Does the Usage of expression " Principal value branch" for range in the Inverse trigonometric function is correct? Does it imply range of inverse trigonometric function?
2026-03-25 08:07:54.1774426074
Does the usage of Principal value branch for range in inverse trig function is correct?
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Yes because this expression is the right one when complex $\log$ function is involved, and because inverse (circular and hyperbolic) trigonometric function can all be described using logarithmic expressions, for example:
$$\arctan(z)=i \dfrac{1}{2}\log\dfrac{i+z}{i-z}$$
The following surface representation of the argument of $\arctan$ displays this branch cut (associated to a $2 \pi$ discontinuity) along the negative $x$ axis: