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# Can anyone solve this equation? watch

1. 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.
2. (Original post by Reneewinters)
...
3. (Original post by ghostwalker)
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?
4. (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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Updated: February 6, 2018
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