## Cameronmx9 3 years ago How to put y=4cos(x) in X= form?

1. cinar

$x=\cos^{-1} (y/4)$

2. BlingBlong

It is only allowed in said domain in order to make it the inverse function (It needs to pass the horizontal line test)

3. BlingBlong

Inverse y = 4cos(x) x/4 = 4cos(x)/4 y/4 = cos(x) take inverse of each side arccos(y/4) = arccos(cos(x)) arccos(y/4) = 1x arccos(y/4) = x Remember that arccos is the inverse function of cos(x) and is limited to the domain [0, pi]

4. BlingBlong

ignore the mistake i made in the variables

5. Cameronmx9

Here is the problem I'm working at:

6. Cameronmx9

Find the volume of the solid generated by revolving the described region about the given axis: The region in the first quadrant bounded above by the line y=4 and by the curve y=4sin(x) for the interval 0≤x≤π2 about the line y=4

7. Cameronmx9

I think I'm using the cross-section method, but am not too sure on the radius.

8. Cameronmx9

Which I think would be (4-4sin(x)

9. BlingBlong

Wait do you want 4sin(x) to equal 4?

10. Cameronmx9

I'm honestly not too sure on where to start with this problem.

11. BlingBlong

I'm confused by your question but if you want it to equal four you can use the unit circle and think where is cos(x) = 1, the answer being pi

12. Cameronmx9

Are you familiar with solids of rotation?

13. BlingBlong

tbh no I know trig functions though but meh you should ask in chat for help

14. Cameronmx9

haha alright, thanks for the help

15. cinar
16. cinar

17. Cameronmx9

@Cinar, do you know which method I would use here?

18. cinar

little bit (: I am trying to find it

19. Cameronmx9

Sweet, thanks

20. cinar

what is the rotation axis?

21. Cameronmx9

it is y=4

22. Cameronmx9

so I'm thinking the radius is (4-4sin(x))

23. Cameronmx9

Any luck?

24. cinar

nope

25. cinar

$V=\pi \int\limits_{0}^{2\pi}(4-4\sin x)^2dx$

26. cinar