http://www.businessinsider.com/7-gifs-trigonometry-sine-cosine-2013-5
This page features 7 animated gifs dealing with trig.
My favorite has a sine wave, a cosine wave, two triangles, and a circle that is being, well, circled. You have to see it for yourself, which is the point. I can't describe it well enough, you just have to see it, which you can, thanks to the magic of the internet.
I am not good at drawing at all and I was very relieved when I got a projector for my classroom so I can show pictures instead of drawing on the board.
These 7 animated gifs show pi, sine, and cosine very well.
The gifs were found at imgur which the district software has blocked as "adult". They were brought to imgur from reddit, which has a Math subreddit, described in this article as "peerless". Hopefully the blocking software will be improved so that students can access approporiate material from sites that also have material we don't want students seeing.