

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

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

Question 20

Find the cosine of θ. ​ ​ ​

A)
B)
C) ​
D) ​
E) ​

Question 21

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

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

Question 22

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. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 23

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. ​ ​

A)
B)
C) ​
D) ​​
E) ​ ​

Question 24

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

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

Question 25

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. ​ ​ ​

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

Question 26

Evaluate without using a calculator,leaving the answers in exact form. ​ ​

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

Question 27

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

A)
B)
C)
D)
E)

Question 28

Find the period of the trigonometric function. ​ ​

A)
B)
C)
D)
E)

Question 29

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. ​ ​

A)
B) ​
C) ​
D) ​
E) ​ ​

Question 30

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. ​ ​ ​

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

Question 31

Match the function below with the correct graph. ​ ​

A) ​
B) ​
C) ​
D) ​
E) ​

Question 32

Find the derivative of the trigonometric function. ​ ​

A)
B)
C)
D)
E)

Question 33

Find a and d for such that the graph of f matches the figure. ​ ​

A)
B)
C)
D)
E)

Question 34

Sketch the graph of the function ​

A) ​
​
B) ​ ​
C) ​ ​
D) ​ ​
E) ​

Question 35

Sketch the graph of the function ​

A) ​
B) ​
C) ​
D) ​ ​
E) ​

Question 36

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

A)
B)
C)
D)
E)

Question 37

Find the period and amplitude of the function ​ ​

A) period: ; amplitude:
B) period: ; amplitude: 3
C) period: ; amplitude: 3
D) period: ; amplitude: 6
E) period: ; amplitude: 3

Question 38

Find the period and amplitude of the function ​ ​

A) Period: 2π; Amplitude: 3
B) Period: 2π; Amplitude:
C) Period: 2; Amplitude:
D) Period: 4; Amplitude: 3
E) Period: 4; Amplitude:

Question 39

Sketch the graph of the function

A) ​
B) ​
C) ​
D) ​ ​
E) ​ ​

Question 40

Find the period of the trigonometric function. ​ ​

A)
B) 6
C)
D)
E)

Question 41

The average monthly precipitation P (in inches),including rain,snow,and ice,for Sacramento,California can be modeled by ​ , ​
Where t is the time (in months),with corresponding to January.Find the total annual precipitation for Sacramento.
​

A) 18.02 in.
B) 17.69 in.
C) 14.52 in.
D) 16.57 in.
E) 18.90 in.

Question 42

Find the indefinite integral of ​

A)
B)
C)
D)
E)

Question 43

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

A)
B)
C)
D)
E)

Question 44

Find the derivative of the function. ​ ​

A)
B) ​
C)
D)
E)

Question 45

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

A)
B)
C)
D)
E)

Question 46

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. ​

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

Question 47

Suppose that the numbers W (in thousands)of construction workers employed in the United States during 2006 can be modeled by where t is the time in months,with corresponding to January 1.Approximate the month t in which the number of construction workers employed was a maximum.What was the maximum number of construction workers employed? Round your answer to nearest whole number. ​

A) May; The maximum number of construction workers employed is 9,059.
B) March; The maximum number of construction workers employed is 9,039.
C) April; The maximum number of construction workers employed is 9,039.
D) March; The maximum number of construction workers employed is 9,049.
E) April; The maximum number of construction workers employed is 9,049.

Question 48

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

A)
B)
C)
D)
E)

Question 49

Find the indefinite integral. ​ ​

A)
B)
C)
D)
E)

Question 50

Find the derivative of the function. ​ ​

A)
B)
C)
D)
E)

Question 51

Evaluate the definite integral. ​ ​

A) -5
B) ​7
C) 0
D) undefined
E) 10

Question 52

The normal average daily temperature in degrees Fahrenheit for a city is given by where t is the time in days,with corresponding to January 1.Find the warmest day. ​

A) March 16
B) March 14
C) April 16
D) April 15
E) April 14

Question 53

Find the indefinite integral of the following function. ​ ​

A)
B)
C)
D)
E)

Question 54

Determine the relative extrema of the function on the interval ​ ​

A) relative minimum:
Relative maximum:
B) relative minimum:
Relative maximum:
C) relative minimum:
​relative maximum:
D) relative minimum:
Relative maximum:
E) relative minimum:
Relative maximum:

Question 55

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

A)
B)
C)
D)
E)

Question 56

Determine the relative extrema of the function on the interval ​

A) relative minimum:
Relative maximum:
B) relative minimum:
Relative maximum:
C) relative minimum:
Relative maximum:
D) relative minimum:
Relative maximum:
E) relative minimum:
Relative maximum:

Question 57

Find the indefinite integral of the following function. ​ ​

A)
B)
C)
D)
E)

Question 58

Find the indefinite integral. ​ ​

A)
B)
C)
D)
E)

Question 59

Evaluate the definite integral ​

A) 9
B) -9
C)
D)
E) ∞

Question 60

Find the indefinite integral of ​

A)
B)
C)
D)
E)