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    A curve has equation y=3sinx+4cos(^3)x

    Find all the x coordinates for the curve's stationary points in the interval
    0<x<pi

    The answers according to the marking scheme are supposed to be
    x=pi/2
    x=5pi/12
    x=pi/12

    I am only getting pi/12 as the answer and am confused as to why 11pi/12 is not one of the answers and how to derive the other two answers.
    It would be a lot of help.
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    (Original post by Reneewinters)
    ...
    Please post your working.
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    (Original post by ghostwalker)
    Please post your working.
    dy/dx= 3cosx-12(cos^2)xsinx
    3cosx(1-2sin2x)=0
    2sin2x=1
    sin 2x=1/2
    2x=pi/6
    x=pi/12

    This I know is right. After this shouldn't this answer be subtracted from pi to get 11pi/12 instead of 5pi/12? Maybe I'm missing something but I don't know what. Also how was pi/2 derived? I'm completely lost.

    Do you have any idea where i'm going wrong?
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    (Original post by Reneewinters)
    dy/dx= 3cosx-12(cos^2)xsinx
    3cosx(1-2sin2x)=0
    2sin2x=1
    You've made a slip here. You can't just delete the cos x, since it could be zero.

    At this stage you'd have:

    cos x = 0

    or

    sin 2x=1/2

    sin 2x=1/2
    2x=pi/6
    x=pi/12

    This I know is right. After this shouldn't this answer be subtracted from pi to get 11pi/12 instead of 5pi/12? Maybe I'm missing something but I don't know what. Also how was pi/2 derived? I'm completely lost.

    Do you have any idea where i'm going wrong?
    sin 2x=1/2

    When you take the inverse sin, at this stage you need to add the additional values.

    So, 2x = pi/6 + 2npi, or pi-pi/6 + 2npi where n is any integer depending on your domain.

    Hence 2x = pi/6 +2npi or 5pi/6 + 2npi

    Then divide the whole thing by 2.
 
 
 
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