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# The graph of r t  is a three-dimensional version of what is known as

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  ?)

#graph #threedimensional #version