Cotangent Calculator – Calculate cot(x)
Find the cotangent of an angle using the cot calculator below. Start by entering the angle in degrees or radians.
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How to Find the Cotangent of an Angle
In a right triangle, the cotangent of angle α, or cot(α), is the ratio between the angle’s adjacent side and its opposite side.
Cotangent is a trigonometric function abbreviated cot. Use the formula below to calculate the cotangent of an angle.
Cotangent Formula
The cotangent formula is:
cot(α) = adjacent b / opposite a
Thus, the cotangent of angle α in a right triangle is equal to the length of the adjacent side b divided by the opposite side a.
To solve cot, simply enter the length of the adjacent and opposite sides, then solve.
This formula might look very similar to the formula to calculate tangent. That’s because cotangent is the reciprocal of tangent.
Cotangent should not be confused with arctan, which is the inverse of the tangent function. The difference being that cotangent is equal to 1 / tan(x), while arctan is the inverse of the tangent function.
cot(x) = 1 / tan(x) = tan(x)-1
arctan(y) x where y = tan(x)
For example, let’s calculate the cotangent of angle α in a triangle with the length of the adjacent side equal to 8 and the opposite side equal to 4.
cot(α) = 8 / 4
cot(α) = 2 / 1
Cotangent Graph
If you graph the cotangent function for every possible angle, it forms a series of repeating curves.
One important property to note in the graph above is that the cotangent of an angle is never equal to 0 or an even multiple of π radians, or 180°
Cotangent Table
The table below shows common angles and the cot value for each of them.
| Angle (degrees) | Angle (radians) | Cotangent |
|---|---|---|
| 0° | 0 | undefined |
| 15° | π / 12 | 2 + √3 |
| 30° | π / 6 | √3 |
| 45° | π / 4 | 1 |
| 60° | π / 3 | 1 / √3 = √3 / 3 |
| 75° | 5π / 12 | 2 – √3 |
| 90° | π / 2 | 0 |
| 105° | 7π / 12 | -2 + √3 |
| 120° | 2π / 3 | –1 / √3 = –√3 / 3 |
| 135° | 3π / 4 | -1 |
| 150° | 5π / 6 | -√3 |
| 165° | 11π / 12 | -2 – √3 |
| 180° | π | undefined |
| 195° | 13π / 12 | 2 + √3 |
| 210° | 7π / 6 | √3 |
| 225° | 5π / 4 | 1 |
| 240° | 4π / 3 | 1 / √3 = √3 / 3 |
| 255° | 17π / 12 | 2 – √3 |
| 270° | 3π / 2 | 0 |
| 285° | 19π / 12 | -2 + √3 |
| 300° | 5π / 3 | –1 / √3 = –√3 / 3 |
| 315° | 7π / 4 | -1 |
| 330° | 11π / 6 | |
| 345° | 23π / 12 | -2 – √3 |
| 360° | 2π | undefined |
You might also be interested in our secant and cosecant calculators.