Parametric Equations

by

Hyeshin Choi

1. Graph x=cos(t), y=sin(t), for 0<t<2pi.

How would you change the equations to explore other graphs?

When I pick t=1. ot is a dot. Whenever I put same value for t, it appears a dot.

Now I change the a =2 and b=2. Then it is a circle which has radius 2.

I put a=-1 ansd b=-1, then it is also a circle whse radius is 1.

Now I square them, then raised to the third power. Then they are still circles whose radius still same for the squaring but for the cubic, it has changed.

Then I changed the a=.5 , and b=1, it shows an oval.

Now I change a=.5 and b=1 for second power and third power, they both stretched vertically.

Now I put cos1t and sin2t, it looks like a bow tie.

Then I switch cos 2t and sin1t, then it looks like below.