We need to sketch r=sin theta-1.

Using the same process for the earlier examples, we obtain:

For the curve above, when θ = 0, r = −1, so the curve starts on the left side of the origin.

### Conversion to Rectangular Form

To convert to rectangular form, we use r2 = x2 + y2 and

sin^2theta=(y^2)/(r^2)=(y^2)/(x^2+y^2)

In rectangular form, r = sin θ − 1 is:

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

x^2+y^2=y-sqrt(x^2+y^2)

x^2+y^2-y=-sqrt(x^2+y^2)

(x^2+y^2-y)^2=x^2+y^2

x^4+2x^2y^2+y^4-2y(x^2+y^2)+y^2 =x^2+y^2

x^4+2x^2y^2+y^4-2y(x^2+y^2)-x^2 =0