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Math Help - Unit Circle-Again

  1. #1
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    Unit Circle-Again

    Hey everyone,

    I really appreciated your help last time, now I have revision for an exam

    Find values for x between -pi and pi if sin2x=root3/2

    I know that sin(pi/3) = root3/2. I have been able to obtain values of pi/3 and pi/6, but the answers say that there are 2 more. I can't see the logic behind it, except I do know that you have to increase the initial range or something because it is 2x. I think.

    Thanks in advance
    Steven
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by Stevo_Evo_22 View Post
    Hey everyone,

    I really appreciated your help last time, now I have revision for an exam

    Find values for x between -pi and pi if sin2x=root3/2

    I know that sin(pi/3) = root3/2. I have been able to obtain values of pi/3 and pi/6, but the answers say that there are 2 more. I can't see the logic behind it, except I do know that you have to increase the initial range or something because it is 2x. I think.

    Thanks in advance
    Steven
    Draw a circle.

    \tfrac{\sqrt{3}}{2}=\left\{\begin{array}{ll} \sin \tfrac \pi 3 \\ \sin \pi-\tfrac \pi 3=\sin \tfrac{2 \pi}{3} \end{array} \right.

    Now, if \sin(a)=\sin(b), look at your circle :
    a=\pi-b+2k \pi

    Now, you're correct to point out the initial range.
    If x \in [-\pi,\pi ], then y=2x \in [-2 \pi, 2 \pi]

    so you'll have to solve for y in \sin y=\sqrt{3}/2 in that new domain !
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  3. #3
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    Thanks! So would 'a' (pi/3) be pi + pi/3? Because we've already gone round a half time?
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