Definition:Inverse Cosine/Complex/Arccosine

Definition

The principal branch of the complex inverse cosine function is defined as:

$\map \arccos z = \dfrac 1 i \map \Ln {z + \sqrt {z^2 - 1} }$

where:

$\Ln$ denotes the principal branch of the complex natural logarithm

$\sqrt {z^2 - 1}$ denotes the principal square root of $z^2 - 1$.

Symbol

The symbol used to denote the arccosine function is variously seen as follows:

arccos

The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the arccosine function is $\arccos$.

acos

A variant symbol used to denote the arccosine function is $\operatorname {acos}$.

Also see

• Derivation of Complex Arcsine from Inverse Cosine Multifunction

Sources

• 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $7$