What is the t parameter of this equation?

Question

x=3sin(2t), y=1.5cos(t)

find the t parameter that graphs the full curve only once

Answer 1

sin(2t) has a period of π; cos(t) has a period of 2π. The smallest common period is 2π, so any t-interval of length 2π (e.g., 0 ≤ t < 2π) will draw the full curve exactly once.