The basic idea is to eliminate t from the equations x= f(t), y= g(t), however you can. Here, assuming you mean x= (1/2)sin t (as opposed to 1/(2sint)) and y= (1/2)cos t, then because for all t. You should be able to recognize as a circle with center at (0,0) and radius 1/2.

You question about the "basics of plane motion" is very general. If x= f(t) and y= g(t), then the "position vector" is . Assuming t is "time", then the "velocity vector" is and the acceleration vector is .

If you are given some force function, then you also need to use the equation .