1. Writing Sinusoidal Equations

2. You ride a Ferris Wheel, the height that you are above the ground varies periodically. Consider the height of the center of the wheel to be the equilibrium point. Suppose the diameter of a Ferris Wheel is 42 feet and travels at a rate of 3 revolutions per minute. At the highest point, a seat on the Ferris wheel is 46 feet above the ground.
a. Write a sinusoidal equation to model the height of your seat if you got on the Ferris Wheel at its lowest point.
b. According to the model, after you have ridden the Ferris Wheel for 4 minutes and 13 seconds, the Ferris Wheel comes to an abrupt stop. What would be the height of your seat at that time?

3. Let’s look at the height every
0 sec
5 sec
2.5 sec
7.5 sec
10 sec
15 sec
20 sec
12.5 sec
17.5 sec
3 revolutions per min. =
= 1 revolution per 20 seconds
Let’s look at the height every
2.5 seconds
= revolution per 10 seconds
= revolution per 5 seconds
= revolution per 2.5 seconds

4. 21 -- 46 ft. -- -- 25 ft. -- -- 4 ft. -- 0 sec 5 sec 2.5 sec 7.5 sec
Amplitude: 21
Phase Shift: 0
Period: 20 seconds
A = -21
C = 0
Vertical Shift: 25
D = 25

5. 21 What is the height at 4 minutes and 13 seconds?
-- 46 ft. -- 21
-- 25 ft. --
-- 4 ft. --
0 sec
5 sec
2.5 sec
7.5 sec
10 sec
15 sec
20 sec
12.5 sec
17.5 sec
What is the height at 4 minutes and 13 seconds?
4(60) = 253 seconds

6. 20 Write the equation of a sine function. (5, 32) (7, 12) (15, 12)
(9, -8)
Period: 8
Phase Shift: 7
Amplitude: 20
A = -20
Vertical Shift: 12
D = 12

7. The center of a piston on a windmill tower is 80 meters above the ground. The blades on the windmill are 30 meters in length and turn at a rate of 2 revolutions per minute. The windmill has 3 blades and at the tip of each blade is a light. Two of the lights are white and the 3rd light is blue. We can use a sinusoidal equation to model the height of the light compared to time. If we begin tracking the path of the blue light when the light is at its lowest position at 12:00 midnight (use this as your 0 time), write a sinusoidal equation relating the height to time. Then use your equation to determine the height of the light at 12:10 a.m.

8. Let’s look at the height every
0 sec
15 sec
3.75 sec
7.5 sec
11.25 sec
18.75 sec
22.5 sec
26.25 sec
30 sec
2 revolutions per min. =
= 1 revolution per 30 seconds
Let’s look at the height every
3.75 seconds
= revolution per 15 seconds
= revolution per 7.5 seconds
= revolution per 3.75 seconds

9. 30 -- 110 m-- -- 80 m -- -- 50 m- 0 sec 15 sec 30 sec 7.5 sec
Amplitude: 30
Phase Shift: 0
Period: 30 seconds
A = -30
C = 0
Vertical Shift: 80
D = 80

10. 30 Now, determine the height of the light at 2:10 a.m. -- 110 m--
0 sec
15 sec
30 sec
7.5 sec
11.25 sec
22.5 sec
3.75 sec
18.75 sec
26.25 sec
Now, determine the height of the light at 2:10 a.m.