Consider the parametric equations x=3+4sinθ and y=1-cosθ. What is the corresponding rectangular equation whose graph represents this curve?

Solve for cos θ and sin θ in the equations.

cos θ=1-y

4sinθ=x-3

sin θ=(x-3)/4

Use the identity sin^{2}θ+cos^{2}θ=1
to form an equation with only x and y.

sin^{2}θ+cos^{2}θ=1

[(x-3)/4]^{2}+(1-y)^{2}=1