Hi,
If you precalculate all the sin wave values and store them in an array, you can congratulate yourself on building your first wave table synthesizer.
Here is a link to one I have done some work on recently -
Here is a link for adding an audio amp to your project to make much better and louder audio from your Arduino -
There also are some clips of various peoples Auduinos (arduino based granualar) synth at the end of the second link
All of these are a good base for music or sound effect production.
Duane B