A particle is moving along the curve $r=4-2\sin(\theta)$ at the moment when $\theta = t^2$. I need to write a x(t) and y(t) function that will model the particle behavior with its x position and y position as a function of time, t.
I've tried converting it to Cartesian and going from there, but I can't figure it out with the multiple degrees of x and y when I do. Any ideas?
Thanks!
$x = r \cos \theta\\ y = r \sin \theta\\ r = 4 - 2 \sin \theta\\ \theta = t^2\\ x = (4 - 2 \sin t^2)(\cos t^2)\\ y = (4 - 2 \sin t^2)(\sin t^2)$