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Math Help - Sin3A

  1. #1
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    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
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by gracey View Post
    it is 'By expressing sin 3A as sin (2A+A), find an expression for sin 3A in terms of Sin A.'
    The expression \sin(3A)=\sin(2A+A) can be expanded using \sin(x+y)=\sin x\cos y+\sin y\cos x with x=2A and y=A. It should give you another expression which you'll have to transform using the three following identities :
    \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 ?
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  3. #3
    MHF Contributor
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    Quote Originally Posted by gracey View Post
    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)
    = 3sinA -4sin^3(A) -----------answer.

    I used:
    sin(2X) = 2sinXcosX
    cos(2X) = cos^2(X) -sin^2(X)
    sin^2(X) +cos^2(X) = 1
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  4. #4
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    thankyou both that is excellent
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