Your function, as written, is just equal to -1, except when [itex]\phi = 1[/itex], where there is a discontinuity because the denominator vanishes there.
If you want an example of a function that has a similar form but isn't trivially some constant and has some applications, see Mobius transformation
. (But note that the Mobius transformation is usually used with complex numbers. I don't know if it is used much in real number applications).