try this

[flexifirm]

This is fun...

prove that:

arctan(x/y) - 90degrees = -arctan(y/x)

I had to do this recently for an electrical engineering problem (in an interview actually). It's ahrd at first, but once you picture things it comes fast.

[cookiemonster]

arctan(x/y) is the angle of a right triangle opposite x, so subtract 90 degrees and you're going to get the negative (since the first angle is less than 90) of the angle opposite side y.

Did you have to do that on the spot in your head? Sounds like a good question.

cookiemonster