Category. Mathematics.
Abstract. Trigonometric arc tangent: definition, plot, properties, identities and table of values for some arguments.
Reference. This article is a part of Librow scientific formula calculator project.
Arc tangent is inverse of the tangent function.
Arc tangent is monotone antisymmetric function defined everywhere on real axis. Its plot is depicted below in fig. 1.
[画像:Fig. 1. Plot of the arc tangent function y = arctan x.] Fig. 1. Plot of the arc tangent function y = arctanx.Function codomain is limited to the range (−π/2, π/2).
Complementary angle:
arctanx + arccotx = π/2and as consequence:
arctan cot φ = π/2 − φNegative argument:
arctan(−x) = −arctanxReciprocal argument:
arctan(1/x) = arccotx for x > 0,Sum and difference:
arctanx + arctany = arctan[(x + y) /(1 − xy)]Some argument values:
| Argument x | Value arctanx |
|---|---|
| 0 | 0 |
| 2 − √3 | π/12 |
| √(1 − 2 /√5) | π/10 |
| √2 − 1 | π/8 |
| √3 /3 | π/6 |
| √(5 − 2√5) | π/5 |
| 1 | π/4 |
| √(1 + 2 /√5) | 3π/10 |
| √3 | π/3 |
| √2 + 1 | 3π/8 |
| √(5 + 2√5) | 2π/5 |
| 2 + √3 | 5π/12 |
Trigonometric arc tangent function arctan or arctg of the real argument is supported by free version of the Librow calculator.
Trigonometric arc tangent function arctan or arctg of the complex argument is supported by professional version of the Librow calculator.
To calculate arc tangent of the number:
arctan(-1);To calculate arc tangent of the current result:
arctan(rslt);To calculate arc tangent of the number x in memory:
arctan(mem[x]);