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.
Where I’m from “mince pie” is dried fruit and spices, while “mince” is equivalent to the US ground beef (or less commonly other meats), and a “meat pie” is made from beef mince.
It made for frustrating Christmasses as a child because mini meat pies (“party pies”) are delicious and available at every other celebration.
I guess, if you don’t like raisins and currants? It’s just a fruit pie, I don’t really see what’s so horrible about that. It’d be more understandable if we were talking about a fly cemetery, a similar pastry with a much more interesting name.
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