Here's some help . . .
1) Given: . . . Find
Both are unit circles, centered at the origin.3) Let and
(a) What does the graphs of and look like?
Consider: .(b) Suppose the graphs of two vector-valued func. and are the same,
. . .then must ? . no
. . . . . different derivatives
Explain whether this is a new result,
or was it also true for functions and ?
This is a new result.
With rectangular functions, and ,
. . if their graphs are identical, then the functions are identical.
. . Hence, their derivatives are equal.
With parametric functions, a graph can be generated in a number of ways.
. . As seen in part (b), their derivatives need not be equal.