My Math Forum Trigonometry - I don't understand the solution

 Trigonometry Trigonometry Math Forum

July 2nd, 2013, 08:23 PM   #1
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Trigonometry - I don't understand the solution

http://i.imgur.com/vYqr0X5.jpg

Area of half a circle is (pi*r^2)/2

What happened to pi?

phi - sin(phi) ????
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 July 2nd, 2013, 08:38 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,210 Thanks: 518 Math Focus: Calculus/ODEs Re: Trigonometry - I don't understand the solution What they have done to find the area $A$ of the shaded portion is to take the area of the circular sector, and subtracted the area of the isosceles triangle. The are of the circular sector is: $A_S=\frac{1}{2}r^2\phi$ The area of the triangle is: $A_T=\frac{1}{2}r^2\sin(\phi)$ Hence: $A=A_S-A_T=\frac{r^2(\phi-\sin(\phi))}{2}$

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