Review for Test 1
Name___________________________________
Find the angle of smallest possible positive measure that is coterminal with the given angle.
1) -292°
Answer: 68°
Convert the angle to decimal degrees and round to the nearest hundredth of a degree.
2) 54°19'41''
Answer: 54.33°
Convert the angle to degrees-minutes-seconds. Round to the nearest whole number of seconds.
3) 123.16°
Answer: 123°9'36''
Convert the degree measure to radian measure. Give the exact answer.
4) 390°
Answer:
13
6
Convert the radian measure to degree measure. Use the value of
decimal places.
43
5)
18
found on a calculator and round answers to two
Answer: 430°
6) 0.9884
Answer: 56.63°
Solve the problem.
7) Use the figure below to determine the radian measure of angle . Round to two decimal places, if necessary.
Answer: 3 radians
8) Use the formula s = r to determine the value of r in the figure. Round to two decimal places.
19 ft
Answer: 16.75 ft
1
9) Find the length of the arc intercepted by a central angle of
2
in a circle of radius 7 cm. Round to two decimal
9
places.
Answer: 4.89 cm
10) A bicycle wheel rotates 54 times in 1 minute. Through how many degrees does a point on the tip of the wheel
move in 15 seconds?
Answer: 4860°
11) Find the distance in kilometers between the cities whose latitudes are given. Assume that the cities are on a
north-south line and that the radius of the earth is 6400 km. City A, 18°N and city B, 39°N
Answer: 2346 km
12) Two pulleys of diameter 9 m and 3 m are connected by a belt. The larger pulley rotates 39 times per min. Find
the angular velocity of the smaller pulley.
Answer: 234 radians/min
Find the exact value of the following expression without using a calculator.
4
13) cos
3
Answer: -
1
2
14) sin (-60°)
Answer: -
3
2
Draw the angle having the radian measure.
3
15)
4
Answer:
2
Solve the problem.
16) Find sin ( ), given that cos ( ) =
Answer: -
Solve.
in quadrant IV.
21
5
17) Find sin ( ), given that cos ( ) =
Answer:
2
and
5
5
and sin ( ) > 0
7
2 6
7
18) The ferris wheel at an amusement park is 44 ft in diameter, turns at a rate of 6 rpm, and is 4 ft off the ground at
the low point. What is the height of a passenger 30 seconds into the ride?
Answer: 4 ft
Match the function with its graph.
2) y = cos (x)
19) 1) y = sin (x)
3) y = -sin (x) 4) y = -cos (x)
A)
B)
C)
D)
Answer: 1C, 2A, 3B, 4D
3
20) 1) y = sin x 3) y = sin x +
3
3
2) y = cos x +
4) y = cos x -
3
3
A)
B)
C)
D)
Answer: 1C, 2A, 3B, 4D
Find the amplitude or period as requested.
21) Find the amplitude of y = 4 cos 2x +
4
.
Answer: 4
22) Find the period of y = -3 cos 5x +
Answer:
2
.
2
5
23) Find the period of y = -5 cos
1
x+
.
4
2
Answer: 8
4
Find the phase shift of the function.
24) y = 4 sin x Answer:
2
2
25) y = -4 cos
1
x+
2
2
Answer: Graph the function.
26) y = 2 cos 2x
Answer:
5
27) y = sin x -
4
Answer:
6
28) y = -3 cos x +
2
Answer:
7
29) y = sin
1
x+
3
2
Answer:
8
Graph the function over a one-period interval.
1
30) y = 2 + sin (2x - )
3
Answer:
Find a function of the form y = A sin [B(x - C)] + D with the given period, phase shift, and range.
31)
, , [-6, 0]
4 3
Answer: y = 3 sin 8 x -
3
-3
Find the equation for the curve in its final position.
32) The graph y = sin (x) is shifted a distance of /3 to the right, stretched by a factor of 4, translated 7 units
downward, then reflected in the x-axis.
Answer: y = -4 sin x -
3
+7
33) The graph y = cos (x) is shifted a distance of /12 to the left, reflected in the x-axis, translated 2 units
downward, then stretched by a factor of 4.
Answer: y = -4 cos x +
12
-2
9
Determine the equation of the function that is graphed.
34)
Answer: y = -2 cos x
Find the exact value of the following expression without using a calculator.
35) csc ( /2)
Answer: 1
36) sec2 (2 ) if
= /6
Answer: 4
37) csc2 (2 ) if
Answer:
= /6
4
3
38) sec (30°)
Answer:
2 3
3
39) csc (45°)
Answer:
2
40) cot (0°)
Answer: Undefined
10
Match the function with its graph.
2) y = -sec x
41) 1) y = -csc x
3) y = -tan x
4) y = -cot x
A)
B)
C)
D)
Answer: 1B, 2D, 3C, 4A
Find the requested characteristic.
42) Find the period for the graph of f(x) = 9 csc(3x - ) - 2.
Answer:
2
3
43) Find the period for the graph of f(x) = cot (5x).
Answer:
5
Find the equation for the curve in its final position.
44) The graph y = csc (x) is shifted a distance of /8 to the right, stretched by a factor of 6, translated 5 units
upward, then reflected in the x-axis.
Answer: y = -6 csc x -
8
-5
11
Find the exact value of the expression without using a calculator or table.
2
45) sin-1
2
Answer:
4
Graph the function.
46) y = sec x +
6
Answer:
12
47) y = csc x -
2
Answer:
Find the requested characteristic.
48) Find the period for the graph of f(x) = sec 5 x +
Answer:
2
.
2
5
Find the exact value of the expression without using a calculator or table.
3
49) cos-1
2
Answer:
50) arcsin -
6
3
2
Answer: -
3
13