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Where do the equations that are given to use the certain trig function in certain cases

if you have a proof , that's what im looking for

bascally you can test them after but i'm wondering how'd you do it with a triangle before guessing

I'm not sure what you mean, but see if the picture below helps you.

not quite i understand this it's where they get these rules

@.Sam.

in other words how'd they know to use sec,sin,and tan...

whered you get the triangle

I mean why do derivatives of certain cartesian functions yield a trig function

You need it only if you have something like this, you can use trig substitution for 1/sqrt(a^2+x^2). But that depends on the overall equation.

|dw:1361606519927:dw|

i'm looking for proofs =/

http://www.youtube.com/watch?v=4-ecaZYZ9po