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While studying in P.75 of inverse trigonometric functions it tells we have to restrict our domain before finding the inverse.But I can't get why we choose $[-\pi/2,\pi/2]$?Why can't we choose $[\pi/2,3\pi/2]$ where the function arcsin is invertible on this interval?


marked as duplicate by lab bhattacharjee trigonometry Jan 20 '16 at 6:40

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You totally can. You can choose any interval where it's invertable. It's just "natural" to choose $[-\pi/2,\pi/2]$ as most "real" angles are around there.

  • $\begingroup$ :Could you tell what did you meant by 'real' angles? $\endgroup$ – justin Jan 20 '16 at 6:40
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    $\begingroup$ @justin Would a carpenter tell you 45 degrees or 765 degrees? $\endgroup$ – user223391 Jan 20 '16 at 6:42
  • $\begingroup$ :That's true.Why do we include negative values in the range when we actually can start from 90 to 270 degrees where it's all positive? $\endgroup$ – justin Jan 20 '16 at 6:44
  • $\begingroup$ @justin You could, but I think having 0 is nice.That's really all there is to it. $\endgroup$ – user223391 Jan 20 '16 at 6:46
  • $\begingroup$ :Yeah they(DKW) might have selected the first half of the sin function. $\endgroup$ – justin Jan 20 '16 at 6:55

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