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Math Help - Special Identities - troubles rationalizing

  1. #1
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    Special Identities - troubles rationalizing

    I'm currently studying for my upcoming precalculus midterm, but I'm having troubles rationalizing denominators and simplifying--and I'm not sure if I'm approaching this correctly. If anyone could lend me pointers to simplify please let me know, I'm really weak in this area.

    Use a sum or difference formula to find the exact value of the given expression:

    \sin \frac{7\pi}{12}
    I figured...
    \frac{\pi}{4} + \frac{\pi}{3}=\frac{7\pi}{12}
    Thus according to the values...
    \frac{\sqrt2}{2}\times\frac{\sqrt2}{2}+\frac{\sqrt  3}{2}\times\frac{1}{2}

    I totally got the wrong answer from here. How should I go about simplifying this?
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  2. #2
    MHF Contributor
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    So we have \frac{\sqrt2}{2}\times\frac{\sqrt2}{2}+\frac{\sqrt  3}{2}\times\frac{1}{2}

    Order of operations says multiply before adding so let's multiply everything together we can.

    \frac{\sqrt{2}*\sqrt{2}}{2*2}+\frac{\sqrt{3}*1}{2*  2}

    \frac{2}{4}+\frac{\sqrt{3}}{4} = \frac{2+\sqrt{3}}{4}
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