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Thread: Confusing trig shape question

  1. #1
    Junior Member
    Mar 2009

    Confusing trig shape question

    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
    May 2009
    We know the area of the sector is $\displaystyle \frac{\theta}{2\pi}\cdot\pi r^2$. The area of the triangle is $\displaystyle \frac{1}{2}r^2 \sin\theta $. (do you see why?). So the area of the shaded region is $\displaystyle \frac{\theta}{2\pi}\cdot\pi r^2-\frac{1}{2}r^2 \sin\theta =\frac{1}{8}\cdot s^2$, where $\displaystyle s$ is the length of the side of the square.

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

    The equation should follow with a little bit of algebra.
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