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  "body": "\n## Definition\n\nThe arccosine is the function $\\arccos \\colon [-1, 1] \\to [0, \\pi]$ such that, for each $x \\in [-1, 1]$, $\\arccos x$ is the unique $y \\in [0, \\pi]$ with $\\cos y = x$.\n\n## Remarks\n\nThe cosine is strictly decreasing and continuous on $[0, \\pi]$, with range $[-1, 1]$. So $\\arccos$ is well defined and [[continuous|07BY47HG5S]].\nFor all $x \\in [-1, 1]$, $\\arccos x = \\frac{\\pi}{2} - \\arcsin x$.\nFor example, $\\arccos 1 = 0$ and $\\arccos(-1) = \\pi$. Mathlib defines `Real.arccos` by the identity above.\n\n## Explanations\n\n### L1 human\n\nThe arccosine of $x$ is the angle between $0$ and $\\pi$ whose cosine is $x$.\n",
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