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Math Help - exact values

  1. #1
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    exact values

    Find the exact value of sin(−7pi/12):
    Last edited by mr fantastic; November 15th 2009 at 02:00 AM. Reason: Clarity
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  2. #2
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    Quote Originally Posted by samtheman17 View Post
    yes it is
    So, the way I'd do this is using the half angle trig identity for Sin. So that turns
    sin\frac{-7\pi}{12}
    intp
    sin\frac{-7\pi}{6}

    the half angle identity lets you stuff that into
    \pm \sqrt{\frac{1-cos\frac{-7\pi}{6}}{2}}

    Can you solve from there?
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  3. #3
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    hmm......im still unsure what to do from this point
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  4. #4
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    ok....so do you know how to turn cos\frac{-7\pi}{6} into an exact answer?

    Assuming you do, the answer is \frac{-\sqrt{3}}{2}

    so plugging that into the equation, you get
    \pm\sqrt{\frac{1+\frac{\sqrt{3}}{2}}{2}}
    simplifying, you get
    \pm\sqrt{\frac{\frac{2+\sqrt{3}}{2}}{2}}
    that then get simplified further to
    \pm\sqrt{\frac{2+\sqrt{3}}{4}}
    and finally
    \pm\frac{\sqrt{2+\sqrt{3}}}{2}

    the initial equation is sin\frac{-7\pi}{12}, which puts it in 3rd quadrant, so we know it needs to be negative, or
    -\frac{\sqrt{2+\sqrt{3}}}{2}

    Is it clearer?
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  5. #5
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    yes thank you!

    can that be simplified any further though??
    just out of curiosity....
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by samtheman17 View Post
    Find the exact value of sin(−7*pi/12):
    Alternatively, note that

    \sin \frac {-7 \pi}{12} = - \sin \frac {7 \pi}{12}

    = - sin \left( \frac {4 \pi}{12} + \frac {3 \pi}{12} \right)

    = - sin \left( \frac {\pi}3 + \frac {\pi}4 \right)

    Now apply the addition formula for sine, and don't forget that you have a negative sign out in front...
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  7. #7
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    that's the most simple exact answer. You could actually solve it and get a decimal value, but it wouldn't be exact any more since you'd have to round it. The (inaccurate) decimal answer is like -0.9659258263.... but if this is for class and your professor/teacher is anything like mine, giving a decimal answer would result in a fail.

    *edit* Good call Jhevon. There are certainly other ways to solve this equation.
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