Trigonometry

Solve sin 2x + sin x = 0 for 0 (Less then or equal to) x (Less then or equal to) 2pi.

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  1. sin(2x)=2sin(x)cos(x)
    so
    sin(2x)+sin(x)=0
    =>
    2sin(x)cos(x)+sin(x)=0
    sin(x)[2cos(x)+1]=0
    sin(x)=0 or cos(x)=-1/2
    sin(x)=0 => x=0, x=π for 0≤x<2π
    cos(x)=-1/2 => x=2π/3 or x=4π/3

    Combining, the solution set
    S={0,2π/3,π 4π/3}
    Add x=2π if the question actually asked for
    0≤x≤2π

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