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Pre-cal

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1) Solve the equation

sinx(sinx+1) = 0

I am having trouble with the first step. Could I do sin x^2 + 1 =0?

  • Pre-cal - ,

    Using distributive property of multiplication over addition:
    p(p+1)=x²+x
    If p=sin(x), then
    sin(x)(sin(x)+1)=sin²(x)+sin(x)

    However, this particular problem does not require the expression to be expanded.
    In fact, if
    p(p+1)=0, it means that either p=0, or p+1=0.
    Substitute p=sin(x), we get:
    sin(x)=0 .......(1) or
    sin(x)+1=0.......(2)

    Solve for x in each of the two cases. The answer is the union of the two sets of answers.

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