Arcsin(1/9)

Arccos(-4/3)

Arctan(11/12)

Arccot(-4)

Arcsec(3Pi)

What exactly is to define a function?

NOw the answer to this is supposed to be Arccos(-4/3) because $\displaystyle -1\leq cos(x) \leq+1$

Is Cos(x) between -1 and +1 because it is DEFINED that way?

What about arcsec(3Pi)? Is that defined? Isn't arcsec 3Pi = 1/(arccos 3Pi)? and again isn't 3Pi greater than 1 thereby rendering it undefined because $\displaystyle -1\leq cos(x) \leq+1 $

?????