ind a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin, oriented clockwise. The point (5,0) should correspond to t=0. Use t as the parameter in your answer.

Answer 1

A common parameterization of a circle of radius r, centered at the point (h,k), is x=h+r*cos(t), y=k+r*sin(t). This parameterization starts at the point (r,0) at t=0 and traces out the circle in a CCW direction. However, */- sin(t) and +/- cos(t) can be interchanged, as long as x or y gets a sin(t) and the other a cos(t), to change the direction and starting point of the circle.

For (h,k)=(0,0), r=5, x(0)=5, y(0)=0, and a CW orientation, the correct parameterization would be

v(t)= <x(t),y(t)> = <5cos(t),-5sin(t)>.