Arcs and sectors in code

You will write functions for the length of an arc, the area of a sector and the angle of an arc. Then you will find the largest sector in a list.

The idea. An arc is $\dfrac{\theta}{360}$ of the circumference, and a sector is $\dfrac{\theta}{360}$ of the circle. To find the angle from a length, divide the arc by the circumference and multiply by $360$.

Your tasks.

1. In arc_length, return the length of the arc for a radius and an angle in degrees, rounded to $4$ decimals.
2. In sector_area, return the area of the sector, rounded to $4$ decimals.
3. In angle_of_arc, return the angle in degrees of an arc of length arc in a circle of radius radius, rounded to $4$ decimals.
4. Set largest to the name of the sector in sectors that has the largest area.