1. ## cartesian and polar

Hello,

I need help with this question,

a) express in polar co-cordinates the cartesian co-ordinates (2, -6)

b) express in cartesian co-ordinates the polar co-cordinates (3, 150degrees)

Thank you.

2. Originally Posted by simon
Hello,

I need help with this question,

a) express in polar co-cordinates the cartesian co-ordinates (2, -6)

b) express in cartesian co-ordinates the polar co-cordinates (3, 150degrees)

Thank you.
For these types of problems you need to recall that:
$x = r cos\theta$
$y = r sin\theta$

Inverting these relations gives:
$r = \sqrt{x^2+y^2}$
$\theta = tan^{-1} \left ( \frac{y}{x} \right )$

So for question a)
(2,-6) => x = 2, y = -6
$r = \sqrt{2^2+(-6)^2}=\sqrt{40}=2 \sqrt{10}$
$\theta = tan^{-1} \left ( \frac{-6}{2} \right ) = tan^{-1}(-3) \approx -71.5651^o$

$\theta$ is a reference angle. The point (2,-6) is in the 4th quadrant, so your angle measured from the +x axis is 360 - 71.5651 = 288.435 degrees.

Thus: (2,-6) => (2sqrt(10), 288.435 degrees).

For question b)
(3, 150 degrees) => r = 3, $\theta$ = 150 degrees
$x = 3 cos(150) \approx -2.59808$
$y = 3 sin(150) = 1.5$

Thus: (3, 150 degrees) => (-2.59808, 1.5).
(And note that it is, in fact, in the second quadrant as the original coordinates state.)

-Dan