Finding the Angle of a Vector

Date: 05/10/2000 at 08:15:20
From: Patrick de Kruif
Subject: Calculating the angle of a vector

I can't figure this one out. I need to know the angle (in radians) for 
a vector (x,y) that originates from O (0,0).

I found some formulas on your page to rotate a point around the 
origin; however, I need it the other way around.

                Pi/2
         (x,y).  |
               \ |
                \|a
       Pi -------+------- 0
                 |
                 |
                 |
               3Pi/2

where a is the angle and '.' is the point in space (x,y). I hope you 
can help me with this.

Many thanks,
Patrick

Date: 05/10/2000 at 08:37:11
From: Doctor Jerry
Subject: Re: Calculating the angle of a vector

Hi Patrick,

If you divide {x,y} by its length sqrt(x^2+y^2), then you have a 
vector of unit length:

     {x/sqrt(x^2+y^2),y/sqrt(x^2+y^2)}

There is a unique number t between 0 and 2pi (or between 0 and 360) 
such that:

     cos(t) = x/sqrt(x^2+y^2)

and

     sin(t) = y/sqrt(x^2+y^2)

t is the angle you want.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/