why is math hard

**SHORTY** · November 12th 2006, 02:16 AM

convert the rectangular to polar (-2,3)

**topsquark** · November 12th 2006, 05:43 AM

Originally Posted by SHORTY

convert the rectangular to polar (-2,3)

We know that
$x = r \, cos \theta$
$y = r \, sin \theta$

So, upon inverting this:
$r = \sqrt{x^2 + y^2}$
$\theta = atn \left ( \frac{y}{\sqrt{x^2+y^2}} \right )$

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

Anyways:
$r = \sqrt{(-2)^2 + 3^2} = \sqrt{4+9} = \sqrt{13}$
$\theta = atn \left ( \frac{3}{\sqrt{(-2)^2+3^2}} \right ) = atn \left ( \frac{3}{\sqrt{13}} \right )$ (radians)

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

-Dan

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