1. ## Sin3A

Hi Guys
I am a bit stuck on a question please could anyone help?

it is 'By expressing sin 3A as sin (2A+A), find an expression for sin 3A in terms of Sin A.'

thankyou

2. Hello
Originally Posted by gracey
it is 'By expressing sin 3A as sin (2A+A), find an expression for sin 3A in terms of Sin A.'
The expression $\displaystyle \sin(3A)=\sin(2A+A)$ can be expanded using $\displaystyle \sin(x+y)=\sin x\cos y+\sin y\cos x$ with $\displaystyle x=2A$ and $\displaystyle y=A$. It should give you another expression which you'll have to transform using the three following identities :
$\displaystyle \begin{cases}\sin (2A)=2\sin A\cos A\\ \cos^2A=1-\sin ^2A\\\cos (2A)=1-2\sin^2A\end{cases}$

Does it help ?

3. Originally Posted by gracey
Hi Guys
I am a bit stuck on a question please could anyone help?

it is 'By expressing sin 3A as sin (2A+A), find an expression for sin 3A in terms of Sin A.'

thankyou
This is good for practice.

sin(3A)
= sin(2A +A)
= sin(2A)cosA +cos(2A)sinA
= [2sinAcosA]cosA +(cos^2(A) -sin^2(A)]sinA
= 2sinAcos^2(A) +sinAcos^2(A) -sin^3(A)
= 3sinAcos^2(A) -sin^3(A)
= 3sinA[1 -sin^2(A)] -sin^3(A)
= 3sinA -3sin^3(A) -sin^3(A)

I used:
sin(2X) = 2sinXcosX
cos(2X) = cos^2(X) -sin^2(X)
sin^2(X) +cos^2(X) = 1

4. thankyou both that is excellent

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# sin3a sina

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