# Math Help - Polar to Rectangular Equations

1. ## Polar to Rectangular Equations

How could you change r=-3sin(Theta) into a rectangular equation?

2. Originally Posted by mi65chael2008
How could you change r=-3sin(Theta) into a rectangular equation?
Call t = theta.

x = r*cos(t)
y = r*sin(t)

So
r = sqrt{x^2 + y^2}

Now, sin(t) = y/r = y/sqrt{x^2 + y^2}

Thus:
r = -3*sin(t) <==> sqrt{x^2 + y^2} = -3*y/sqrt{x^2 + y^2}

Now simplify until you have a form that satisfies you.

-Dan

(If you mulitply both sides by sqrt{x^2 + y^2} it starts looking suspisciously like a circle. See if you can prove that.)