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# (OCR, C4) Trig/Stationary Points Question

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1. I am having some trouble with Q4 on the June 2013 Paper:

The question:

So dy/dx = -2sin2x + 2cos x = 0

Rearanging and using identities gets me
2cosx = 2 sin2x,
cosx = sin2x
cosx= 2sinxcosx
1= 2sin x
1/2 = sin x

so
x= sin^-1 (1/2) = 1/6 pi and 5/6 pi
(and using those values of x, I found the values of y as they are on the mark scheme)

However the mark scheme has an aditonal stationary point with the coordinates, (1/2 pi, 1). I am having trouble figuring out how to get that answer.

Any help would be greatly appreciated!
2. (Original post by MohammedPatel610)
I am having some trouble with Q4 on the June 2013 Paper:

The question:

So dy/dx = -2sin2x + 2cos 2x = 0

Rearanging and using identities gets me
2cos2x = 2 sin2x,
cos2x = sin2x
cos2x= 2sinxcosx
1= 2sin x
1/2 = sin x

so
x= sin^-1 (1/2) = 1/6 pi and 5/6 pi
(and using those values of x, I found the values of y as they are on the mark scheme)

However the mark scheme has an aditonal stationary point with the coordinates, (1/2 pi, 1). I am having trouble figuring out how to get that answer.

Any help would be greatly appreciated!
You differentiated wrong.
3. (Original post by MohammedPatel610)
I am having some trouble with Q4 on the June 2013 Paper:
So dy/dx = -2sin2x + 2cos 2x = 0
Should be 2cos(x) rather than 2cos(2x)
4. (Original post by RDKGames)
Should be 2cos(x) rather than 2cos(2x)
Ah, yes- I made an error when typing out my working (but differentiated right when I did the original question) - im still unable to arrive at the other stationary point
5. (Original post by MohammedPatel610)
Ah, yes- I made an error when typing out my working (but differentiated right when I did the original question) - im still unable to arrive at the other stationary point
At you divided through by cos(x) when you shouldn't do that. By dividing, you are getting rid off one of the solutions, hence the one you are missing. Instead, subtract cos(x) from both sides and factor it out. Then solve two products, each equaling 0.
6. (Original post by RDKGames)
At you divided through by cos(x) when you shouldn't do that. By dividing, you are getting rid off one of the solutions, hence the one you are missing. Instead, subtract cos(x) from both sides and factor it out. Then solve two products, each equaling 0.

Thank you!

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