Question

How many possible values for y are there where y = cos^-1 0?

Answer 1

If you mean \[y= \cos^{-1}(0) \] then are infinitly many of them.
Like \[ \pm \frac \pi 2 + 2 k \pi, k=0,\pm 1, \pm 2, ....
\]

Answer 2

hell no

Answer 3

arccosine is a well defined function
one input
one output

\[\cos^{-1}(0)=\frac{\pi}{2}\] and no other number

Answer 4

I agree with you if you restrict the domain to get a function. But there are infinite values x so that cos(x)=0

Answer 5

and i agree with you that there are infinitely many x such that \(\cos(x)=0\)
however there is only one \(\cos^{-1}(0)\)

Answer 6

Depending how you define the question.

Answer 7

In some books Arccos is the one valued function and \[ \cos^{-1} \] is the multivalued function.