The cotangent is the reciprocal of the tangent: adjacent over opposite. It equals tan(90° − α) and appears in surveying, in the identity 1 + cot²α = csc²α and in complex analysis.
How to use the Cotangent Calculator
- Angle unit
- Angle α
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter the angle and pick its unit. The angle is converted to radians and cot is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.
Formula
cot α = 1 / tan α = cos α / sin α = adjacent / opposite
Range: all real numbers · Domain: α ≠ k·180° · Period: π (180°)
Worked example
Inputs — Angle unit: Degrees (°); Angle α: 30.
Results — cot(α) = 1.732050808; sin(α) = 1/2 ≈ 0.5; cos(α) = √3/2 ≈ 0.8660254038; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; sec(α) = 1.154700538.
Key terms
- Cotangent
- cot α = 1 / tan α = cos α / sin α = adjacent / opposite.
- Exact value
- A value written with integers and square roots instead of decimals.
Frequently asked questions
What is cot 45°?
1.
When is cotangent undefined?
When sin α = 0: at 0°, 180°, 360°…
What is cot 90°?
0, because cos 90° = 0.
Is cot the same as arctan?
No – cot is 1/tan; arctan is the inverse of tan.