Chapter 10.3, Problem 62E

(a)

To determine

To-graph: The parametric equations, $x=4\cot \theta$ and $y=4{\sin }^2\theta$.

(b)

To determine

To-determine: The points of horizontal tangency to the curve in part (a) with use of graphing utility.

(c)

To determine

To-calculate: The arc length of the curve in part (a) with the use of graphing utility over the interval $\left[\frac{\pi }{4},\frac{\pi }{2}\right]$.