Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to write powers of inverse trigonometric functions?

  1. Sep 30, 2012 #1
    Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?
     
  2. jcsd
  3. Sep 30, 2012 #2
    I think we use ##\arcsin## for the functional inverse of ##\sin## and ##\csc## for its multiplicative inverse, instead of ##\sin^{-1}##, in order to avoid this confusion. As ##\sin^n## is multiplicative for ##n>0##, I would say that ##\sin^{-n}=\csc^n##. If one needed to write many times the functional iterates and inverses of ##\sin##, I would recommend to use a notation like ##\sin^{[n]}## or ##\sin^{\circ n}##, which I've found in papers dealing with iterated functions.
     
  4. Sep 30, 2012 #3
    why would you even come across something like that?

    would be easier to just use the inverse function mate.
     
  5. Oct 1, 2012 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    To put it simply, "[itex]sin^{-1}(x)[/itex]" for the inverse function is an unfortunate notation!
     
  6. Oct 11, 2012 #5
    Thanks! now it makes sense. I used to use ##\sin^{-1}\theta## instead of ##\arcsin\theta## . They just aren't the same, I guess. Basically,
    ##\sin^{-1}\theta=\csc\theta##
     
  7. Oct 11, 2012 #6
  8. Oct 11, 2012 #7
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to write powers of inverse trigonometric functions?
Loading...