Editing Euler angles (section)

===Last remarks===
Note that the inverse sine and cosine functions yield two possible values for the argument. In this geometrical description, only one of the solutions is valid. When Euler angles are defined as a sequence of rotations, all the solutions can be valid, but there will be only one inside the angle ranges. This is because the sequence of rotations to reach the target frame is not unique if the ranges are not previously defined.<ref>[http://eecs.qmul.ac.uk/~gslabaugh/publications/euler.pdf Gregory G. Slabaugh, Computing Euler angles from a rotation matrix]</ref>

For computational purposes, it may be useful to represent the angles using {{nowrap|[[atan2]](''y'', ''x'')}}. For example, in the case of proper Euler angles:

:<math>\alpha = \operatorname{atan2}(Z_1 , -Z_2),</math>
:<math>\gamma = \operatorname{atan2}(X_3 , Y_3).</math>