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  "body": "\n## Summary\n\nThe trigonometric functions are the six functions sine, cosine, tangent, cotangent, secant and cosecant of a real angle.\n[[Sine and cosine|08WFZP6P89]] give the coordinates of a point on the unit circle.\nThe other four are quotients built from them, such as the [[tangent|05CG0S20S3]] $\\tan = \\sin / \\cos$.\nThey are periodic, they describe rotations and oscillations, and they are the building blocks of Fourier series.\nIn analysis they are defined by power series, which makes the geometric facts into theorems.\n\n## Explanations\n\n### L1 human\n\nWalk an angle $x$ (in radians) around the circle of radius $1$ starting from the point $(1, 0)$.\nThe point you reach is $(\\cos x, \\sin x)$.\nThe tangent $\\tan x = \\sin x / \\cos x$ is the slope of the line from the centre to that point.\nThe secant, cosecant and cotangent are the reciprocals $1/\\cos x$, $1/\\sin x$ and $\\cos x / \\sin x$.\nFor example, at $x = \\pi/4$ the point is $(\\frac{\\sqrt2}{2}, \\frac{\\sqrt2}{2})$, so $\\tan(\\pi/4) = 1$.\n",
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