MATH 1316
Review for Test 2
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the right triangle. If two sides are given, give angles in degrees and minutes.
1)
1)
A = 11° 32 , c = 213 ft
Round side lengths to two decimal places.
Solve the right triangle.
2) a = 2.6 cm, b = 1.3 cm, C = 90°
Round values to one decimal place.
2)
Solve the problem.
3) On a sunny day, a flag pole and its shadow form the sides of a right triangle. If the
hypotenuse is 35 meters long and the shadow is 28 meters, how tall is the flag pole?
3)
4) To measure the width of a river, a surveyor starts at point A on one bank and walks 74
feet down the river to point B. He then measures the angle ABC to be 25°36'14''. Estimate
the width of the river to the nearest foot. See the figure below.
C
A
74 ft
4)
B
An observer for a radar station is located at the origin of a coordinate system. For the point given, find the bearing of an
airplane located at that point. Express the bearing using both methods.
5) ( , -7)
5)
Solve the problem.
6) A fire is sighted due west of lookout A. The bearing of the fire from lookout B, 14.1 miles
due south of A, is N 32°57'W. How far is the fire from B (to the nearest tenth of a mile)?
1
6)
7) Find h as indicated in the figure. Round to the nearest foot.
24.2°
7)
56.5°
131 ft
8) A person is watching a car from the top of a building. The car is traveling on a straight
road directly toward the building. When first noticed, the angle of depression to the car is
26° 53 . When the car stops, the angle of depression is 42° 31 . The building is 240 feet tall.
How far did the car travel from when it was first noticed until it stopped? Round to the
nearest foot.
Convert the degree measure to radians. Leave answer as a multiple of .
9) 510°
Convert the radian measure to degrees. Round to the nearest hundredth if necessary.
9
10) 6
Convert the degree measure to radians, correct to four decimal places. Use 3.1416 for .
11) -160°41
8)
9)
10)
11)
Convert the radian measure to degrees. Give answer using decimal degrees to the nearest hundredth. Use 3.1416 for .
12) 0.8996
12)
Find the exact value without using a calculator.
5
13) sin
3
14) cot
13)
-5
6
14)
Solve the problem.
15) A circular pulley is rotating about its center. Through how many radians would it turn in
22 rotations?
Find the length of an arc intercepted by a central angle
16) r = 115.19 in.; = 195°
15)
in a circle of radius r. Round your answer to 1 decimal place.
16)
2
17) r = 16.12 ft;
=
11
17)
radians
Assume that the cities lie on the same north-south line and that the radius of the earth is 6400 km.
18) Find the distance between City A, 34° N and City B, 37° N. (Round to the nearest
kilometer.)
19) Find the latitude of Winnipeg, Canada if Winnipeg and Austin, TX, 30°N, are 2234 km
apart.
Solve the problem.
20) 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?
21) 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°?
18)
19)
20)
21)
Find the area of a sector of a circle having radius r and central angle . If necessary, express the answer to the nearest
tenth.
22) r = 44.6 cm,
23) r = 7.4 mi,
=
13
22)
radians
= 314°
23)
Solve the problem.
24) A circular sector has an area of 18 in2 and an arc length of 3 inches. What is the measure of
the central angle in degrees? Round to the nearest degree.
24)
25) What is the difference in area covered by a single 12-inch windshield wiper operating
with a central angle of 126° compared to a pair of 2-inch wipers operating together each
having a central angle of 108°? Round to the nearest hundredth.
25)
Find the exact circular function value.
-2
26) cos
3
27) tan
26)
7
6
27)
3
The figure shows an angle in standard position with its terminal side intersecting the unit circle. Evaluate the
indicated circular function value of .
28) Find cos .
28)
-
5 12
,
13 13
29) Find csc .
29)
7
24
,25
25
Use a table or a calculator to evaluate the function. Round to four decimal places.
30) csc 0.2475
31) cot 0.2258
30)
31)
4
Suppose an arc of length s lies on the unit circle x 2 + y2 = 1, starting at point (1, 0) and terminating at the point (x, y). Use
a calculator to find the approximate coordinates (x, y). Round coordinates to four decimal places when appropriate.
32) s = 5.6
32)
For the given value of s, decide in which quadrant an angle of s radians lies by evaluating sin s and cos s.
33) s = 66
33)
Find the value of s in the interval [0, /2] that makes the statement true. Round to four decimal places.
34) sec s = 3.7404
34)
35) csc s = 1.1691
35)
Find the exact value of s in the given interval that has the given circular function value.
3
, ; cos s = 36)
2
2
37)
3
1
, 2 ; cos s =
2
2
37)
Find the exact values of s in the given interval that satisfy the given condition.
2
38) [0, 2 ); cos s = 2
Use the formula
39)
=
6
=
t
38)
to find the value of the missing variable. Give an exact answer unless otherwise indicated.
39)
radian, t = 11 sec
Use the formula v = r
40) r = 16 cm,
36)
to find the value of the missing variable. Give an exact answer unless otherwise indicated.
=
3
40)
radian per sec
5
Use the formula s = r t to find the value of the missing variable. Give an exact answer.
41) s =
3
41)
m, r = 3 m, t = 4 sec
Solve the problem.
42) Find for the minute hand of a clock.
42)
43) A wheel is rotating at 5 radians/sec, and the wheel has a 83-inch diameter. To the nearest
foot, what is the speed of a point on the rim in ft/min?
43)
44) Two pulleys of diameters 6 m and 3 m are connected by a belt. The larger pulley rotates 42
times per min. Find the angular speed of the smaller pulley.
44)
45) Each tire of an automobile has a radius of 1.25 feet. How many revolutions per minute
(rpm) does a tire make when the automobile is traveling at a speed of 115 feet per sec?
Round your answer to the nearest tenth.
45)
Match the function with its graph.
2) y = 3 cos x
46) 1) y = sin 3x
3) y = 3 sin x
4) y = cos 3x
46)
A)
B)
C)
D)
6
Graph the function.
4
47) y = sin x
3
47)
Give the amplitude or period as requested.
1
48) Amplitude of y = cos x
3
49) Period of y = cos
48)
1
x
3
49)
50) Period of y = sin 3x
50)
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.
51)
51)
7
52)
52)
Graph the function.
2
1
53) y = sin x
3
2
53)
8
Answer Key
Testname: UNTITLED1
1) B = 78° 28 ; a = 42.59 ft; b = 208.70 ft
2) A = 63.4°, B = 26.6°, c = 2.9 cm
3) 21 m
4) 35 ft
5) 135°; S 45° E
6) 16.8 mi
7) 84 ft
8) 212 ft
17
9)
6
10) -270°
11) -2.8045
12) 51.54°
3
13) 2
14) 3
15) 44
16) 392.0 in.
17) 4.6 ft
18) 335 km
19) 50°N
20) 2.37 in.
21) 93.73°
22) 240.4 cm2
23) 150.1 mi2
24) 14°
25) 150.80 in.2
1
2
26) -
3
3
27)
28) -
5
13
29) -
25
24
30) 4.0820
31) 4.3532
32) (0.7756, -0.6313)
33) III
34) 1.3002
35) 1.0262
5
36) s =
6
37) s =
5
3
38)
,
4
4
9
Answer Key
Testname: UNTITLED1
39)
40)
41)
42)
66
16
3
36
30
radian per sec
cm per sec
radian per sec
radians per min
43) 1038 ft/min
44) 168 radians per min
45) 878.5 rpm
46) 1B, 2D, 3C, 4A
47)
48) 4
49) 6
2
50)
3
51) y = 5 cos
1
x
2
52) y = -4 cos (2x)
53)
10