Question

how do you sketch the curve represented by
x=2+3cosθ
y=2sinθ ?

Answer 1

same as the others. pick values for θ, figure x and y, then just plot the points!

Note that since cos^2θ+sin^2θ=1,

((x-2)/3)^2 + (y/2)^2 = 1

Looks like an ellipse to me.