# polar coordinates

• Aug 30th 2008, 12:06 PM
Apprentice123
polar coordinates
Determine the main set of polar coordinates of points which are rectangular coordinates:

$\displaystyle (0,-2)$

$\displaystyle p=\sqrt{0^2+(-2)^2}$
$\displaystyle p=+or-2$

How do I find the angle?

$\displaystyle (2,270°)$
• Aug 30th 2008, 12:25 PM
Sean12345
Hi Apprentice123,

Given the coordinates $\displaystyle (a,b)$ the angle $\displaystyle (\theta)$ is given by $\displaystyle \arctan\left(\frac{b}{a}\right)$ Thus in this case $\displaystyle \theta=\arctan\left(\frac{-2}{0}\right)$ Note two things. The first is that $\displaystyle \frac{-2}{0}$ is undefined so we want $\displaystyle \theta$ such that $\displaystyle \tan(\theta)$ is undefined. The second is that the coordinates $\displaystyle (0,-2)$ are in the fourth quadrant and thus so is your angle.

• Aug 30th 2008, 12:30 PM
o_O
Code:

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* (0, -2)

We see that the angle is $\displaystyle \frac{3\pi}{2}$ away from the polar axis.
• Aug 30th 2008, 03:33 PM
Apprentice123
Thanks to all