find the polar coordinates from the cartesian coordinates?

[Messagehelp]

The Cartesian coordinates of a point are given.

(a) Find polar coordinates (r, ?) of the point (2?3, 2), where r > 0 and 0 ? ? ? 2?.
(b) Find polar coordinates (r, ?) of the point (2?3, 2), where r < 0 and 0 ? ? ? 2?.
(c) Find polar coordinates (r, ?) of the point (1, -5), where r > 0 and 0 ? ? ? 2?.
(d) Find polar coordinates (r, ?) of the point (1, -5), where r < 0 and 0 ? ? ? 2?.

 

[skeeter]

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

\(\displaystyle \theta = \arctan\left(\frac{y}{x}\right)\)

remember that the arctan function gives values of \(\displaystyle \theta\) in quadrants I and IV, from \(\displaystyle -\frac{\pi}{2}\) to \(\displaystyle \frac{\pi}{2}\).
angles in quad IV are negative, so add \(\displaystyle 2\pi\) ... also, you'll have to add \(\displaystyle \pi\) for values of \(\displaystyle \theta\) in quadrants II and III, so pay attention to what quadrant you're working in.