The polar angle of a point with respect to another

[twoflower]

Hi all,

could you please tell me how to count polar angle of a point with respect to another one using cross product?

I know that polar angle of a point p_0 with respect to point p_1 is the angle of vector p_1 - p_0.

For example, polar angle of (3,3) with respect to (2,4) is the angle of (1,-1) which is 315 degrees or \frac{7 \pi}{4} radians.

How to count it using cross product?

Thank you.

 

[vsage]

The crossproduct may be alternately defined as the magnitude of the product of the distances between the two points and the origin and the sine of the angle between the two points.

(in formula, p_0 \times p_1 = |p_o||p_1|sin(\theta))

 

[twoflower]

The crossproduct may be alternately defined as the magnitude of the product of the distances between the two points and the origin and the sine of the angle between the two points.
(in formula, p_0 \times p_1 = |p_o||p_1|sin(\theta))

Thank you. So, if one of those vector will be that mine p_1 - p_0 and the second one in the formula will be (1,0), will be ok to compute the angle from it? (using arcsin function).

Now I tried it on two examples and it works well, I just have to take care of negative angles I get from it.