Question

How to put y=4cos(x) in X= form?

Answer 1

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

Answer 2

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

Answer 3

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]

Answer 4

ignore the mistake i made in the variables

Answer 5

Here is the problem I'm working at:

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

Are you familiar with solids of rotation?

Answer 13

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

Answer 14

haha alright, thanks for the help

Answer 15

http://www.wolframalpha.com/input/?i=plot+y%3D4sin%28x%29

Answer 16

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

Answer 17

little bit (:
I am trying to find it

Answer 18

Sweet, thanks

Answer 19

what is the rotation axis?

Answer 20

it is y=4

Answer 21

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

Answer 22

Any luck?

Answer 23

nope

Answer 24

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