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Riemann Surfaces of Inverses of Sums of Two Trigonometric Functions

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The graphic shows some sheets of the Riemann surface of for inverses of sums of trigonometric functions and . For purely real or imaginary parts ( or ), multiple sheets can degenerate into a single sheet.

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Contributed by: Michael Trott with permission of Springer (March 2011)
From: The Mathematica Guidebook for Programming, second edition by Michael Trott (© Springer, 2008).
Open content licensed under CC BY-NC-SA

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Closed\[Hyphen]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):

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