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.