# The polar angle of a point with respect to another

1. Dec 2, 2005

### 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.

2. Dec 2, 2005

### 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, $$p_0 \times p_1 = |p_o||p_1|sin(\theta)$$)

3. Dec 2, 2005

### twoflower

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.