Consider the parametric equations x = 4 cos2 t and y = 4 sin t. (a) Create a table of x-

Chapter 10, Problem 10

(choose chapter or problem)

Using Parametric Equations   Consider the parametric equations \(x=4 \cos^2 t\) and y = 4 sin t.

(a) Create a table of x- and y-values using \(t=-\pi/2\), \(-\pi/4\), 0, \(\pi/4\), and \(\pi/2\).

(b) Plot the points (x, y) generated in part (a) and sketch a graph of the parametric equations for \(-\frac{\pi}{2} \le t \le \frac{\pi}{2}\). Describe the orientation of the curve.

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

(d) Find the rectangular equation by eliminating the parameter. (Hint: Use the trigonometric identity \(\cos^2t+\sin^2t=1\).) Sketch its graph. How does the graph differ from those in parts (b) and (c)?

Text Transcription:

x=4 cos^2 t

t=-pi/2

-pi/4

pi/4

pi/2

pi/2 <= t <= pi/2

cos^2t+sin^2t=1