Cotangent Calculator
Calculate cot(x) = 1/tan(x) for any angle
Common Cotangent Values
0°
Undefined
30°
√3 ≈ 1.732
45°
1
60°
√3/3 ≈ 0.577
90°
0
180°
Undefined
How to Use This Calculator
Enter the Angle
Input the angle value you want to calculate the cotangent for. You can use degrees or radians.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad).
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).