Question

Find the parametric equations of a circle centered at the origin with radius of 4 where you start at point (-4,0) at s=0 and you travel counterclockwise with a period of 2π.

Answer 1

x = a cos s
y = a sin s

when s = 0, x = -4
so =-4 = a cos 0 = a
so
x = - 4 cos s
when s = pi/2 , y = -4
so -4 = a sin pi/2 = a
so y = -4 sin s

Answer 2

you know that
y = 4 sint
x = 4 cost
starts at (4,0)
You are 180° out of phase, starting at (-4,0)
So,
y = 4sin(t+π)
x = 4cos(t+π)
and Damon's equations work.