May someone explain how to fill out the table ?

You have the formula written above the table.



where

s = arc length
r = radius

The third lines of both tables need the angle. Since the formula is already solved for theta, the central angle, just plug in s and r and calculate theta.

Left table, third line



Right table, third line



For the first line of both tables, you are looking for the arc length. Solve the formula for s, arc length.





Left table, first line

You have the radius, r = 8 in., and theta, but theta is in degrees. We need theta in radians.






(You're correct.)

Right table, first line



For the second line of both tables, you are solving for the radius. We now solve the formula for r.







Left table, second line



Right table, second line

These graph is cross the yaxis and x axis two ways.