Symbols:A/Arccosine/acos

Arccosine

$\operatorname {acos}$

Real Arccosine Function

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 domain of arccosine is $\closedint {-1} 1$

The image of arccosine is $\closedint 0 \pi$.

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

The $\LaTeX$ code for \(\operatorname {acos}\) is \operatorname {acos} .

Also denoted as

arccos

$\arccos$

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

The $\LaTeX$ code for \(\arccos\) is \arccos .

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): acos