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))

