Pre-Calculus
Chapter 7 Review
Name ________________________
1. A Ferris wheel is 26 meters in diameter, and must be boarded from a platform that is 1.5
meters above the ground. The wheel makes one complete revolution every 6 minutes. At the
initial time t = 0, you are in the 12:00 position. If h(t ) gives your height above ground level t
minutes after the initial time, the midline of h(t ) is y = _____.
2. An animal population in a national park dropped from a high of 232,000 in 1943 to a low of
76,000 in 1989, and has risen since then. Scientists hypothesize that the population follows a
sinusoidal cycle affected by predation and other environmental conditions, and that the caribou
will again reach their previous high. Predict the next year when the population will again be
232,000.
3. Suppose the table below is for a periodic function with period 3:
x
0
1
2
3
f ( x)
1
7
10
1
Evaluate f (86) .
4. In the following figure, the coordinates of P are (0.26, 0.97). Find
the measure of angle  . Round to the nearest degree.
5. A circle of radius 2 is centered at the origin. Point A lies on the circle at angle 200 . Point B
lies outside the circle and has coordinates (5, -2). What is the distance between these two points?
6. Evaluate without a calculator: sin 210  tan(225 )  cos 540
7. Two boats leave port at the same time at headings 35 degrees apart. The first travels at 15 mph
and the second at 20 mph. How far apart are they after 2 hours?
8. Solve for  , an angle in a right triangle, if 12sin 3  3  1  sin 3 . Give the answer correct to
1 decimal places.
9. In triangle ABC, suppose c = 1.5, b = 2.5, and C = 22 . Find a, and round your answer to two
decimal places. If there are two possible answers, list both.
10. In the revolving door in the figure below, each panel is 0.9 meters long. How many meters
is the distance along a straight line between A and D? Round to 2 decimal places.
11. Evaluate the following. Give answers to 4 decimal places.
1
A) cos x, x  0.58
B)
 sin x 
1
,
x  34
C) tan x, x  53
 3
D) sin 1 

 2 
12
12. Solve without a calculator: sin  
3
2
13. At what point(s) does y  cos reach its minimum?
Answers:
1. 14.5
2. 2035
3. 10
4. 795
5. 7
6. -1/2
7. 23.1 miles
8. 7.1
9. 3.49, 1.15
10. 1.56
11. a. 54.5495
b.
1
 1.7883
0.5592
c. 1.327
d. 60
12.
60  360n,
nW
120  360n,
nW
13. Min at (180 , 1) and every 360 from there