![[Graphics:Images/ComplexFunTrigInverseMod_gr_22.gif]](../Images/ComplexFunTrigInverseMod_gr_22.gif)
The principal value used by Mathematica for the inverse
trigonometric functions are
Exploration
The first two identities are easy to explore.
![[Graphics:../Images/ComplexFunTrigInverseMod_gr_23.gif]](../Images/ComplexFunTrigInverseMod_gr_23.gif)
![[Graphics:../Images/ComplexFunTrigInverseMod_gr_24.gif]](../Images/ComplexFunTrigInverseMod_gr_24.gif)
![[Graphics:../Images/ComplexFunTrigInverseMod_gr_25.gif]](../Images/ComplexFunTrigInverseMod_gr_25.gif)
![[Graphics:../Images/ComplexFunTrigInverseMod_gr_26.gif]](../Images/ComplexFunTrigInverseMod_gr_26.gif)
The last identity requires manipulation of the real and imaginary parts.
![[Graphics:../Images/ComplexFunTrigInverseMod_gr_27.gif]](../Images/ComplexFunTrigInverseMod_gr_27.gif)
![[Graphics:../Images/ComplexFunTrigInverseMod_gr_28.gif]](../Images/ComplexFunTrigInverseMod_gr_28.gif)
The real parts should be equal in some domain set.