Question

Eliminate the parameter to find a description of the following circles or circular arc in terms of x and y. Give the center and radius and indicate the positive orientation.

x=3sin(t), y=-3cos(t) ; 0 < t < 2pi

Answer 1

x=3sin(t), y=-3cos(t) ; 0 < t < 2pi
x^2 = 9 sin^2 t
y^2 = 9 cos^2 t
x^2 + y^2 = 9 (sin^2 t + cos^2 t)
but we all know sin^2+cos^2 = 1
x^2 + y^2 = 3^2
center at (0,0) radius 3

Answer 2

x=3sin(t), y=-3cos(t)
sint = x/3
cost = y/-3

sin^2 t + cos^2 t = 1
x^2/9 + y^2/9 = 1
x^2 + y^2 = 9

circle with centre (0,0) and radius 3

verification:
https://www.wolframalpha.com/input/?i=parametric+plot+x%3D3sin%28t%29%2C+y%3D-3cos%28t%29+