I apologize if this seems like a newbie question but it's been really messing with my head.
I'm reading about using trig substitution in integration and everyone seems to simply construct a right triangle to get what the trig functions will be (in terms of the original variable).
Shouldn't that only work for cases where the angle is acute and positive? What about the cases where the angle is obtuse or where some trig functions might be negative. As far as I know, using the right triangle will always give a positive cos/sin/tan (because sides are always positive).
Can you please explain in as much detail as possible how to correctly use a right triangle in cases where the angle is obtuse or one of the trig functions is negative. Thanks a lot in advance.