# Thread: Please explain sine

1. ## Please explain sine

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?

2. ## Re: Please explain sine

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

3. ## Re: Please explain sine

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
sin(theta/2)=(width of half triangle)/radius
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

4. ## Re: Please explain sine

I see... I did the area of a sector. oh well

5. ## Re: Please explain sine

@prasum: just curious, when you say "apply heroes formulas" what does that mean?

6. ## Re: Please explain sine

Originally Posted by hisajesh
@prasum: just curious, when you say "apply heroes formulas" what does that mean?
Heron's formula - Wikipedia, the free encyclopedia