How to write powers of inverse trigonometric functions?

  • Thread starter Kuhan
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  • #1
Kuhan
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Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?
 

Answers and Replies

  • #2
alberto7
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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.
 
  • #3
chief10
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why would you even come across something like that?

would be easier to just use the inverse function mate.
 
  • #4
HallsofIvy
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To put it simply, "[itex]sin^{-1}(x)[/itex]" for the inverse function is an unfortunate notation!
 
  • #5
Kuhan
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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.

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##
 

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