2

I have kind of a random question I'm hoping someone could help me with.

So I was thinking about the interval $[-\pi, \pi]$ for a trig functions. Isn't this is the same interval as $[0, 2\pi]?$ The reason why I say that (and maybe this is where my confusion is) is because couldn't $[-\pi, \pi]$ be split as $[-\pi, 0] \cup [0, \pi],$ which when drawn the angle of rotation hits all the vital points on the unit circle just like $[0, 2\pi]?$

Thanks in advance!

mfl
  • 29,399
Astro
  • 257
  • 3
    If you mean to ask why we pick one over the other, there is no reason. Both capture a full cycle of a sine or cosine wave. Some mathematicians have preference for $[-\pi,\pi]$ because it's symmetric. Some have preference for $[0,2\pi]$ because of tradition. It doesn't matter which you choose as long as you are consistent with your choice. – Cameron Williams Jun 21 '14 at 23:36
  • Thank you! Also, neat little side note about preference. Appreciate the input! – Astro Jun 21 '14 at 23:39
  • You're very welcome :) – Cameron Williams Jun 21 '14 at 23:39

1 Answers1

0

I feel it would depend on the specific trig function only if you include hyperbolic.

Sam
  • 143
  • 6