Question

Give a parameter interval that traces the curve exactly once.
x = 3sin(2t)
y = 1.5cos(t)

Answer 1

Yo @jim_thompson5910 buddy can you help me out here a bit? :D

Answer 2

Start by letting \(t=0\).

Answer 3

Find the initial position on the interval.

Answer 4

you get \((x,y)=(0,1.5)\)

Answer 5

Now we need to find solutions:\[
0 = 3\sin(2t),\quad 1.5=1.5\cos(t)
\]

Answer 6

Solutions for the first equation are: \[
\frac \pi 2 n
\]And solutions for the second one are: \[
2\pi n
\]

Answer 7

The least common multiple is \(2\pi\) so I'd say that is the period.