cot θ = 1 / tan θ
Cotangent equals one divided by tangent
Enter a decimal number (2 or 2.5), fraction (1/2), or expression with square root (√3, √3/3)
This cotangent calculator computes the cotangent value from a given tangent input. The cotangent function is the reciprocal of the tangent function and represents the ratio of the adjacent side to the opposite side in a right triangle.
cot θ = 1 / tan θ
Cotangent equals one divided by tangent
Also expressed as: cot θ = cos θ / sin θ
Calculation Example:
If tan θ = √3, then:
cot θ = 1 / √3
cot θ = 1 / 1.7321
cot θ ≈ 0.5774
This corresponds to an angle of 60° (π/3 radians)
Multiple Input Formats
Accepts decimal numbers (2.5), fractions (1/2), and expressions with square roots (√3, √3/3)
Quick Value Buttons
Common trigonometric values like √3, 1, √3/3 for standard angles
Additional Information
Shows corresponding angle in degrees and radians, plus sine and cosine values
Visual Representation
Unit circle diagram showing the geometric relationship between tangent and cotangent
Mathematical Note: The cotangent function has the same period as tangent (π radians or 180°) and is positive in quadrants I and III, negative in quadrants II and IV.
Important: Cotangent is undefined when tangent equals zero (at angles 0°, 180°, 360°, etc.), as this would result in division by zero.
The calculator provides precise results with adjustable decimal places (2-8 digits) and handles both positive and negative tangent values. This tool is useful for trigonometry students, engineers, and anyone working with right triangle calculations or periodic functions.