Practice!

Sample Problem

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

Solution

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 sin2θ+cos2θ=1 to form an equation with only x and y.

sin2θ+cos2θ=1

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