TeXipedia

cotg

Represents the cotangent trigonometric function, calculated as the ratio of the cosine to the sine of an angle.

Overview

Serves as a fundamental trigonometric function in mathematical expressions, particularly in calculus, physics, and engineering applications.

  • Common in advanced trigonometric calculations and identities
  • Used in wave analysis and periodic functions
  • Appears frequently in differential equations and complex analysis
  • Alternative to the more common \cot notation, primarily used in certain European mathematical traditions

Examples

Defining the cotangent of angle theta in a trigonometric equation.

cotg⁡θ=cos⁡θsin⁡θ\cotg \theta = \frac{\cos \theta}{\sin \theta} 
\cotg \theta = \frac{\cos \theta}{\sin \theta}

Using cotangent in a trigonometric identity.

1+cotg⁡2α=1sin⁡2α1 + \cotg^2 \alpha = \frac{1}{\sin^2 \alpha} 
1 + \cotg^2 \alpha = \frac{1}{\sin^2 \alpha}

Expressing the derivative of cotangent.

ddxcotg⁡x=−1sin⁡2x\frac{d}{dx} \cotg x = -\frac{1}{\sin^2 x} 
\frac{d}{dx} \cotg x = -\frac{1}{\sin^2 x}