Polygons on a circle

You will write functions for the area of a regular polygon on a circle. Then you will see how many corners are needed before the polygon nearly fills the circle.

The idea. A regular polygon with $n$ corners on a circle of radius $r$ is made of $n$ thin triangles. Each has the area $\dfrac{1}{2}r^2\sin\dfrac{360^\circ}{n}$.

Your tasks.

1. In polygon_area, return the area of the regular polygon with n corners on a circle of radius r, rounded to $4$ decimals.
2. In left_over, return the area of the circle minus the area of the polygon, rounded to $4$ decimals.
3. In fraction_left, return the left-over area as a fraction of the circle, rounded to $4$ decimals.
4. Set enough to the smallest number of corners n for which the polygon fills at least $99\%$ of the circle.