Write in Rectangular Form?

Question

The letters r and theta represent polar coordinates. Write each equation in rectangular coordinates (x, y) form.

Let t = theta

(1) r = sin(t) + 1

(2) r = sin(t) - cos(t)

Answer 1

x=r cos t and y = r sin t and x^2+y^2=r^2
1)r= y/r+1 so r^2= y+r and x^2+y^2=y+sqrt(x^2+y^2)
2)r=(y-x)/r so x^2+y^2+x-y=0 ( circunference center(-1/2,1/2) and radius =sqrt(1/2)

Answer 2

x = rcostheta
y = rsintheta
x^2 + y^2 = r
tan^-1(y/x) = theta
you do the math/conversions