Advanced Engineering Mathematics, 7th Edition

17.8 Inverse Trigonometric and Hyperbolic Functions

INTRODUCTION

As functions of a complex variable z, we have seen that both the trigonometric and hyperbolic functions are periodic. Consequently, these functions do not possess inverses that are functions in the strictest interpretation of that word. The inverses of these analytic functions are multiple-valued functions. As we did in Section 17.6, in the examination of the logarithmic function, we shall drop the adjective multiple-valued throughout the discussion that follows.

Inverse Sine

The inverse sine function, written as sin⁻¹z or arcsin z, is defined by

(1)

The inverse sine can be ...