Displaying part of piecewise function

If I define a piecewise function

f[t_] := Piecewise[{{t^2, t < 0}, {Sin[t], t > 0}}]
Which[f[t], t > 0]


how do I display only one part of the function? e.g. I want to know what f is when t>0, how do I get Mathematica to output Sin[t]?

(This is a MWE. My actual piecewise function contains thousands of terms when t<0, and I only want to study the function at t>0.)

Edit: Thanks for the responses. I should add that the piecewise function is the solution to a Convolve operation. So I'm not sure if the piecewise function is a "Mathematica function" in the strict sense.

• What else could it be if it's not a "Mathematica function in the strict sense"? – Roman Jun 7 at 12:04
• I don't know, I'm a Mathematica newbie. What I mean is, it's a function that isn't expressed as f[t_] :=. Instead it's f = . Does this make sense? – Medulla Oblongata Jun 7 at 12:22
• No, it doesn't make sense. Please read a tutorial on immediate and delayed definitions. Both are functions. – Roman Jun 7 at 13:11

PiecewiseExpand[f[t], t > 0]

Simplify gives the desired result:
Simplify[f[t], t > 0]