I present for your enjoyment, Trigonometry: A Sequel to Floating Point.
Here's the source: Trig_1_0.zip. The test program is too big to run on the CPU emulator so I needed to split it in two. Trig-test.hack and Trig-plot.hack are included in the source zip. Warning: Trig-plot.hack takes about 40 minutes on my home PC.
The trig functions are built around the CORDIC algorithm.