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Calculate the cotangent of any angle. Cotangent is the reciprocal of tangent: cot(θ) = 1/tan(θ) = cos(θ)/sin(θ).
| Degrees | Radians | Exact Value | Decimal |
|---|---|---|---|
| 0° | 0 | undefined | — |
| 30° | π/6 | √3 | 1.7321 |
| 45° | π/4 | 1 | 1.0000 |
| 60° | π/3 | √3/3 | 0.5774 |
| 90° | π/2 | 0 | 0.0000 |
| 120° | 2π/3 | -√3/3 | -0.5774 |
| 135° | 3π/4 | -1 | -1.0000 |
| 150° | 5π/6 | -√3 | -1.7321 |
| 180° | π | undefined | — |
| 270° | 3π/2 | 0 | 0.0000 |
All θ except 0°, 180°, 360°, ...
Where sin(θ) ≠ 0
All real numbers (-∞, ∞)
Same as tangent
π radians (180°)
cot(θ + π) = cot(θ)
Odd function: cot(-θ) = -cot(θ)
Origin symmetry
Cotangent is the reciprocal of tangent. It can be expressed as cos/sin or adjacent/opposite in a right triangle.
cot(θ) = 1/tan(θ). Their asymptotes and zeros are swapped: where tan is undefined, cot is zero, and vice versa.
Cotangent is positive in Quadrants I and III (same as tangent), where sin and cos have the same sign.