math

Cotangent Calculator

Calculate cot(θ) for any angle in degrees or radians — returns cos ÷ sin.

Angle

cot(θ)

cot(θ) = cos(θ) ÷ sin(θ) = 1 ÷ tan(θ). Undefined at 0°, 180°, 360°, … (and multiples of π rad) where sin(θ) = 0.

How it works

1Enter any angle and choose Degrees or Radians using the unit toggle.
2The calculator evaluates cot(θ) = cos(θ) ÷ sin(θ); boundary angles (0°, 180°, …) correctly return —.
3The result is displayed to 6 figures; — appears whenever sin(θ) = 0 and cotangent is undefined.

Solving oblique triangles and verifying trigonometric identities in precalculus and calculus.
Engineering and physics problems involving slope, inclination, and wave analysis.
Quick sanity-checking: cot(45°) = 1, cot(30°) ≈ 1.732, cot(60°) ≈ 0.577.

Why does the calculator show — for 0°?

Cotangent is cos(θ) ÷ sin(θ). At 0° (and every multiple of 180°) sin(θ) = 0, making the expression undefined — like division by zero.

How does cotangent relate to tangent?

cot(θ) = 1 ÷ tan(θ); they are reciprocals. Wherever tan(θ) = 0 the cotangent is undefined, and vice versa.

Can I enter negative angles or angles over 360°?

Yes. Cotangent is periodic with period 180°, so cot(−45°) = cot(135°) = −1 and cot(405°) = cot(45°) = 1. Any real angle works.

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