The trigonometric functions ($ \sin, \cos, \tan,...$) aren't invertible in $ R $ so we restrain it's domain to create inverses for them, the inverse trigonometric functions ($ \arcsin, \arccos, \arctan,...$). I'm not sure if it's a convention but all the books i've read restrain the sine function to the interval $ [-\pi/2, \pi/2] $ and the cosine function to the interval $ [0, \pi] $. My question is:
For what reasons mathematicians chose these intervals?
Thanks in advance