Definition:Inverse Cosine/Complex/Arccosine
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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:
The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the arccosine function is $\arccos$.
A variant symbol used to denote the arccosine function is $\operatorname {acos}$.
Also see
Sources
- 1981: Murray R. Spiegel: Theory and Problems of Complex Variables (SI ed.) ... (previous) ... (next): $2$: Functions, Limits and Continuity: The Elementary Functions: $7$