Trigonometric function: Cotangent of an angle (ctg)

Definition

Cotangent of an acute angle α (ctg α or cotan α) is the ratio of the adjacent leg (b) to the opposite (a) in a right triangle.

ctg α = b / a

For example:

a = 3

b = 4

ctg α = b / a = 4 / 3 ≈ 1,334.

cotangent plot

The cotangent function is written as y = ctg (x). The graph in general looks like this:x ≠ nπ, –∞ y < +∞):

Cotangent Properties

The main properties of the cotangent with formulas are presented in tabular form below.

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Property	Formula
Parity/symmetry	Parity/symmetry	Trigonometric identities	Double angle cotangent	Cotangent of sum of angles	Cotangent of angle difference	Sum of cotangents
Cotangent difference
Product of cotangents	«>
Producing cotangent and tangent	«>
Cotangent derivative	Cotangent integral	Euler formula	Обратная к котангенсу функция – это обратная функция к котангенсу x. Если котангенс угла у равняется х (ctg y = x), значит арккотангенс x равен у: arcctg x = ctg-1 x = y Таблица котангенсов 0 0 ∞ 30 Π / 6 45 Π / 4 1 60 Π / 3 90 Π / 2 0 120 2p/3 135 3p/4 -1 150 5p/6 180 π ∞ 210 7p/6 225 5p/4 1 240 4p/3 270 3p/2 0 300 5p/3 315 7p/4 -1 330 11p/6 360 2p ∞ microexcel.ru