Let's consider unit circle with central point x=0 ;y=0

a is an angle in rad                     x is cosine of angle a                                y is sine of angle a

Area of tryangle is       A_t=y*x/2

Area of segment a   = a/2

Area of half of sector 2a =area of segment of a - area of tryangle = a/2 - yx/2= a - y(1-y²)^1/2

Can area of half of sector 2a be calculated by integration if x=3^1/2/2    then x₂=1

_(3^1/2)/2f¹ (1 - x²)^1/2 dx

How to calculate the integral?

Edited December 19, 20187 yr by DimaMazin

I suspect you will get more help if you draw a diagram.

7 hours ago, John Cuthber said:

I suspect you will get more help if you draw a diagram.