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Math Help - General Solutions

  1. #1
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    Exclamation General Solutions

    Find the general solution of sin (3x) + sin (x) = 0. The textbook says the answer is (pi*n)/2 but I canít seem to get it. Please help?
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  2. #2
    MHF Contributor Amer's Avatar
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    do you know the formula

    sinA+sinB=2{sin(\frac{A+B}{2})cos(\frac{A-B}{2})}

    so

    sin3x+sinx=2sin(\frac{4x}{2})cos(\frac{2x}{2})=2si  n(2x)cos(x)=0

    so sin2x=0 or cosx=0

    sin2x=0

    sin2x=0.....2x=n\pi....x=\frac{n\pi}{2}

    cosx=0.....x=\frac{n\pi}{2}
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  3. #3
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    Quote Originally Posted by xwrathbringerx View Post
    Find the general solution of sin (3x) + sin (x) = 0. The textbook says the answer is (pi*n)/2 but I canít seem to get it. Please help?
    A simple approach:

    \sin (3x) + \sin (x) = 0 \Rightarrow \sin (3x) = - \sin (x) = \sin (-x).

    Case 1: 3x = -x + 2 n \pi where n is an integer.

    Case 2: 3x = (\pi - (-x)) + 2 n \pi = x + (2n + 1) \pi. The solutions here are a subset of those in Case 1.
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  4. #4
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    Exclamation

    hmmmm can x = (pi*n)/(3+(-1)^n)?
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  5. #5
    MHF Contributor Amer's Avatar
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    yeah it can be I think
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  6. #6
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    Quote Originally Posted by xwrathbringerx View Post
    hmmmm can x = (pi*n)/(3+(-1)^n)?
    This is a complicated way of saying x = \frac{n \pi}{2} where n is an integer.
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