Cot Calculator — Cotangent of Any Angle
Enter an angle in degrees or radians to calculate cot(θ) = cos(θ) / sin(θ), and also see sin, cos and tan for the same angle.
Angle unit
Cotangent = cos(θ) / sin(θ) = 1 / tan(θ)
- 1
Convert to radians
45° × π ÷ 180 = 0,785398 - 2
sin(θ)
sin(0,785398) = 0,707107 - 3
cos(θ)
cos(0,785398) = 0,707107 - 4
cot(θ) = cos(θ) ÷ sin(θ)
0,707107 ÷ 0,707107 = 1
Как работи този калкулатор?
cot(θ) = cos(θ) / sin(θ) = 1 / tan(θ). It is zero at 90° (π/2), equals 1 at 45° (π/4), and is undefined at multiples of 180° (π) where sin = 0. The period is 180° (π rad) and the function decreases from +∞ to −∞ within each period.
Формула
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.
Често задавани въпроси
Yes. cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ). Both expressions give the same result, but the cos/sin form is more numerically stable near 90° where tan(θ) → ∞ while cos(90°) = 0 exactly.
cot(θ) is undefined wherever sin(θ) = 0, which happens at 0°, ±180°, ±360°, and every multiple of π radians. At these angles the denominator is zero, so the result does not exist. Contrast with tangent, which is undefined where cos(θ) = 0 (at ±90°, ±270°, …).
The cotangent function repeats every π radians (180°). This is the same period as tangent. Cosine and sine both have period 2π (360°), so cotangent (their ratio) completes two cycles for every one cycle of sine or cosine.
Известен също като
TG we-Calculate Editorial Team. (2026). Cot Calculator — Cotangent of Any Angle [Online calculator]. TG we-Calculate. https://we-calculate.com/bg/calculator/cot-calculator
TG we-Calculate Editorial Team. "Cot Calculator — Cotangent of Any Angle." TG we-Calculate. 2026. https://we-calculate.com/bg/calculator/cot-calculator.
TG we-Calculate Editorial Team, "Cot Calculator — Cotangent of Any Angle," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/bg/calculator/cot-calculator
@misc{wecalculate_cot_calculator, title = {Cot Calculator — Cotangent of Any Angle}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/bg/calculator/cot-calculator}}, year = {2026}, note = {TG we-Calculate} }
Помогна ли ви този калкулатор?