You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
23 lines
946 B
Markdown
23 lines
946 B
Markdown
# Arcus Tangent
|
|
|
|
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*.
|
|
|
|
**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%:
|
|
|
|
*atan(x) ~= (x * (2.96088 + 4.9348 * x))/(3.2 + 3.88496 * x + pi * x^2)*
|
|
|
|
```
|
|
| y
|
|
pi/2 +
|
|
| _..---''''''
|
|
| _.''
|
|
| .'
|
|
-----------.+'-+--+--+--+--+--> x
|
|
_.' |0 1 2 3 4 5
|
|
_-' |
|
|
.--'' |
|
|
-pi/2 +
|
|
|
|
|
```
|
|
|
|
*plot of atan(x)* |