Question

A particle moves along the polar curve r=4-2 costheta so that at time t seconds, theta=t^2.

Answer 1

Find the time t in the interval \[1 \le t \le 2 \] for which the x-coordinate of the particle's position is -1.

Answer 2

I don't want the answer, I'm not sure how to start.

Answer 3

How to start: You need your x-coordinates to =-1, recall that equation for converting from polar to rectangular

\[x(\theta) = rcos(\theta) \]\[y(\theta) = rsin(\theta) \]

Note that \[ \theta(t), r(\theta)\]
so, it would follow that x is a function of time. Use that x equation with what you know to find x as a function of t and solve when it = -1

Answer 4

That makes sense. I remembered the first part (converting polar to rectangular), but forgot the second part. Thank you.