Find a Cartesian equation for the curve and identify it.

[tangibleLime]

Homework Statement

Find a Cartesian equation for the curve and identify it.

r = 3sin(θ)

Homework Equations

The Attempt at a Solution

I know that the answer is as follows...

$$r^2=3(r*sin(\theta))$$
$$x^2+y^2 = 3y$$
$$x^2 + (y-\frac{3}{2})^2 = (\frac{3}{2})^2$$

I understand everything but the last part. Where the hell is (3/2) coming from? I know if I want to solve the equation, x can be (3/2) and y can be (3/2) or... but x is still in here and so is y.

 

[Mark44]

Homework Statement

Find a Cartesian equation for the curve and identify it.

r = 3sin(θ)

Homework Equations

The Attempt at a Solution

I know that the answer is as follows...

$$r^2=3(r*sin(\theta))$$
$$x^2+y^2 = 3y$$
$$x^2 + (y-\frac{3}{2})^2 = (\frac{3}{2})^2$$

I understand everything but the last part. Where the hell is (3/2) coming from? I know if I want to solve the equation, x can be (3/2) and y can be (3/2) or... but x is still in here and so is y.

Whoever wrote the answer is completing the square in the y terms.
x² + y² - (3/2)y = 0
To complete the square, (3/2)² must be added to both sides.

 

[tangibleLime]

Oooh thanks. It would have been cool if he said that instead of just doing it (it was a video).

 

[Mark44]

Whoever made the video is assuming that you are familiar with the operation of completing the square.