Compute cot(θ) = cos(θ)/sin(θ) for single or thousands of angles. Degrees or radians. Upload CSV/TXT. Download results instantly.
🔢 Launch Calculator ↓Paste hundreds or thousands of angles, one per line. Process them all with a single click — no waiting, no limits.
Drag and drop or browse for your .csv or .txt file. Angles are loaded into the bulk processor instantly.
Single-angle mode shows full trig context: cos(θ), sin(θ), tan(θ), sec(θ), csc(θ), arccot and more.
Real-time validation catches non-numeric inputs and flags undefined cot(θ) values (at 0°, 180°, etc.) clearly.
After each calculation, view count, min, max, and mean cot(θ) instantly in the summary dashboard.
Copy to clipboard or download a ready-to-use CSV with all angles and computed values in one click.
Drag & Drop or click to upload
.csv or .txt · max 5 MB · one angle per line
Or paste angles (one per line):
| # | Angle | Unit | cot(θ) | cos(θ) | sin(θ) | tan(θ) | Status |
|---|
The cotangent function, written as cot(θ), is one of six fundamental trigonometric functions and is defined as the ratio of cosine to sine: cot(θ) = cos(θ) / sin(θ) = 1 / tan(θ). In a right-angled triangle, cotangent represents the ratio of the adjacent side to the opposite side — essentially the reciprocal of tangent. Though often overshadowed by sine, cosine, and tangent in introductory courses, cotangent is indispensable in advanced calculus, Fourier analysis, signal processing, and geometry proofs.
Cotangent's central identity emerges from dividing the Pythagorean identity sin²(θ) + cos²(θ) = 1 by sin²(θ), yielding the cotangent-cosecant identity: cot²(θ) + 1 = csc²(θ). This relationship is routinely used in integral calculus, especially when evaluating integrals involving √(x² − 1) through trigonometric substitution. Unlike tangent, cotangent is defined at 90° and undefined at 0° — a fact frequently tested in examinations. Cotangent is a periodic function with a period of 180° (π radians), and its graph produces evenly spaced vertical asymptotes wherever sin(θ) = 0.
The domain of cotangent excludes all angles where sin(θ) = 0, namely θ = n·180° (or nπ in radians) for any integer n — that is, 0°, 180°, 360°, and so on. At these points, cot(θ) is undefined, trending toward ±∞. Elsewhere, the range of cot(θ) is (−∞, +∞), meaning it spans all real numbers — making it quite different from the bounded sine and cosine functions.
Mastering standard cotangent values accelerates problem-solving in tests and real-world computations. cot(30°) = √3 ≈ 1.7321, cot(45°) = 1, cot(60°) = 1/√3 ≈ 0.5774, cot(90°) = 0, cot(120°) = −1/√3 ≈ −0.5774, cot(135°) = −1, cot(150°) = −√3 ≈ −1.7321, cot(0°) = undefined, cot(180°) = undefined. Cotangent is an odd function, so cot(−θ) = −cot(θ), and its period is 180° (π radians).
Our tool operates in two intuitive modes. Single Angle Mode: enter your angle, select degrees or radians, choose decimal precision (up to 15 places), and click Compute cot(θ). A comprehensive related-numbers panel instantly displays cot(θ), sin(θ), cos(θ), tan(θ), sec(θ), csc(θ), arccot(θ), cot²(θ), and more. Bulk Mode: paste up to thousands of angles (one per line) or upload a .csv or .txt file. The tool validates all input in real time, processes every value, and presents results in a clean table with per-row status badges and a full summary statistics dashboard — then lets you copy or download the entire output as a CSV file.
In calculus, the derivative of cot(x) is −csc²(x), and its integral is the elegant result ∫ cot(x) dx = ln|sin(x)| + C. These results appear consistently in differential equations, arc-length calculations, and physics problems involving oscillatory motion. The identity cot²(x) = csc²(x) − 1 is frequently employed to simplify integrands before applying standard integration techniques.
Cotangent has rich practical applications across multiple disciplines. In surveying and geodesy, cotangent is used to calculate horizontal distances from measured vertical angles — the horizontal distance equals the vertical height multiplied by cot(elevation angle). In electrical engineering, cotangent appears in the phase relationships of RLC circuits and in impedance calculations for transmission lines. In astronomy, the cotangent rule for spherical triangles links angles and sides on the celestial sphere, enabling precise star-position calculations. In architecture, roof pitch calculations use cotangent to determine the horizontal run from a known rise and angle of inclination.
The six trigonometric functions split into three primary (sine, cosine, tangent) and three reciprocal (cosecant, secant, cotangent) functions. cot(θ) = 1/tan(θ) = cos(θ)/sin(θ), sec(θ) = 1/cos(θ), and csc(θ) = 1/sin(θ). The companion Pythagorean identities — 1 + tan²θ = sec²θ and 1 + cot²θ = csc²θ — pair these reciprocal functions in powerful ways for simplification and proof. Whether you are a student practising for trigonometry exams, an engineer pre-computing angle lookup tables, or a data scientist applying circular statistics, this free bulk cotangent calculator delivers fast, precise, exportable results entirely in your browser — zero installation, zero registration, zero data collection.
Period: 180° (π rad) · Range: (−∞, +∞) · Odd function: cot(−θ) = −cot(θ)
Type a single angle or paste a list (one per line). Alternatively, drag and drop or upload your .csv / .txt file.
Select degrees or radians and pick your decimal precision from 2 up to 15 places for maximum accuracy.
Click Compute. View the results table with status badges, then clear, copy to clipboard, or download as CSV.
Cotangent is defined as cot(θ) = cos(θ)/sin(θ) = 1/tan(θ) = Adjacent/Opposite. It is the reciprocal of the tangent function. Its range is (−∞, +∞) and it is undefined at angles where sine equals zero (0°, 180°, 360°, etc.).
Either type a single angle in the Single Angle card, or paste multiple angles (one per line) in the Bulk Angles card, or upload a .csv / .txt file. Select your unit (degrees or radians) and decimal precision, then click the compute button. Results appear in the section below.
cot(θ) is undefined whenever sin(θ) = 0 — that is at θ = 0°, 180°, 360°, −180°, etc. (0, π, 2π, −π in radians). The calculator labels these rows as UNDEFINED with a pink badge.
Yes. Prepare a .csv or .txt file with one angle value per line — no header row needed. Files up to 5 MB are accepted. Upload via drag-and-drop or the file picker. All values are validated and processed instantly in your browser.
Completely free, no registration required. All calculations run client-side in your browser using JavaScript — no data is ever transmitted to a server. Your angles stay private.
This identity is derived from the Pythagorean identity sin²(θ) + cos²(θ) = 1 by dividing every term by sin²(θ). It yields cot²(θ) + 1 = csc²(θ). This is widely used in calculus for simplifying integrals and proving advanced trigonometric identities.
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