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6.1E: Sinusoidal Graphs (Exercises)

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Section 6.1 Exercises

1. Sketch a graph of f(x)=3sin(x).

2. Sketch a graph of f(x)=4sin(x).

3. Sketch a graph of f(x)=2cos(x).

4. Sketch a graph of f(x)=4cos(x).

For the graphs below, determine the amplitude, midline, and period, then find a formula for the function.

5. 屏幕快照 2019-07-09 上午3.39.30.png 6. 屏幕快照 2019-07-09 上午3.40.06.png

7. 屏幕快照 2019-07-09 上午3.40.53.png8. 屏幕快照 2019-07-09 上午3.41.12.png

9. 屏幕快照 2019-07-09 上午3.41.42.png 10.屏幕快照 2019-07-09 上午3.42.11.png

For each of the following equations, find the amplitude, period, horizontal shift, and midline.

11. y=3sin(8(x+4))+5

12. y=4sin(π2(x3))+7

13. y=2sin(3x21)+4

14. y=5sin(5x+20)2

15. y=sin(π6x+π)3

16. y=8sin(7π6x+7π2)+6

Find a formula for each of the functions graphed below.

17. 屏幕快照 2019-07-09 上午3.44.07.png

18. 屏幕快照 2019-07-09 上午3.44.45.png

19. 屏幕快照 2019-07-09 上午3.45.22.png

20. 屏幕快照 2019-07-09 上午3.45.49.png

21. Outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 50 degrees at midnight and the high and low temperature during the day are 57 and 43 degrees, respectively. Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.

22. Outside temperature over the course of a day can be modeled as a sinusoidal function. Suppose you know the temperature is 68 degrees at midnight and the high and low temperature during the day are 80 and 56 degrees, respectively. Assuming t is the number of hours since midnight, find a function for the temperature, D, in terms of t.

23. A Ferris wheel is 25 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 10 minutes. The function h(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

a. Find the amplitude, midline, and period of h(t).
b. Find a formula for the height function h(t).
c. How high are you off the ground after 5 minutes?

24. A Ferris wheel is 35 meters in diameter and boarded from a platform that is 3 meters above the ground. The six o’clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. The function h(t) gives your height in meters above the ground t minutes after the wheel begins to turn.

a. Find the amplitude, midline, and period of h(t).
b. Find a formula for the height function h(t).
c. How high are you off the ground after 4 minutes?

Answer

1. Screen Shot 2019-10-11 at 1.49.16 PM.png

3. Screen Shot 2019-10-11 at 1.49.38 PM.png

5. Amp: 3. Period = 2. Midline: y=4. f(t)=3sin(πt)4

7. Amp: 2. Period = 4π. Midline: y=1. f(t)=2cos(12t)+1

9. Amp: 2. Period = 5. Midline: y=3. f(t)=2cos(2π5t)+3

11. Amp: 3, Period = π4, Shift: 4 left, Midline: y=5

13. Amp: 2, Period = 2π3, Shift: 7 left, Midline: y=4

15. Amp: 1, Period = 12, Shift: 6 left, Midline: y=3

17. f(x)=4sin(π5(x+1))

19. f(x)=cos(π5(x+2))

21. D(t)=507sin(π12t)

23. a. Amp: 12.5. Midline: y=13.5. Period: 10
b. h(t)=12.5cos(π5t)+13.5
c. h(t)=26 meters


This page titled 6.1E: Sinusoidal Graphs (Exercises) is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by David Lippman & Melonie Rasmussen (The OpenTextBookStore) via source content that was edited to the style and standards of the LibreTexts platform.

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