If you have some uncertainty above the value of H, you can represent
it as h+dh
for some presumably small quantity dh. Then how does the value of dh affect
the value of sin(H) = sin(h+dh)?
A simple way is to compute taylor(sin(h+dh),dh,0, 1) which tells
you sin(h)+ cos(h)*dh to
a 1stt order linear approximation. You can carry more terms and/or you
can do this for more variables, e.g.
taylor(sin(h+dh)*cos(g+dg) ,[dh,dg],0,2);
gives terms up to total degree 2, e.g. dh*dg or dg^2.
I don't see how there is a problem if dh, dg etc are small -- so that
dh^2 is very small etc.
Another way would be to use interval arithmetic, and represent H =
interval(h_low, h_high),
and propagate uncertainty that way. In spite of several interval
arithmetic proposals,
and implementations in Lisp, nothing has been installed in Maxima by
default. It works
only if h_low and h_high are numeric, and gives worst case
"containment" values that
guarantee to contain the right answer, but may be unnecessarily wide.
I didn't see that the original poster was asking about using Maxima for
arithmetic on
distributions, but maybe that's my uninformed reading.