is the area of a circle sector, like a slice of pie.
(1/2)×sin(θ)×side1×side2
is the side-angle-side formula for the area of a triangle.
We know that the triangle encompassed by the sector has two sides that are equal to the radius, so we replace side1×side2 with r^2. Since the area of the arc segment is equal to the area of a sector minus the triangle, we can subtract triangle area from sector area to get
(1/2)×(θ-sin(θ))×r^2
which is the area of the arc segment, as shown with pie in the picture.