Cosine Calculator
Sine's Partner, Shifted by 90 Degrees
Cosine is the adjacent side over the hypotenuse in a right triangle — and viewed on a graph, it's identical to a sine wave shifted a quarter cycle to the left. That fixed relationship makes cosine indispensable anywhere sine is used, especially when a second, out-of-phase signal is needed, such as decomposing motion or force into perpendicular components.
The Formula
cos(θ)
As with sine, an angle given in degrees is converted to radians first, since the calculation itself operates in radians.
Where Cosine Is Used
- Vector components — the horizontal component of a vector at angle θ is its magnitude times cos(θ).
- Physics — work done by a force at an angle uses the cosine of that angle.
- Signal processing — cosine transforms are the basis of JPEG image compression and other frequency-domain techniques.
- Navigation — the law of cosines extends this ratio to solve non-right triangles entirely.
| Angle | cos(θ) |
|---|---|
| 0° | 1 |
| 30° | 0.866025 |
| 45° | 0.707107 |
| 60° | 0.5 |
| 90° | 0 |
How to Use This Calculator
- Enter the Angle.
- Select the unit: Degrees or Radians.
- Select Calculate to see the cosine value.
Related Calculations
Need the reciprocal ratio? The Secant Calculator computes 1/cos(θ) directly. See also the Sine Calculator for the complementary ratio.