Enter any angle and instantly get its cotangent — cot(θ) = cos(θ)/sin(θ) — plus the reciprocal tangent value, with clear "Undefined" results at every asymptote.
Enter an angle and choose degrees or radians
This cot calculator (short for cotangent calculator) finds the cotangent of any angle you enter, in either degrees or radians, and returns the result instantly. Cotangent is the ratio cos(θ)/sin(θ) — the reciprocal of tangent — and it appears less often in textbooks than sine, cosine, or tangent, which makes a dedicated cot of an angle calculator genuinely useful when you don't want to manually compute cos and sin and divide them yourself. This tool also displays the reciprocal tangent value alongside cot(θ) so you can immediately see the relationship, and it explicitly flags "Undefined" at 0°, 180°, 360°, and every other multiple of 180° where cotangent's vertical asymptotes occur, instead of returning a misleading Infinity or error.
Given one angle, this calculator converts it to radians (if you entered degrees), computes sin(θ) and cos(θ), and divides cos(θ) by sin(θ) to get cot(θ). It also reports tan(θ) = sin(θ)/cos(θ) for reference, since the two functions are reciprocals of each other everywhere both are defined.
Trigonometry and precalculus students working through unit-circle problems, engineering and physics students who need cotangent for AC circuit or wave-related coursework, teachers building answer keys, and anyone verifying a hand calculation of cos(θ)/sin(θ) will find this tool faster and less error-prone than working the ratio out by hand.
Cotangent is one of the three "reciprocal" trig functions (alongside secant and cosecant) that complete the full picture of the six trigonometric ratios. While it is used less frequently day-to-day than sine, cosine, and tangent, it turns up in specific formulas — from AC circuit phase-angle relationships to the field-of-view term in 3D graphics projection matrices — where expressing a ratio as cos/sin (rather than sin/cos) is the natural or conventional choice.
Electrical engineers use cotangent when relating resistance and reactance in AC power-factor calculations. Computer graphics programmers use cot(fov/2) directly in perspective projection matrices. Civil engineers express slope batters (horizontal run per unit of vertical rise) as a cotangent ratio. Surveyors and drafting students use it in angle-ratio problems, and math students use it throughout unit-circle and trigonometric-identity coursework.
How cot(θ) is derived from sine and cosine, and how it relates to tangent
Cotangent and tangent are reciprocals: cot(θ) = 1/tan(θ), so wherever one is zero, the other is undefined.
Because cot(θ) = cos(θ)/sin(θ), the function has vertical asymptotes wherever sin(θ) = 0.
Cotangent repeats every 180° (π radians) — half the period of sine and cosine.
From entering an angle to reading the cotangent result
Type your angle into the numeric input field, for example 45.
Select the correct unit using the toggle so the conversion is accurate.
The calculator converts to radians (if needed) and computes cos(θ) and sin(θ).
At 0°, 180°, 360°, and so on, cotangent has no value; the calculator flags this instead of showing an error.
Both values are displayed together in the results panel for quick reference.
Finding the cotangent of a 45° angle
A student needs cot(45°) for a homework problem and wants to verify the calculator's result by hand.
Explanation: 45° is the one angle (per 180° cycle) where cotangent and tangent are both exactly 1, because sin(45°) and cos(45°) are equal. This makes it a convenient angle for verifying the reciprocal relationship cot(θ) × tan(θ) = 1.
Domain, range, and period of cotangent compared with its reciprocal tangent
| Function | Domain | Range | Period |
|---|---|---|---|
| cot(θ) | All reals except 0°, 180°, 360°, ... (nπ) | All real numbers | 180° (π rad) |
| tan(θ) (reciprocal) | All reals except 90°, 270°, ... (90°+n180°) | All real numbers | 180° (π rad) |
Reading the result: a numeric cot(θ) value tells you the ratio of cos(θ) to sin(θ) at that angle; an "Undefined" result means the angle falls on one of cotangent's vertical asymptotes, where sin(θ) is zero.
Typical ranges: cot(θ) can be any real number — near an asymptote it grows very large in magnitude, and it crosses zero exactly where tan(θ) is undefined (at 90°, 270°, and so on).
Manual verification: compute sin(θ) and cos(θ) yourself (a scientific calculator or unit circle table works), divide cos(θ) by sin(θ), and confirm it matches the displayed cot(θ) — then multiply your result by the displayed tan(θ) and confirm you get 1.
Where cotangent genuinely shows up outside the classroom
Relate resistance and reactance through cot(φ) = R/X in electrical engineering.
Perspective projection matrices scale by cot(field-of-view ÷ 2).
Civil engineers express embankment slopes as a horizontal-to-vertical cotangent ratio.
The bilinear transform in audio and signal-processing filters uses cot(ωT/2).
Angle-ratio calculations in classical surveying and leveling methods.
Solve joint angles from position ratios when adjacent-over-opposite form is convenient.
Phase-angle and simple-harmonic-motion problems that naturally invert a tangent ratio.
Express member force ratios using cotangent of the truss angle.
Cross-check bearing calculations expressed as adjacent-over-opposite ratios.
Convert between elevation-angle ratios in observational calculations.
Check unit-circle and identity problems that call for cotangent specifically.
Verify cotangent terms in worked problems before an exam or lab report.
Verify a tangent table or calculator result using the reciprocal relationship.
What this cot calculator does well, and where it doesn't apply
How cot(θ) and its reciprocal tan(θ) compare at the standard reference angles
| Angle (θ) | cot(θ) | tan(θ) |
|---|---|---|
| 0° | Undefined | 0 |
| 30° | √3 ≈ 1.7321 | 1/√3 ≈ 0.5774 |
| 45° | 1 | 1 |
| 60° | 1/√3 ≈ 0.5774 | √3 ≈ 1.7321 |
| 90° | 0 | Undefined |
Summary: This cot calculator gives you an instant, free way to find the cotangent of any angle in degrees or radians, along with its reciprocal tangent value and clear "Undefined" flags at every asymptote. Pair it with related tools like the Sec Calculator and Cosec Calculator to cover all three reciprocal trig functions.
Common questions about the cotangent function
Trusted educational references to go deeper on cotangent and the trig functions
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