Riemann Surfaces of Inverse Trigonometric Functions

arcsin

arccos

arcsec

arccsc

arctan

arccot

Re/Im ratio α

The graphic shows some sheets of the Riemann surface of

(1-α)Re(f(z))+αIm(f(z))

for an inverse trigonometric function

f

. For purely real or imaginary parts (

α=0

or

α=1

), multiple sheets can degenerate into a single sheet.