## Cameronmx9 Group Title How to put y=4cos(x) in X= form? 2 years ago 2 years ago

1. cinar Group Title

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

2. BlingBlong Group Title

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 Group Title

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 Group Title

ignore the mistake i made in the variables

5. Cameronmx9 Group Title

Here is the problem I'm working at:

6. Cameronmx9 Group Title

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 Group Title

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

8. Cameronmx9 Group Title

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

9. BlingBlong Group Title

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

10. Cameronmx9 Group Title

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

11. BlingBlong Group Title

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 Group Title

Are you familiar with solids of rotation?

13. BlingBlong Group Title

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

14. Cameronmx9 Group Title

haha alright, thanks for the help

15. cinar Group Title
16. cinar Group Title

17. Cameronmx9 Group Title

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

18. cinar Group Title

little bit (: I am trying to find it

19. Cameronmx9 Group Title

Sweet, thanks

20. cinar Group Title

what is the rotation axis?

21. Cameronmx9 Group Title

it is y=4

22. Cameronmx9 Group Title

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

23. Cameronmx9 Group Title

Any luck?

24. cinar Group Title

nope

25. cinar Group Title

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

26. cinar Group Title