Category:Examples of Use of Real Arccosine

This category contains examples of Real Arccosine.

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 $\closedint 0 \pi$.