Math 1316 Exam 2 Review (Chapters 3 and 4)
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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the corresponding angle measure in radians.
1) 45°
1)
2
1
-2
-1
1
2 r
-1
-2
Convert the degree measure to radians. Leave answer as a multiple of π.
2) -470°
2)
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
3) -13π
3)
Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for π.
4) 83.88°
4)
Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for π.
5) 0.8996
5)
Find the exact value without using a calculator.
-5π
6) tan 6
7) sec 6)
3π
4
7)
Find the length of an arc intercepted by a central angle θ in a circle of radius r. Round your answer to 1 decimal place.
4
8) r = 16.05 cm.; θ = π radians
8)
3
Assume that the cities lie on the same north -south line and that the radius of the earth is 6400 km.
9) Find the distance between City E, 35° N and City F, 44° S. (Round to the nearest
kilometer.)
1
9)
Solve the problem.
10) A pendulum of length 12.1 inches swings 5°37′ to each side of its vertical position. What is
the length (to the nearest hundredth of an inch) of the arc through which the end of the
pendulum swings?
10)
11) A car wheel has a 14-inch radius. Through what angle (to the nearest tenth of a degree)
does the wheel turn when the car rolls forward 3 ft?
11)
12) Two wheels are rotating in such a way that the rotation of the smaller wheel causes the
larger wheel to rotate. The radius of the smaller wheel is 8.8 centimeters and the radius of
the larger wheel is 16.9 centimeters. Through how many degrees (to the nearest hundredth
of a degree) will the larger wheel rotate if the smaller one rotates 180°?
12)
13) A pulley rotates through 57° in one minute. How many rotations (to the nearest tenth of a
rotation) does the pulley make in an hour?
13)
14) Suppose the tip of the minute hand of a clock is 5 in. from the center of the clock.
1
Determine the distance traveled by the tip of the minute hand in 3 hours. Give an exact
2
14)
answer.
15) A center-pivot irrigation system waters a sector-shaped field. Find the area of the field if
the central angle, θ = 44° and the radius, r = 148 meters. Round to the nearest whole
number.
15)
16) Find the measure (in radians) of a central angle of a sector of area 55 square inches in a
circle of radius 8 inches. Round to the nearest hundredth.
16)
The figure shows an angle θ in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of θ.
17) Find cot θ.
17)
- 5 12
, 13 13
2
Find the value of s in the interval [0, π/2] that makes the statement true. Round to four decimal places.
18) cot s = 0.6921
18)
Find the exact value of s in the given interval that has the given circular function value.
3
π
, π ; cos s = - 19)
2
2
Find the exact values of s in the given interval that satisfy the given condition.
3
20) [0, 2π); sin s = 2
Solve the problem.
21) Find ω for a spoke on a bike tire revolving 60 times per minute.
19)
20)
21)
22) A pulley of radius 25 cm rotates 7 times in 4 sec. Find the angular speed of the pulley.
22)
23) A wheel is rotating at 4 radians per sec, and the wheel has a 96-inch diameter. To the
nearest foot per minute, what is the speed of a point on the rim?
23)
Find s. Give an exact answer.
π
24) r = 2 cm, ω = radian per sec, t = 16 sec
5
24)
Graph the function.
25) y = -3 cos x
25)
2
1
26) y = sin x
3
2
27) y = -2 + sin x + 26)
π
2
27)
Graph the function over a one-period interval.
1
2π
28) y = + cos 2x - 2
3
28)
3
Solve the problem.
29) The temperature in Fairbanks is approximated by
T(x) = 37 sin 29)
2π
(x - 101) + 25,
365
where T(x) is the temperature on day x, with x = 1 corresponding to Jan. 1 and x = 365
corresponding to Dec. 31. Estimate the temperature on day 49.
Find the phase shift of the function.
π
30) y = -3 - 2 sin 4x - 3
30)
Find the specified quantity.
31) Find the period of y = -5 cos 1
π
x + .
4
3
32) Find the range of y = -2 + 2 sin 3x + 31)
π
.
6
32)
The function graphed is of the form y = a sin bx or y = a cos bx, where b > 0. Determine the equation of the graph.
33)
33)
6
y
5
4
3
2
1
-1
-2

2

3
2
2
x
-3
-4
-5
Solve the problem.
34) The voltage E in an electrical circuit is given by E = 5.7 cos 110πt, where t is time measured
in seconds. Find the amplitude.
Give the amplitude or period as requested.
1
35) Period of y = 2 cos x
3
34)
35)
4
Match the function with its graph.
36) 1) y = tan x
2) y = cot x
3) y = -tan x
4) y = -cot x
36)
A)
B)
3
-2
y
3
2
2
1
1

-
2
x
-2
-
-1
-1
-2
-2
-3
-3
C)
y

2

2
x
D)
3
-2
y
3
2
2
1
1

-
2
x
-2
-
-1
-1
-2
-2
-3
-3
Write the period, domain and range
37) y = 2 sec x
y
x
37)
5
Match the function with its graph.
38) 1) y = sec x
2) y = csc x
3) y = -sec x
4) y = -csc x
38)
A)
B)
3
-2
y
3
2
2
1
1

-
2
x
-2
-
-1
-1
-2
-2
-3
-3
C)
y

2

2
x
D)
3
-2
y
3
2
2
1
1

-
2
x
-2
-
-1
-1
-2
-2
-3
-3
Find the period.
1
39) y = tan 2x
4
y
x
39)
Write the vertical asymptote
40) y = cot x
40)
6
Answer Key
Testname: MATH 1316 EXAM 2 REVIEW
1)
π
4
2) - 47π
18
3) -2340°
4) 1.4640
5) 51.54°
3
6)
3
7) - 2
8) 67.2 cm
9) 8824 km
10) 2.37 in.
11) 147.3°
12) 93.73°
13) 9.5 rotations
14) 35π in.
15) 8411 m 2
16) 1.72 radians
5
17) - 12
18) 0.9654
5π
19) s = 6
20)
π 2π
, 3 3
21) 120π radians per min
7π
22)
radians per sec
2
23) 960 ft per min
32π
cm
24)
5
25)
y
4
2
-2

-
2
x
-2
-4
7
Answer Key
Testname: MATH 1316 EXAM 2 REVIEW
26)
y
2
1
-2
2
x
-1
-2
27)
3
y
3 x
-3
-3
28)
y
2
1

3
2
3

4
3
x
-1
29) -4°
π
units to the right
30)
12
31) 8π
32) [-4,0]
33) y = 5 sin (2x)
34) 5.7
35) 6π
36) 1C, 2A, 3B, 4D
8
Answer Key
Testname: MATH 1316 EXAM 2 REVIEW
37) Domain: Period: Range: 38) 1C, 2A, 3B, 4D
π
39) 2
40) x = nπ
9