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A2 Statistics

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Reply 20
Avatar for uzer
uzer
OP
9
by first writing sin3@ as sin(2@ +@), express sin3@ in terms of sin@
Hence solve the equation sin3@ =sin@ 0<=@<=360 degrees


@ = thetre
Original post by uzer
by first writing sin3@ as sin(2@ +@), express sin3@ in terms of sin@
Hence solve the equation sin3@ =sin@ 0<=@<=360 degrees


@ = thetre

*theta. It might be beneficial to learn some basic LaTex, there's a guide here:
http://www.thestudentroom.co.uk/wiki/LaTeX
How many of these are you actually getting out? Did you get the last one out?


Use the sine double angle formula for A=2θA = 2\theta, B=θB = \theta, then use the double angle formulae again.
Reply 22
Avatar for uzer
uzer
OP
9
yes dont worry i have done all the sums so far

i have tried double angle foormula no luck
Original post by uzer
yes dont worry i have done all the sums so far

i have tried double angle foormula no luck

I was getting a little worried. If you're getting them out that's fine.

sin⁡(A+B)=sin⁡Acos⁡B+cos⁡Asin⁡B\sin(A+B) = \sin A \cos B + \cos A \sin B

∴sin⁡(2θ+θ)=sin⁡2θcos⁡θ+cos⁡2θsin⁡θ\therefore \sin(2\theta + \theta) = \sin 2\theta \cos \theta + \cos 2\theta \sin \theta
∴sin⁡3θ=(2sin⁡θcos⁡θ)cos⁡θ+(cos⁡2θ−sin⁡2θ)sin⁡θ\therefore \sin 3\theta = (2\sin\theta\cos\theta)\cos\theta + (\cos^2 \theta - \sin^2 \theta)\sin \theta

Then you expand and use cos⁡2θ+sin⁡2θ=1\cos^2 \theta + \sin^2 \theta = 1.

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