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