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Really difficult parametric question

Hey.
There's a really difficult parametric question, worth 8 marks, that I have really no idea how to integrate.
Find the total area enclosed by the curve, as a multiple of π\pi
x=3sintsin3t,y=3costcos3t x = 3sint - sin3t, y = 3cost - cos3t

The limits are
Unparseable latex formula:

\frac {3\pi}{2}}

and
Unparseable latex formula:

\frac {\pi}{2}}



I've got as far as
9cos2t+3cos23t12costcos3t \int 9cos^2t + 3cos^23t - 12costcos3t
I can change the first two into terms of cos2t and cos6t, removing the sqaures so that I can integrate but I have no idea how to tackle the last part of the question.
Any hints? I 've worked out in another part of the question that cos3t=4cos3t3cost cos3t = 4cos^3t - 3cost but I've played with that and it doesn't seem to get me anywhere...
Thanks.
Reply 1
cos(x-a)cos(x+a) = ...
Personally to integrate costcos3t, I would use factor formulae, if you don't know about these think about what cos(A+B)+cos(A-B) is.
Reply 3
what are the parameters and how are they calculated?