The graph of r t  is a three-dimensional version of what is known as a Lissajous figure. The graph of  t  clearly shows some points of maximum curvature; can you see where those points of maximum curvature are on the graph of r t  ?)

In each case you will simply modify the code provided in the demo to produce the

graphs you want. You’ll need to revise not only the definitions of r t  and of its domain, but

also the viewing window for the graph of r t  . Use %% as in the demo to divide your m-file into

sections, with appropriate labeling.

1. r t   sint, t,cost , 0  t  4 . (This is a simplified version of one of the examples; is

the graph of  t  surprising?)

2.   2 r t  sint, t ,cost , 0  t  4 . (You’ll need y = t.^2, not y = t^2, and

similarly for td. But not in the symbolic portion: There you just want

r = [sin(tt) tt^2 cos(tt)]. Note the fall-off in  t  .)

3.   2 ,4 , t t t e e t  r  , 0  t 1. (Think about an appropriate viewing box.)

4. r t   sin 4t,sin5t,cost , 0  t  2 . (Again: sin(4.*t). The graph of r t  is a

three-dimensional version of what is known as a Lissajous figure. The graph of  t 

clearly shows some points of maximum curvature; can you see where those points of

maximum curvature are on the graph of r t  ?)