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Math Help - Confusing trig shape question

  1. #1
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    Confusing trig shape question

    http://i42.tinypic.com/29yh6c6.jpg

    I'm really stuck here. I've tried getting the area of the sector/triangle etc. but I'm getting nowhere near that equation. Can anyone please help?
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  2. #2
    Junior Member
    Joined
    May 2009
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    We know the area of the sector is \frac{\theta}{2\pi}\cdot\pi r^2. The area of the triangle is \frac{1}{2}r^2 \sin\theta . (do you see why?). So the area of the shaded region is \frac{\theta}{2\pi}\cdot\pi r^2-\frac{1}{2}r^2 \sin\theta =\frac{1}{8}\cdot s^2, where s is the length of the side of the square.

    But we can find s^2 in terms of r using Law of Cosines. s^2=r^2+r^2-2r^2\cdot \cos\theta.

    The equation should follow with a little bit of algebra.
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