Cosine Calculator – Calculate cos(x)
Find the cosine of an angle using the cos calculator below. Start by entering the angle in degrees or radians.
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How to Find the Cosine of an Angle
In a right triangle, the cosine of angle α, or cos(α), is the ratio between the angle’s adjacent side and the hypotenuse.
Cosine is one of the three primary trigonometric functions and is abbreviated cos.
You might be asking how to find the cosine of an angle? Use the formula below to calculate cos.
Cosine Formula
The cosine formula is:
cos(α) = adjacent b / hypotenuse c
Thus, the cosine of angle α in a right triangle is equal to the adjacent side’s length divided by the hypotenuse.
To solve cos, simply enter the length of the adjacent and hypotenuse and solve.
For example, let’s calculate the cosine of angle α in a triangle with the length of the adjacent side equal to 6 and the hypotenuse equal to 8.
cos(α) = 6 / 8
cos(α) = 3 / 4
Cosine Graph
If you graph the cosine function for every possible angle, it forms a repeating up/down curve. This is known as a cosine wave.
The curve starts with an angle of 0, then decreases to a value of -1 before increasing to a value of 1, and continues indefinitely.
Cosine Table
The table below shows common angles and the cos value for each of them.
| Angle (degrees) | Angle (radians) | Cosine |
|---|---|---|
| 0° | 0 | 1 |
| 15° | π / 12 | √6 + √2 / 4 |
| 30° | π / 6 | √3 / 2 |
| 45° | π / 4 | √2 / 2 |
| 60° | π / 3 | 1 / 2 |
| 75° | 5π / 12 | √6 – √2 / 4 |
| 90° | π / 2 | 0 |
| 105° | 7π / 12 | –√6 – √2 / 4 |
| 120° | 2π / 3 | –1 / 2 |
| 135° | 3π / 4 | –√2 / 2 |
| 150° | 5π / 6 | –√3 / 2 |
| 165° | 11π / 12 | –√6 + √2 / 4 |
| 180° | π | -1 |
| 195° | 13π / 12 | –√6 + √2 / 4 |
| 210° | 7π / 6 | –√3 / 2 |
| 225° | 5π / 4 | –√2 / 2 |
| 240° | 4π / 3 | –1 / 2 |
| 255° | 17π / 12 | –√6 – √2 / 4 |
| 270° | 3π / 2 | 0 |
| 285° | 19π / 12 | √6 – √2 / 4 |
| 300° | 5π / 3 | 1 / 2 |
| 315° | 7π / 4 | √2 / 2 |
| 330° | 11π / 6 | √3 / 2 |
| 345° | 23π / 12 | √6 + √2 / 4 |
| 360° | 2π | 1 |
Inverse Cosine and Secant
The inverse of the cosine function is the arccos function. Thus, if you know the cos of an angle, you can use arccos to find the angle.
Secant, on the other hand, is the reciprocal of the cosine value. The following formulas show the relationship between cosine and secant.
cos(α) = adjacent / hypotenuse
sec(α) = hypotenuse / adjacent = 1 / cos(α)
You might also be interested in our sine and tangent calculators.