Hy friends!
Is there any special reason for the definition ot inverse trigonometric functions domains? It is clear thar we have many possibilities of resriction in the domains that still keep the funcitions bijectives (in order to garantee the existence of their inverses). But always than possible, we choose domains that contains or are close to zero, where the functions are monotonous and that garantee a continuous function after the restriction. If we choose another domain, some calculations as strenght of a curve could be wrong? (for example, when we determine a definite integral)Thanks a lot for the clarification.