Help with Polar Coordinates

• Apr 16th 2013, 05:07 PM
ambitionty9
Help with Polar Coordinates
Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.
• Apr 16th 2013, 05:42 PM
Plato
Re: Help with Polar Coordinates
Quote:

Originally Posted by ambitionty9
Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

I would really like to help you, but I cannot deal with the fact you are saddled with a totally outdated system.

Almost all modern mathematics does not recognized "two pairs of polar coordinates" as meaningful.
Moreover, we also insist that $=\pi<\theta\le\pi$, nobody uses degrees in mathematics.

Now if you can accept those conventions then $(2,-2)$ has polar form;
$r=2\sqrt{2}$ and $\theta = \arctan \left( {\frac{{ - 2}}{2}} \right) = \frac{{ - \pi }}{4}$.

You might tell your instructor to get with the modern usage.
• Apr 16th 2013, 06:04 PM
Soroban
Re: Help with Polar Coordinates
Hello, ambitionty9!

I agree with Plato completely.
However, if we must use this outdated notation . . .

Quote:

Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

We find that: . $r \:=\:\sqrt{2^2 + (\text{-}2)^2} \:=\:\sqrt{4+4}\:=\:\sqrt{8} \:=\:2\sqrt{2}$

One pair of coordinates is: . $\left(2\sqrt{2},\:315^o\right)$

. . . . . . . . . . .Another is: . $\left(\text{-}2\sqrt{2},\:135^o\right)$