In Exercises 6368, find and such that where and w 1, 1.v 0, 3

Chapter 10, Problem 64

(choose chapter or problem)

Witch of Agnesi  Consider the parametric equations

\(x=4 \cot \theta\) and \(y=4 \sin^2 \theta,\ \ \ -\frac{\pi}{2}\ \leq\ \theta\ \leq\ \frac{\pi}{2}\).

(a) Use a graphing utility to graph the curve represented by the parametric equations.

(b) Use a graphing utility to find the points of horizontal tangency to the curve.

(c) Use the integration capabilities of a graphing utility to approximate the arc length over the interval \(\pi/4\ \leq\ \theta\ \leq\ \pi/2\)

Text Transcription:

x=4 cot theta

y = 4 sin^2 theta,  -pi/2 leq theta leq pi/2

pi/4 leq theta leq pi/2