Manipulate works in Mathematica but not in Wolfram Player

This is most likely a very naive question, but I’m puzzled as to why the following code runs smoothly in Mathematica 12.1.1.0 but does not generate a working plot in Wolfram Player 12.1.1.0.

f[a_, x_] := Sin[a x];
Manipulate[ 
 Plot[f[a, x], {x, 0, 20}],
 {{a, 1}, 0, 3}
 ]

In Mathematica, I get the expected interactive Sin graph. In Wolfram Player, I get the axes and the slider, but no graph.

If I replace the separate function definition with

Manipulate[Plot[Sin[a x]....

everything works fine in Wolfram Player.

I must not understand what Wolfram Player is supposed to do, but I’ve struggled to find adequate documentation.

Thank you in advance.