Cotangent Calculator

Calculate cot(x) = 1/tan(x) for any angle

Common Cotangent Values

Undefined

30°

√3 ≈ 1.732

45°

1

60°

√3/3 ≈ 0.577

90°

0

180°

Undefined

How to Use This Calculator

1

Enter the Angle

Input the angle value you want to calculate the cotangent for. You can use degrees or radians.

2

Select Unit

Choose whether your angle is in degrees (°) or radians (rad).

3

Calculate

Click "Calculate Cotangent" to get the result. Note that cotangent is undefined when tan(θ) = 0.

Formula

cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ)

Reciprocal of tangent

Properties:

  • Range: All real numbers (-∞ to +∞)
  • Period: 180° (π radians)
  • Undefined: When tan(θ) = 0 (at 0°, 180°, 360°, etc.)
  • Odd Function: cot(-θ) = -cot(θ)

Right Triangle Definition:

cot(θ) = adjacent / opposite

About Cotangent Calculator

The Cotangent Calculator calculates cot(x) = 1/tan(x) = cos(x)/sin(x) for any angle. Cotangent is the reciprocal of tangent and one of the six fundamental trigonometric functions, widely used in advanced mathematics and engineering.

When to Use This Calculator

  • Trigonometric Calculations: Find cotangent values for any angle
  • Engineering: Solve problems involving periodic functions
  • Mathematics: Simplify trigonometric expressions
  • Verification: Check manual calculations

Why Use Our Calculator?

  • Instant Results: Get accurate cotangent values immediately
  • Multiple Units: Supports both degrees and radians
  • Related Functions: Shows sine, cosine, and tangent for comparison
  • 100% Free: No registration required

Frequently Asked Questions

What is cot(90°)?

cot(90°) = 0. This is because tan(90°) is undefined, but more precisely, as the angle approaches 90°, tan approaches infinity, so 1/tan approaches 0.

Why is cotangent undefined at 0°?

Cotangent is undefined when tan(θ) = 0. At 0°, tan(0°) = 0, so we would be dividing by zero: cot(θ) = 1/0, which is undefined.

What's the relationship between cotangent and tangent?

Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ). When tangent is large, cotangent is small, and vice versa. They multiply to 1: tan(θ) × cot(θ) = 1 (when both are defined).