TeXipedia

arcctg

Represents the inverse (arc) cotangent function in mathematical expressions, returning angles from cotangent values.

Overview

Serves as a fundamental inverse trigonometric function, particularly important in calculus, trigonometry, and mathematical analysis.

  • Returns angles in radians when given a cotangent value
  • Common in solving trigonometric equations and geometric problems
  • Often used alongside other inverse trig functions in advanced mathematics
  • Particularly relevant in engineering calculations and physics problems involving angular measurements
  • Alternative notation to arccot, though less commonly used in modern mathematical writing

Examples

Finding the inverse cotangent of x in a trigonometric equation

y=arcctg(x)y = \arcctg(x)
y = \arcctg(x)

Solving a trigonometric identity involving inverse cotangent

arcctg(x)+arctan(x)=π2\arcctg(x) + \arctan(x) = \frac{\pi}{2}
\arcctg(x) + \arctan(x) = \frac{\pi}{2}

Computing the derivative of inverse cotangent

ddxarcctg(x)=11+x2\frac{d}{dx}\arcctg(x) = -\frac{1}{1 + x^2}
\frac{d}{dx}\arcctg(x) = -\frac{1}{1 + x^2}