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April 19, 2014

Homework Help: Math

Posted by Torre on Wednesday, May 9, 2012 at 9:50am.

Hello, I have this question to which it's solution I'm not quite sure of. The question is based on a diagram, and I can't really present it but I'll explain it to my very best, thank you very much for trying to understand my bad presentation of the question.

The diagram is a circle, with center O and points A and B lying on the circle. Radius is 6cm therefore OA=OB=6cm, such that angle AOB = 79 degrees.
Find the area of the shaded segment of the circle contained between the arc AB and the chord [AB].

The solution was a simple sentence, [ (79degrees/360 degrees) x pi x 6^2 ] - [(1/2)(6)(6)sin79]
I understand that [(1/2)(6)(6)sin79] was derived from the rule 1/2absinc and we're finding the area of the triangle.
Therefore, [ (79degrees/360 degrees) x pi x 6^2 ] must be the area of the sector. However, when I looked up the formula for the area of sector, it's (1/2)(delta)(r)^2, where delta is the angle measured in radians.
Primarily, how did [ (79degrees/360 degrees) x pi x 6^2 ] come about then?

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