convert the rectangular to polar (-2,3)

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- Nov 12th 2006, 02:16 AMSHORTYwhy is math hard
convert the rectangular to polar (-2,3)

- Nov 12th 2006, 05:43 AMtopsquark
We know that

$\displaystyle x = r \, cos \theta$

$\displaystyle y = r \, sin \theta$

So, upon inverting this:

$\displaystyle r = \sqrt{x^2 + y^2}$

$\displaystyle \theta = atn \left ( \frac{y}{\sqrt{x^2+y^2}} \right )$

(Which you can likely look up. I can never seem to remember the equations, so I derive them.)

Anyways:

$\displaystyle r = \sqrt{(-2)^2 + 3^2} = \sqrt{4+9} = \sqrt{13}$

$\displaystyle \theta = atn \left ( \frac{3}{\sqrt{(-2)^2+3^2}} \right ) = atn \left ( \frac{3}{\sqrt{13}} \right )$ (radians)

Off the top of my head I don't believe that the angle simplifies.

-Dan