TeXipedia

cot

Represents the cotangent trigonometric function, defined as the ratio of the adjacent side to the opposite side in a right triangle.

Overview

Essential in trigonometry and mathematical analysis, serving as a fundamental trigonometric function with period π.

  • Commonly used in calculus for derivatives and integrals involving trigonometric expressions
  • Appears frequently in physics equations, particularly in oscillation and wave problems
  • Often encountered alongside other trigonometric functions in mathematical proofs and identities
  • Valuable in engineering applications, especially in signal processing and electrical engineering

Examples

Expressing a trigonometric identity involving cotangent.

cot⁡x=cos⁡xsin⁡x\cot x = \frac{\cos x}{\sin x} 
\cot x = \frac{\cos x}{\sin x}

Using cotangent in a calculus derivative formula.

ddxcot⁡x=−csc⁡2x\frac{d}{dx} \cot x = -\csc^2 x 
\frac{d}{dx} \cot x = -\csc^2 x

Showing the relationship between cotangent and tangent.

cot⁡x=1tan⁡x\cot x = \frac{1}{\tan x} 
\cot x = \frac{1}{\tan x}