Question

Identify the parametric equations that represent the same path as the following parametric equations.

x(t)=2cos2t
y(t)=sin3t

a. x(t)=2cos2t
y(t)=sin6t
b. x(t)=4cos4t
y(t)=sin6t
c. x(t)=2cos4t
y(t)=sin6t
d. x(t)=4cos2t
y(t)=2sin3t

Answer 1

Looks like (c) to me. Just set u=2t and you have
x(t)=2cos2u
y(t)=sin3u
The names have been changed to protect the innocent parameters.