Cotangent Calculator
Calculate cot θ for any angle in degrees, radians or multiples of π, with exact values for standard angles and the matching sin, cos and tan.
The cotangent of an angle is its cosine divided by its sine, which is the same as 1 ÷ tan θ. In a right triangle it is the adjacent side divided by the opposite side. Enter an angle in degrees, radians or multiples of π to get cot θ, the exact value for standard angles, and the matching sine, cosine and tangent.
How to use this tool
- Enter the angle.
- Choose degrees, radians or multiples of π (0.5 means π/2).
- Read cot θ, its exact form for standard angles, and sin, cos and tan of the same angle.
- Use the table for the standard angles from 0° to 180°.
Formula
cot θ = cos θ ÷ sin θ = 1 ÷ tan θ
cot θ is undefined wherever sin θ = 0 (0°, 180°, 360° …) and equals 0 wherever cos θ = 0 (90°, 270° …). It repeats every 180°, or π radians. Most calculators have no cot key; typing 1 ÷ tan θ works except at 90°, where tan is undefined but cot is exactly 0.
Example
For θ = 30°, sin 30° = 0.5 and cos 30° = √3/2 ≈ 0.866025, so cot 30° = 0.866025 ÷ 0.5 = √3 ≈ 1.7320508076. For θ = 1 radian (about 57.29578°), cot 1 = 0.540302 ÷ 0.841471 ≈ 0.6420926159.
Frequently asked questions
Is cotangent the same as inverse tangent?
No. cot θ = 1 ÷ tan θ is a reciprocal and returns a ratio. The inverse tangent, tan⁻¹ or arctan, takes a ratio and returns an angle.
Where is cotangent negative?
In the second and fourth quadrants (between 90° and 180°, and between 270° and 360°), where sine and cosine have opposite signs.
What is cot 0°?
Undefined. sin 0° = 0, and dividing cos 0° = 1 by zero has no value. As θ approaches 0° from above, cot θ grows without bound.
How do I find an angle from its cotangent?
Use θ = arctan(1 ÷ cot θ) for positive values, which gives an angle between 0° and 90°. For example, cot θ = 1 gives θ = 45°.
Last updated: 2026-10-30