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Math Help - Help with finding values of sin^2x=3/4

  1. #1
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    Help with finding values of sin^2x=3/4

    x should be theta but I don't where the theta symbol is.

    I need to find all the values of x, 0<=x<=2Pi for:

    sin2x=3/4

    but the sin2 has thrown me out, can anyone please help?
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Help with finding values of sin^2x=3/4

    Take the square root of both sides, what do you find?
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  3. #3
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    Re: Help with finding values of sin^2x=3/4

    sin x = square root of 3/4
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Help with finding values of sin^2x=3/4

    Don't forget the \pm when you take the square root. So you have:

    \sin(x)=\pm\frac{\sqrt{3}}{2}

    You will have 4 solutions on the given interval...can you find them?
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  5. #5
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    Re: Help with finding values of sin^2x=3/4

    I see. The square root of 3/4 is, square root 3/2, which is Pi/3

    Therefore as it is Positive in quadrants I and II the angle must be Pi - Pi/3 = 2Pi/3

    so for + square root 3/2 the angles are Pi/3 and 2Pi/3

    and for - square root 3/2 the angles are 4Pi/3 and 5Pi/3
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Help with finding values of sin^2x=3/4

    Yes, good work!

    You found the quadrant I solution, then used the identity \sin(\pi-x)=\sin(x) to get the quadrant II solution, then used the identity -\sin(x)=\sin(-x) along with \sin(x+2\pi)=\sin(x) to get the quadrant III and IV solutions.
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  7. #7
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    Re: Help with finding values of sin^2x=3/4

    You're a genius! Thank you for your help.
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  8. #8
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    Re: Help with finding values of sin^2x=3/4

    just think like normal equation when u solve sin,tan and cos the only diffrent is kinda you have to take away or add pi to get to your intervall :P. Took me so long time to understand this and its so simple (I feel stupid that i did not understand this alot early <.<) btw i recomend to always draw unit circle
    Last edited by Petrus; November 8th 2012 at 12:39 AM.
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