As far I know, Inverse trigonometric function and inverse circular function are same but, I don't know what is the significance when we say inverse circular function rather than inverse trigonometric function or inverse trigonometric function as inverse circular function! So, my question is; Why we call inverse trigonometric function as inverse circular function ?
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Inverse or not, the descriptor "circular" is used to distinguish the functions from their "hyperbolic" counterparts. See "hyperbolic function" on Wikipedia.. So, in the grand scheme of things "inverse trigonometric functions" and "inverse circular functions" are NOT the same, since the former also includes "inverse hyperbolic functions". – Blue Aug 26 '16 at 11:47
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I think the term "circular functions" for "trigonometric functions" is more common in some languages other than English. – GEdgar Aug 26 '16 at 12:13
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Why we call inverse trigonometric function as inverse circular function ?
Because "trigonometric function" and "circular function" are synonymous, although usage varies depending on culture, etc. It was mentioned in the comments that "inverse trig functions" also includes the inverse hyperbolic trig functions, but perhaps that also varies by culture because I've never before seen "inverse trig functions" used to also include the inverse hyperbolic trig functions.
So then the question really becomes why are "trigonometric" and "circular" synonymous/interchangeable? Because we can define the trigonometric functions in terms of the unit circle:
Image taken from here.
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