23 lines
946 B
Markdown
23 lines
946 B
Markdown
# Arcus Tangent
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Arcus tangent, written as *atan* or *tan^-1*, is the inverse [function](function.md) to the [tangent](tan.md) function. For given argument *x* (any real number) it returns a number *y* (from -[pi](pi.md)/2 to pi/2) such that *tan(y) = x*.
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**Approximation**: Near 0 *atan(x)* can very rougly be approximated simply by *x*. For a large argument *atan(x)* can be approximated by *pi/2 - 1/x* (as *atan*'s [limit](limit.md) is pi/2). The following formula { created by me ~drummyfish } approximates atan with a [poylnomial](polynomial.md) for non-negative argument with error smaller than 2%:
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*atan(x) ~= (x * (2.96088 + 4.9348 * x))/(3.2 + 3.88496 * x + pi * x^2)*
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```
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| y
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pi/2 +
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| _..---''''''
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| _.''
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| .'
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-----------.+'-+--+--+--+--+--> x
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_.' |0 1 2 3 4 5
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_-' |
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.--'' |
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-pi/2 +
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```
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*plot of atan(x)* |