## skullofreak one year ago help!!

1. skullofreak

2. skullofreak

how do I write the equation of the graph?

3. alffer1

Tell me what the graph of y = cos x looks like.

4. skullofreak

its (0,1) (pi,-1) (2pi,1) (3pi,-1) etc

5. skullofreak

but with the dots in um the up and down motions (from half of 0 and pi , pi and 2pi,

6. alffer1

So what is the difference between this one and cosx?

7. skullofreak

its sin ? and the graph is given but I don't know how to get an equation

8. skullofreak

nvm its cos

9. ranga

The sine function is zero when x = 0. A cosine function is 1 when x = 0. So we need to choose the acos(bx) here. a is the amplitude. Amplitude is how much above or how much below the mean line (which is x axis here) the curve swings. Could you figure out the amplitude from the diagram?

10. skullofreak

a = 3

11. skullofreak

so y = 3cos.. bx

12. ranga

Yes. a = 3. So the equation is y = 3cos(bx). We still need to figure out b. The period of a cosine or a sine function is how long before the curve repeats itself. Could you look at two successive peaks in the diagram and figure out after how much x the function repeats itself?

13. skullofreak

every 3pi?

14. skullofreak

or every 6pi/2?

15. ranga

No. The curve attains a peak at x = 0. The next peak occurs at x = 6pi. The period is how much x has passed before the curve starts to repeat itself. So what is the x distance between peak-to-peak?

16. skullofreak

6pi/2

17. ranga

No. At x = 0, first peak. At x = 6pi the next peak. The difference in x is: 6pi - 0 = 6pi. Every 6pi the curve repeats itself. You can take the distance between two successive low points also and it will still be 6pi. So the period of this curve is 6pi.

18. skullofreak

OH

19. skullofreak

y=3cos (6pi)x ?

20. ranga

The formula for the period of cos(bx) is: Period = 2pi / b Looking at the graph we found the period to be 6pi. Plug that into the formula: 6pi = 2pi / b Find b.

21. skullofreak

2pi/6pi = pi/3pi

22. ranga

The pi will cancel out. so b = ?

23. skullofreak

yes sorry

24. skullofreak

1/3

25. ranga

Yes. Put them all together and the curve represented in the graph is: y = 3cos(1/3*x)

26. skullofreak

okay thank you!! a lot!

27. ranga

You are welcome.