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  "body": "\n## Definition\n\nThe arcsine is the function $\\arcsin \\colon [-1, 1] \\to [-\\pi/2, \\pi/2]$ such that, for each $x \\in [-1, 1]$, $\\arcsin x$ is the unique $y \\in [-\\pi/2, \\pi/2]$ with $\\sin y = x$.\n\n## Remarks\n\nThe sine is strictly increasing and continuous on $[-\\pi/2, \\pi/2]$, with range $[-1, 1]$. So $\\arcsin$ is well defined and [[continuous|07BY47HG5S]].\nFor example, $\\arcsin 0 = 0$, $\\arcsin 1 = \\pi/2$, and $\\arcsin \\frac{1}{2} = \\pi/6$.\nThe function is odd and strictly increasing. Mathlib defines `Real.arcsin` on all of $\\mathbb{R}$, constant outside $[-1, 1]$.\n\n## Explanations\n\n### L1 human\n\nThe arcsine of $x$ is the angle between $-\\pi/2$ and $\\pi/2$ whose sine is $x$.\n",
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