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Intuitive Trigonometry

I was very fortunate to have been taking electronics at the same time I was learning high school trigonometry.  Like most folks, I was never good at abstract math, but being able to see physical demonstrations of math principles was a huge help.
One of the real "bears" for most math students is the concept of the imaginary number...and yet it's crucial to working with all alternating current electrical and electronics problems.
When I teach electronics, I have students ranging from postgraduate math majors to middle school students who want to take a few shop classes before high school.  (Nice thing about working at a technical arts extension of the local University!)
I introduce practical trigonometry without even using the term, using nothing more than a straightedge, some graph paper, and a protractor.  I avoid trig tables entirely UNTIL they understand how to manipulate the Pythagorean theorem inside out and upside down.
I then demonstrate how the Imaginary Number is anything but imaginary in physical systems, using pendulums, vibrating strings, and other very intuitive, familiar phenomena.
 
It's been my experience that lots of kids are turned away from the sciences because of the daunting mathematical prerequisites for such classes.  This is because math is generally taught in such an abstract manner, which I think is a mistake.  I do it backwards....I use the sciences to teach the math.  I think MOST kids' brains work better this way.
 
Eric