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Preparing for a test, I've had to go through some very basic trigonometry and I've got to thinking why reference angles "work". I've gone through my study material and through another trigonometry book I have around the house and references angles are never proven, the theorem is just stated and then used.

Intuitively it makes sense right away; for example how sine goes from 0 to 1 as the angle goes from 0 to π/2, then as the angle increases, the reference angle in quadrant 2 has the same value as the angle in standard position. But after that I'm thinking that it only works because it's defined that way ...

Anyway, it's probably *really* easy, that's why it's not explained anywhere (that I've searched) but, starting from the basic definition of sin/cos/etc. in a right angled triangle I can't see how the theorem of reference angle is proven; any pointer is much appreciated.

Thank you very much!

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# Basic trig question: reference angles

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