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Article 11 — Appendix A.4

arccot or arcctg — trigonometric arc cotangent function

Category. Mathematics.

Abstract. Trigonometric arc cotangent: definition, graph, properties, identities and table of values for some arguments.

References. This article is a part of scientific calculator Li-L, scientific calculator Li-X, scientific calculator Li-Lc and scientific calculator Li-Xc products.

1. Definition

Arc cotangent is inverse of the cotangent function.

2. Graph

Arc cotangent is monotone function defined everywhere on real axis. Its graph is depicted below — fig. 1.

Fig. 1. Graph of the arc cotangent function y = arccot x Fig. 1. Graph of the arc cotangent function y = arccotx.

Function codomain is limited to the range (0, π).

3. Identities

Complementary angle:

arctanx + arccotx = π/2

and as consequence:

arccot tan φ = π/2 − φ

Negative argument:

arccot(−x) = π − arccotx

Reciprocal argument:

arccot(1/x) = arctanx for x > 0,
arccot(1/x) = arctanx + π for x < 0

Sum and difference:

arccotx + arccoty = arccot[(xy − 1) /(x + y)]
arccotx − arccoty = arccot[(xy + 1) /(yx)]

Some argument values:

Argument xValue arccotx
0π/2
2 − √35π/12
√(1 − 2 /√5)2π/5
√2 − 13π/8
√3 /3π/3
√(5 − 2 √5)3π/10
1π/4
√(1 + 2 /√5)π/5
√3π/6
√2 + 1π/8
√(5 + 2 √5)π/10
2 + √3π/12
Table 1. Arc cotangent for some argument values.

4. Support

Trigonometric arc cotangent function arccot or arcctg is supported in:

Trigonometric arc cotangent function of the complex argument arccot or arcctg is supported in:

5. How to use

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]);