How to write powers of inverse trigonometric functions?

  • Thread starter Kuhan
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Does ##(\sin^{-1}\theta)^2 =\sin^{-2}\theta## ?
 
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.
 
why would you even come across something like that?

would be easier to just use the inverse function mate.
 

HallsofIvy

Science Advisor
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To put it simply, "[itex]sin^{-1}(x)[/itex]" for the inverse function is an unfortunate notation!
 
44
0
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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