TeXipedia

csc

Represents the cosecant trigonometric function, defined as the reciprocal of sine.

Overview

Essential in trigonometry and mathematical analysis for expressing reciprocal relationships and solving trigonometric equations.

  • Commonly used in calculus for derivative and integral calculations
  • Appears frequently in physics and engineering problems involving periodic motion
  • Often paired with other trigonometric functions in complex expressions
  • Particularly useful in problems involving triangles and wave analysis

Examples

Expressing the cosecant of an angle theta in a trigonometric equation.

csc⁡θ=1sin⁡θ\csc \theta = \frac{1}{\sin \theta} 
\csc \theta = \frac{1}{\sin \theta}

Using cosecant in a trigonometric identity.

csc⁡2θ−1=cot⁡2θ\csc^2 \theta - 1 = \cot^2 \theta 
\csc^2 \theta - 1 = \cot^2 \theta

Calculating the derivative of cosecant.

ddxcsc⁡x=−csc⁡xcot⁡x\frac{d}{dx} \csc x = -\csc x \cot x 
\frac{d}{dx} \csc x = -\csc x \cot x