NEW DIAGRAM:

Question

On a unit circle, sin x = square root 3 over 2, with center O.

Vertical line from top to center of circle is PO.
Horizontal line from middle to right of circle is OE.
Another vertical line of AB is parallel to PO.
And radius of circle (line from O to A) is 1 unit.
From A to E is the arc.
From E to B is another arc.
) is the angle 60 degree

Fine the area of the shaded region (where the ::::: are).
Sorry it's a bad diagram, can't really draw a circle on here..

..............P
..............|.........A
..............|....... "|:
..............|......"..|::
..............|...."....|::.
..............|.." )....|:::
..----------- O --------+--- E
..............|.."......|:::
..............|...."....|::'
..............|......"..|::
..............|........"|:
..............|.........B

Answer 1

a 30,60 , 90 triangle has sides
1 =AO, sqrt 3 = EA and hypotenuse 2
AB = 2 sqrt 3
your angle AOB is 2*60 = 120
OE the altitude is 1

Your area = (1/2)(1)(2 sqrt 3)
= sqrt 3

Answer 2

sorry 1 = EO, the side along the x axis

Answer 3

But the question ask to find the area of AE and EB together