How many possible values for y are there where y = tan ^-1 3

A. 1

B. 2

C. Infinite

D. 0

The answer is infinite

The reason for that is that arctan (which is inverse function of tan) gives 2 values of angles between 0 and 2pi but we can go below 0 and above 2pi radians as much as we like (for example there is angle - 10000pi or + 3000000pi) up to infinity which means there are infinite answers.

It is important to remember that arctan gives infinite numbers of answer but function tan gives only 1 answer.