Problem $1.$ a$)$ Develop a polar formula for computing the arc length of polar curves. $[$Hint: Start with the rectangular equation for an arc length and using the parametric setup:

$x=rcos=f()cos$ and $y=rsin=f()sin,$

create a polar formula for the polar curve $r=f().$

b$)$ Use the formula from a$)$ to calculate the length of the four$-$leaf rose $r=2cos(2).$