Symbols:A/Arccosine/arccos
Arccosine
- $\arccos$
From Shape of Cosine Function, we have that $\cos x$ is continuous and strictly decreasing on the interval $\closedint 0 \pi$.
From Cosine of Multiple of Pi, $\cos \pi = -1$ and $\cos 0 = 1$.
Therefore, let $g: \closedint 0 \pi \to \closedint {-1} 1$ be the restriction of $\cos x$ to $\closedint 0 \pi$.
Thus from Inverse of Strictly Monotone Function, $\map g x$ admits an inverse function, which will be continuous and strictly decreasing on $\closedint {-1} 1$.
This function is called the arccosine of $x$.
Thus:
The usual symbol used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote the arccosine function is $\arccos$.
The $\LaTeX$ code for \(\arccos\) is \arccos
.
Also denoted as
acos
- $\operatorname {acos}$
A variant symbol used to denote the arccosine function is $\operatorname {acos}$.
The $\LaTeX$ code for \(\operatorname {acos}\) is \operatorname {acos}
.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): inverse trigonometric functions (antitrigonometric functions)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): arccos, arcsin, arctan, etc.${}$
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): inverse trigonometric functions (antitrigonometric functions)