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Math Help - Solve for All possible values of x: 4sin^(x)-1=0?

  1. #1
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    Solve for All possible values of x: 4sin^(x)-1=0?

    I can't seem to figure the rest of this out:

    Solve for All possible values of x: 4sin^2(x)-1=0?

    So far I have:

    Let m = sinx


    So: 4m^2-1=0


    How would I go about solving the rest?

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  2. #2
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    Quote Originally Posted by Jd09 View Post
    I can't seem to figure the rest of this out:

    Solve for All possible values of x: 4sin^2(x)-1=0?

    So far I have:

    Let m = sinx


    So: 4m^2-1=0


    How would I go about solving the rest?

    Actually I don't really see the need for the substitution.

    4sin^2x-1=0

    sin^2x=1/4

    sinx=1/2, -1/2

    The critical angle is pi/6. Thus if you are looking for angles between 0 and 2*pi, the possible angles are pi/6, 5*pi/6, 7*pi/6, 11*pi/6.

    Hope this helps.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jd09 View Post
    I can't seem to figure the rest of this out:

    Solve for All possible values of x: 4sin^2(x)-1=0?

    So far I have:

    Let m = sinx


    So: 4m^2-1=0


    How would I go about solving the rest?

    This is equivalent to m^2=\frac{1}{4}\implies m=\pm\frac{1}{2}

    Since m=\sin x, then \sin x=-\frac{1}{2} or \sin x=\frac{1}{2}.

    Can you continue from here?
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