Question

describe the parameters of the unit circle , and when the particle is moving clockwise/counterclockwise (how do i determine this)in this problem x=cost and y= -sin t

Answer 1

First part:
the equation of unit circle: x^2+y^2=1
the Pythagorean Trig Identity: [sin(t)]^2+[cos(t)]^2=1
Based on these two equations, I'd guess that the parameters of a unit circle are the absolute values of sine and cosine (x and y respectively).

2nd part:
the parameters given simply describe a unit circle with y=-sin(t), since sine is an odd function (odd functions means f(-x)=-f(x)), -sin(t)=sin(-t) so this parametric function travels in the opposite direction of y=sin(t). Thus for all t<0 it is traveling counterclockwise, for all t>0, it's going to be clockwise, and if t=0, then there's no direction. Plug in the typical unit circle angles (pi/6, pi/4, pi/2 etc.) and see what direction it takes to get a geometric explanation.