PROJECT: PARAMETRIC EQUATIONS

Directions

1. In the essay box below, write a pair of parametric equations for an object moving along the unit circle. (Hint: How is a point on the unit circle defined?)

2. On a separate sheet of graph paper, graph the curve that is traced by a point for the following parametric equations as the parameter varies over the domain 0 t 2:

x = 2cost

y = 2sint

Create a table of values like the one shown above (you may need to upload your table from a word processing program). Show at least five points.

3. On a separate sheet of graph paper, graph the curve that is traced by a point for the following parametric equations as the parameter varies over the domain 0 t 2:

x = 4cost

y = 2sint

Create a table of values like the one shown above (you may need to upload your table from a word processing program). Show at least five points.

4. Based on your work above, write any inferences you have about parametric equations of the form x = acost and y = bsint, for a = b and a b.