1. Warm Up Apr. 22nd Graph two full periods.
State 3 vertical asymptotes for the function.

2. Writing Equations of Sine & Cosine Graphs with Applications

3. What is the amplitude?

4. What is the period?

5. Is it possible to write an equation with no horizontal shift?

6. What is the vertical shift?

7. What is an equation of the graph?

8. What is the amplitude?

9. What is the period?

10. Is it possible to write an equation with no horizontal shift?

11. What is the vertical shift?

12. What is an equation of the graph?

13. What is the amplitude?

14. What is the period?

15. Is it possible to write an equation with no horizontal shift?

16. What is the vertical shift?

17. What is an equation of the graph?

18. Tidal motion is periodic
Tidal motion is periodic. If the height of the water in a harbor rose to a maximum height of 15 feet at 6:00pm, dropped to a minimum level of 3 feet by 3:00am and then rose back to a maximum of 15 feet at 12:00pm.
Sketch a graph for the height of the water in terms of the number of hours after noon on the first day. (t = 0 is noon)
Write a function that represents the height, h, of the water, t hours after noon on the first day.

19. What will the height of the water be at midnight on the first day?
Tidal motion is periodic. If the height of the water in a harbor rose to a maximum height of 15 feet at 6:00pm, dropped to a minimum level of 3 feet by 3:00am and then rose back to a maximum of 15 feet at 12:00pm.
What will the height of the water be at midnight on the first day?
What is the first time that the height of the water will be 12 ft?

20. A Ferris wheel has a diameter of 300 feet, the center of the wheel is 153 feet above the ground and the wheel takes 36 seconds to make one revolution in a counter-clockwise direction.
You board the wheel at its lowest point at time t = 0. Sketch a graph to illustrate your height above the ground versus time after you first board the wheel.
Write a function to represent your height above ground versus time after you first board.

21. A Ferris wheel has a diameter of 300 feet, the center of the wheel is 153 feet above the ground and the wheel takes 36 seconds to make one revolution in a counter-clockwise direction.
Use you equation to find your height above the ground after 22 seconds.
(Round to 3 decimal places)
What is the first time after you board the Ferris wheel that your height above the ground will be 27 feet?

22. What appears to be the period, amplitude and vertical shift?
A block mounted on a spring is set into motion directly above a motion detector, which registers the distance to the block at intervals of 0.1 seconds. When the block is released it is 7.2 meters above the motion detector. The table shows the data collected by the motion detector during the first 2 seconds.
time
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9 1
distance
9.2
13.9
18.8
21.4
20.0
15.6
10.5
7.4
8.1
12.1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9 2
17.3
20.8
17.2
12.0
8.1
7.5
10.5
15.6
19.9
Graph the data.
What appears to be the period, amplitude and vertical shift?
Write an equation to fit this data.

23. How many “iterations” are shown in this scatter plot?
Use your calculator to write an equation of the sine function that best fits the data. “SinReg interations,L1,L2,period”