> plot([sin(t),cos(2*t),t=0..2*Pi],
x=-2..2,y=-2..2,color=blue,thickness=3,
title=`Example from class`);

So, the picture I drew in class was WRONG. What happened? The function is tracing over the curve twice. Is it really a parabola? x=sin t and y = cos 2t = 1- 2 sin^2 t = 1-2x^2. Thus, the curve is a parabola. Now for a fun one.

> plot([sin(5*t),cos(3*t),t=0..2*Pi],
x=-2..2,y=-2..2,color=blue,thickness=3,title=`Outter Limits`);

Notice the number of turn around points along the top and bottom is 3 each while along the left and right sides it is 5 each. Is this a general pattern? Can you prove it? Can you use this to develop a quick way to

sketch graphs of <sin (mt), cos(nt) > ?

Below is an animation:

> animate([sin(5*s*t),cos(3*s*t),t=0..2*Pi],s=0..1,
color=green,thickness=3,title=`Outter Limits`,numpoints=100,frames=100,
view=[-2..2,-2..2]);

>