TeXipedia

sec

Represents the trigonometric secant function, which is defined as the ratio of the hypotenuse to the adjacent side in a right triangle.

Overview

Essential in trigonometry and mathematical analysis, particularly when working with angular measurements and periodic functions.

  • Commonly used in calculus for derivatives and integrals involving trigonometric functions
  • Appears frequently in physics problems involving oscillations and waves
  • Often paired with other trigonometric functions in mathematical identities
  • Particularly important in complex analysis and engineering applications where periodic behavior is studied

Examples

Expressing a trigonometric secant function in an equation.

sec⁡x=1cos⁡x\sec x = \frac{1}{\cos x} 
\sec x = \frac{1}{\cos x}

Using secant in a trigonometric identity.

sec⁡2x−tan⁡2x=1\sec^2 x - \tan^2 x = 1 
\sec^2 x - \tan^2 x = 1

Calculating the derivative of secant.

ddxsec⁡x=sec⁡xtan⁡x\frac{d}{dx} \sec x = \sec x \tan x 
\frac{d}{dx} \sec x = \sec x \tan x