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  "body": "\n## Definition\n\nThe arctangent is the function $\\arctan \\colon \\mathbb{R} \\to (-\\pi/2, \\pi/2)$ such that, for each real $x$, $\\arctan x$ is the unique $y \\in (-\\pi/2, \\pi/2)$ with $\\tan y = x$.\n\n## Remarks\n\nThe [[tangent|06T0HS14PP]] is strictly increasing and continuous on $(-\\pi/2, \\pi/2)$, with range $\\mathbb{R}$. So $\\arctan$ is well defined and [[continuous|07BY47HG5S]].\nFor example, $\\arctan 0 = 0$ and $\\arctan 1 = \\pi/4$.\nAlso $\\arctan x \\to \\pi/2$ as $x \\to \\infty$, and $\\arctan x \\to -\\pi/2$ as $x \\to -\\infty$. Mathlib defines it as `Real.arctan`.\n\n## Explanations\n\n### L1 human\n\nThe arctangent of $x$ is the angle between $-\\pi/2$ and $\\pi/2$ whose tangent is $x$.\nIt is the angle of a line with slope $x$.\n",
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