TeXipedia

ctg

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 trigonometric identities and equations
  • Used in analyzing periodic phenomena and wave functions
  • Appears frequently in advanced calculus problems involving trigonometric substitution
  • Often encountered in mathematical physics when dealing with oscillations and waves
  • Alternative to writing cot, though cot is more commonly used in modern LaTeX documents

Examples

Expressing a trigonometric identity involving cotangent.

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

Calculating the derivative of cotangent.

ddxctg⁡x=−1sin⁡2x\frac{d}{dx} \ctg x = -\frac{1}{\sin^2 x} 
\frac{d}{dx} \ctg x = -\frac{1}{\sin^2 x}

Using cotangent in a double angle formula.

ctg⁡2x=ctg⁡x−tan⁡x2\ctg 2x = \frac{\ctg x - \tan x}{2} 
\ctg 2x = \frac{\ctg x - \tan x}{2}