Assign function to a variable and solve it symbolically

I have a function such as y = sin(x) + c. I’d like to solve it symbolically for c (but first assign the function to a variable, so I don’t have to enter it multiple times in case I want to solve it for x as well. Any suggestions how I can do this?

I’ve tried this:

fn[x_, c_] := Sin[x] + c Solve[fn, c] 

but getting an error ‘fn is not a quantified system of equations’.

Any help is appreciated.