Why does my active low pass filter produce triangle waves?
But I can never seem to get what sounds to me like a sine wave. I play
  back a youtube 1000Hz sine wave (or pick your frequency) and compare
  that to the output of my active RC filter and they just don't sound
  alike. When I listen to the 1000Hz triangle wave, then that sounds
  exactly like what I'm hearing from the output of my active RC low-pass
  filter. But why?


One thing to keep in mind is that even a small deviation from a sine wave will produce a sound very different from that of a sine wave. It very strongly depends on the harmonics that were not filtered out by your active filter circuit. You definitely need an oscilloscope.

The good news is, you can make an audio-frequency scope for peanuts:
http://www.instructables.com/id/Use-Your-Laptop-as-Oscilloscope/