Wolfram Demonstrations Project

The graphic shows some sheets of the Riemann surface of

for inverses of sums of trigonometric functions

and

. For purely real or imaginary parts (

), multiple sheets can degenerate into a single sheet.

Contributed by: Michael Trott with permission of Springer
From: The Mathematica Guidebook for Programming, second edition by Michael Trott (© Springer, 2008).

Closed-form representation of these inverse functions can be given (say by using

in Mathematica), but they can be quite complicated.

For instance (in shortened form):

Contributed by: Michael Trott with permission of Springer

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Riemann Surfaces of Inverses of Sums of Two Trigonometric Functions