Question

Where are the different trig functions constrained to? In which quadrants?

Answer 1

This is not a good question. All trig function are well-defined in all quadrants. Can you provide the exact wording of the question?

Answer 2

When you are finding the inverse of a trig function, you might get two answers, but only one of them is valid because for example sin(x) is constrained from π/2 to negative π/2. i just don't know the rest of them

Answer 3

Now, see, you did not say "INVERSE" trig functions.

For the Range of inverse trig functions, a good general rule is formed by considering the most convenient way to cover the entire RANGE of the trig function whose inverse we are considering.

\(-1 \le \sin(x) \le 1\) This can be achieved be \([-\pi/2,\pi/2]\) or \([\pi/2,3\pi/2]\) or on and on and on. Generally, we pick the one centered on zero (0), \([-\pi/2,\pi/2]\).

\(-1 \le \cos(x) \le 1\) This can be achieved be \([0,\pi]\) or \([\pi,2\pi]\) or on and on and on. Generally, we pick the one that starts with zero (0), \([0,\pi]\).

Really, it's not magic or written in stone. "We" just picked one so that fewer people would be confused.

Answer 4

thank you!