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  "body": "\n## Statement\n\n$$\\lim_{x \\to 0} \\frac{\\sin x}{x} = 1.$$\n\n## Remarks\n\nThe quotient is the difference quotient of $\\sin$ at $0$. So the limit is $\\sin'(0) = \\cos 0 = 1$, by the [[derivative of sine|00R4MWW532]].\nThe [[series|02KTRHQMHN]] gives $\\frac{\\sin x}{x} = 1 - \\frac{x^2}{6} + \\cdots$ for $x \\ne 0$.\nA geometric proof uses $\\cos x \\le \\frac{\\sin x}{x} \\le 1$ for $0 \u003c |x| \u003c \\pi/2$ and the squeeze theorem. Mathlib states it as `Real.tendsto_sin_div_nhdsNE_zero`.\n\n## Explanations\n\n### L1 human\n\nFor small angles in radians, $\\sin x$ is almost equal to $x$.\nThe ratio of the two tends to $1$.\n",
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