HP -15C Advanced Functions Handbook page 72

70 Section 3: Calculating in Complex Mode
The illustrations that follow show the principal branches of the
inverse relations. The left-hand graph in each figure represents the
cut domain of the inverse function; the right-hand graph shows the
range of the principal branch.
For some inverse relations, the definitions of the principal
branches are not universally agreed upon. The principal branches
used by the HP-15C were carefully chosen. First, they are analytic
in the regions where the arguments of the real-valued inverse
functions are defined. That is, the branch cut occurs where its
corresponding real-valued inverse function is undefined. Second,
most of the important symmetries are preserved. For example,
z) = -SIN^z) for all z.
d
'
z — \ j r e
for -TT < 9 «S
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-in