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Cameronmx9

  • 4 years ago

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

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  1. cinar
    • 4 years ago
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    \[x=\cos^{-1} (y/4)\]

  2. BlingBlong
    • 4 years ago
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    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
    • 4 years ago
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    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
    • 4 years ago
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    ignore the mistake i made in the variables

  5. Cameronmx9
    • 4 years ago
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    Here is the problem I'm working at:

  6. Cameronmx9
    • 4 years ago
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    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
    • 4 years ago
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    I think I'm using the cross-section method, but am not too sure on the radius.

  8. Cameronmx9
    • 4 years ago
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    Which I think would be (4-4sin(x)

  9. BlingBlong
    • 4 years ago
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    Wait do you want 4sin(x) to equal 4?

  10. Cameronmx9
    • 4 years ago
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    I'm honestly not too sure on where to start with this problem.

  11. BlingBlong
    • 4 years ago
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    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
    • 4 years ago
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    Are you familiar with solids of rotation?

  13. BlingBlong
    • 4 years ago
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    tbh no I know trig functions though but meh you should ask in chat for help

  14. Cameronmx9
    • 4 years ago
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    haha alright, thanks for the help

  15. cinar
    • 4 years ago
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    http://www.wolframalpha.com/input/?i=plot+y%3D4sin%28x%29

  16. cinar
    • 4 years ago
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  17. Cameronmx9
    • 4 years ago
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    @Cinar, do you know which method I would use here?

  18. cinar
    • 4 years ago
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    little bit (: I am trying to find it

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  19. Cameronmx9
    • 4 years ago
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    Sweet, thanks

  20. cinar
    • 4 years ago
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    what is the rotation axis?

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  21. Cameronmx9
    • 4 years ago
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    it is y=4

  22. Cameronmx9
    • 4 years ago
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    so I'm thinking the radius is (4-4sin(x))

  23. Cameronmx9
    • 4 years ago
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    Any luck?

  24. cinar
    • 4 years ago
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    nope

  25. cinar
    • 4 years ago
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    \[V=\pi \int\limits_{0}^{2\pi}(4-4\sin x)^2dx\]

  26. cinar
    • 4 years ago
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