Question

Convert the polar equation to rectangular form.
r=-3sinθ

Answer 1

r = -3*sin(theta)


r*r = r(-3*sin(theta))


r*r = -3r*sin(theta)


r*r = -3(r*sin(theta))


r*r = -3y


r^2 = -3y


x^2 + y^2 = -3y


x^2 + y^2 + 3y = 0

Answer 2

Okay, I understand it up to that point. I know that it forms a circle, I just don't know how to put it in the standard form so I can find the radius.

Answer 3

where are you stuck

Answer 4

I have the last equation that you typed out, I just need help putting that into x^2+y^2=r^2 so that I can find the radius of the circle that it forms.

Answer 5

Let's complete the square for the y terms

x^2 + y^2 + 3y = 0

x^2 + y^2 + 3y + 9/4 = 0 + 9/4

x^2 + y^2 + 3y + 9/4 = 9/4

x^2 + (y^2 + 3y + 9/4) = 9/4

x^2 + (y + 3/2)^2 = 9/4

x^2 + (y + 3/2)^2 = (3/2)^2

(x-0)^2 + (y - (-3/2))^2 = (3/2)^2

The equation is now in (x-h)^2 + (y-k)^2 = r^2 form where

h = 0
k = -3/2
r = 3/2

So the center is (0, -3/2)

The radius is 3/2 units

Answer 6

Can you briefly explain how you got the 9/4? I haven't really gotten the hang of the whole completing the square process. I forgot how to go about that. Everything else, though, I understand. :)

Answer 7

well I'm focusing on y^2 + 3y and I want to complete the square for that

Answer 8

so I take half of the 3 to get 3/2

then I square it to get (3/2)^2 = 9/4

Answer 9

then add this to both sides

Answer 10

this will give me y^2 + 3y + 9/4 on the left side which will factor to (y + 3/2)^2

Answer 11

Oh my goodness, thank you! Everything just clicked for me. Thanks!

Answer 12

yay lol

Answer 13

you're welcome