Cot Calculator — Cotangent of Any Angle

公式

How this is calculated

Cotangent is the reciprocal of tangent: cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ). In a right triangle, it equals the adjacent leg divided by the opposite leg — the inverse of the tangent ratio. Like tangent, it is defined for all angles except where sin(θ) = 0, which occurs at every multiple of 180° (0, π, 2π, …). At those angles, the denominator is zero and the result is undefined (the function has vertical asymptotes).

The cotangent function has the same period as tangent — π radians (180°) — but is a decreasing function within each period rather than increasing. Near an asymptote at 0°, cot(θ) → +∞ from the right and → −∞ from the left. At θ = 90° (π/2), cot(θ) = 0, because cos(90°) = 0. At θ = 45° (π/4), cot(θ) = 1, the same value as tan(45°).

When you enter degrees the angle is first converted to radians (θ_rad = θ° × π / 180) before the trigonometric functions are evaluated. The graph shows two consecutive periods of the cotangent function with vertical asymptotes represented by gaps in the curve, and a marker at your input angle.