The cosine of an angle is the ratio of the adjacent side to the hypotenuse; on the unit circle it is the x-coordinate. Cosine gives the horizontal component of forces and velocities, and appears in the law of cosines, dot products and Fourier series.
How to use the Cosine Calculator
- Angle unit
- Angle α
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter the angle and pick its unit. The angle is converted to radians and cos is evaluated; for multiples of 15° the exact value with square roots is shown as well (for example √3/2). Where the function is undefined, the calculator says so instead of printing a huge number.
Formula
cos α = adjacent / hypotenuse = x-coordinate on the unit circle
Range: [−1, 1] · Domain: all real numbers · Period: 2π (360°)
Worked example
Inputs — Angle unit: Degrees (°); Angle α: 30.
Results — cos(α) = √3/2 ≈ 0.8660254038; sin(α) = 1/2 ≈ 0.5; tan(α) = √3/3 ≈ 0.5773502692; csc(α) = 2; sec(α) = 1.154700538; cot(α) = 1.732050808.
Key terms
- Cosine
- cos α = adjacent / hypotenuse = x-coordinate on the unit circle.
- Exact value
- A value written with integers and square roots instead of decimals.
Frequently asked questions
What is cos 60°?
Exactly 1/2.
Is cosine even or odd?
Even: cos(−α) = cos α.
Where is cosine negative?
In quadrants II and III.
How are sine and cosine related?
cos α = sin(90° − α), and sin²α + cos²α = 1.