• Apr 20th 2014, 04:52 PM
hisajesh
There is a formula:
Area of segment of circle = r^2 (pi*theta/360) - (sin theta/2), where theta is a measure of corresponding arc in degrees.

Could you please explain how they introduce sine in this formula? why not cosine?
• Apr 20th 2014, 05:06 PM
romsek
Quote:

Originally Posted by hisajesh
There is a formula:
Area of segment of circle = r^2 (pi*theta/360) - (sin theta/2), where theta is a measure of corresponding arc in degrees.

Could you please explain how they introduce sine in this formula? why not cosine?

it shouldn't have been introduced at all. The correct formula, assuming $\theta$ is in degrees is

$A=\pi r^2 \dfrac \theta {360}$

The $\dfrac \theta {360}$ just represents what fraction of the total area of the circle the segment is
• Apr 20th 2014, 08:59 PM
prasum
sector area=(pi*(r^2))(theta)/360
sin is introduced here because if you bisect the sector angle theta into two: theta/2,theta/2 then
therefore
so we get side of triangle as 2*r*sin(theta/2)
now you have other two sides of triangle as r
apply heroes formula
then subtract this area from the sector area mentioned above
apply approximations and u will get ur result
• Apr 20th 2014, 09:36 PM
romsek
I see... I did the area of a sector. oh well
• Apr 28th 2014, 12:22 PM
hisajesh