Exercises $1-18$ give parametric equations and parameter intervals for the motion of a particle in the $xy-$plane. Identify the particle's path by finding a Cartesian equation for it$.$ Graph the Cartesian equation. $($The graphs will vary with the equation used.$)$ Indicate the portion of the graph traced by the particle and the direction of motion.

$x=1+sint,y=cost-2,0t$