A clock has a minute hand of length $10$ inches that makes one full revolution every $3600$ seconds. Let $(x,y)$ be the position of the tip relative to the clock center, and take $t$ in seconds with $t=0$ when the tip points to the $3$ o'clock position. Write parametric equations $x\left(t\right)$ and $y\left(t\right)$ for the motion.

$x\left(t\right)=10\cos \left(\frac{\pi }{3600}t\right)$

$y\left(t\right)=-10\sin \left(\frac{\pi }{3600}t\right)$

$x\left(t\right)=10\cos \left(\frac{\pi }{1800}t\right)$

$y\left(t\right)=-10\sin \left(\frac{\pi }{1800}t\right)$

$x\left(t\right)=10\cos \left(\frac{\pi }{1800}t\right)$

$y\left(t\right)=10\sin \left(\frac{\pi }{1800}t\right)$

$x\left(t\right)=10\cos \left(\frac{\pi }{3600}t\right)$

$y\left(t\right)=10\sin \left(\frac{\pi }{3600}t\right)$