Mathematics

Problem

68. Parametric Circles and Ellipses Set your grapher to parametric and radian mode and your window as follows: Tmin

=0

, Tmax

=7

, Tstep

=0.1

\mathrm{Xmin}=-4.7, \mathrm{Xmax}=4.7, \mathrm{Xscl}=1

\mathrm{Ymin}=-3.1, \mathrm{Ymax}=3.1, \mathrm{Yscl}=1

(a) Graph the parametric equations

x=\cos t

and

y=\sin t

. You should get a circle of radius 1 . (b) Use a transformation of the parametric function of

x

to produce the graph of an ellipse that is 4 units wide and 2 units tall. (c) Use a transformation of both parametric functions to produce a circle of radius 3 . (d) Use a transformation of both functions to produce an ellipse that is 8 units wide and 4 units tall. (You will learn more about ellipses in Chapter 8.)

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