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Riemann Surfaces of Inverses of Sums of Two Trigonometric Functions

​
f
1
sin
cos
sec
csc
tan
cot
f
2
sin
cos
sec
csc
tan
cot
Re/Im ratio α
ξ
The graphic shows some sheets of the Riemann surface of
g
for inverses of sums of trigonometric functions
f
1
and
f
2
. For purely real or imaginary parts (
α=0
or
α=1
), multiple sheets can degenerate into a single sheet.
g(z)=(1-α)Re
(-1)
(((1-ξ)
f
1
(z))+ξ
f
2
(z))
+αIm
(-1)
(((1-ξ)
f
1
(z))+ξ
f
2
(z))
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