Category:Examples of Use of Real Arccosine
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This category contains examples of Real Arccosine.
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:
Pages in category "Examples of Use of Real Arccosine"
The following 2 pages are in this category, out of 2 total.