may be solved for and , respectively. One gets the equations
where the signs have to be chosen according to the quadrant where the angle is. Changing to and dividing these equations gives us the formula
Also here one must chose the sign according to the quadrant of .
We obtain two alternative forms of (1) when we multiply both the numerator and the denominator of the radicand the first time by and the second time by ; note that :
Here, determines the sign of the right hand sides; it can be justified that it has always the same sign as .