> P(n) =3D x - (x^3/6) + (x^5/120) - (x^7/5040)
> I don't know what this approximation is called or if it really works the
> way it's supposed to. I got it from a local math whiz; supposedly it
> will approximate sine of x where x is the angle in radians.

This looks like the "standard" taylor series approximation for Sine (the
beginning of it, anyway.  (it continues on with X^N/N! for odd N, IIRC.)
This WILL produce Sine(x), but it is NOT particularly quickly converging,
nor is it particularly easy for a computer to calculate, both of which
would be desirable on a PIC.

Lookup tables are easier but have a reputation for being quite large (for
the table), but the table size is actually very dependent on how much
accuracy you need.  Relative sizes will also depend on how much math library
you need to include for any algorithm - a lookup table can yield results
that are already in useful and minimized form (ie a byte fraction N/256
instead of a four byte "floating point" number.)

There are also algorithms that are quicker and easier to compute, but I
can't come up with one off the top of my head...

BillW