Cosine Calculator
Calculate cosine values in degrees and radians with step-by-step calculations, unit circle visualization, and trigonometric identities. Perfect for trigonometry and calculus.
Calculate Cosine (cos)
Common Cosine Values
Click on these links to see instant calculations with common angles:
Cosine Function
The cosine function is one of the fundamental trigonometric functions. In a right triangle, cosine is the ratio of the adjacent side to the hypotenuse. On the unit circle, cosine represents the x-coordinate of a point.
Cosine Properties
- Domain: All real numbers (-∞, ∞)
- Range: [-1, 1]
- Period: 2π radians (360°)
- Even Function: cos(-x) = cos(x)
- Maximum Value: 1 at x = 0°, 360°, 720°, ...
- Minimum Value: -1 at x = 180°, 540°, ...
Special Cosine Values
| Angle (Degrees) | Angle (Radians) | Cosine Value | Exact Value |
|---|---|---|---|
| 0° | 0 | 1 | 1 |
| 30° | π/6 | 0.866 | √3/2 |
| 45° | π/4 | 0.707 | √2/2 |
| 60° | π/3 | 0.5 | 1/2 |
| 90° | π/2 | 0 | 0 |
| 120° | 2π/3 | -0.5 | -1/2 |
| 135° | 3π/4 | -0.707 | -√2/2 |
| 150° | 5π/6 | -0.866 | -√3/2 |
| 180° | π | -1 | -1 |
- Engineering: Signal processing, wave analysis, and electrical engineering
- Physics: Oscillations, waves, and harmonic motion calculations
- Mathematics: Calculus, trigonometry, and analytical geometry
- Computer Graphics: 3D rotations, animations, and transformations
- Navigation: GPS calculations, surveying, and astronomical calculations
Frequently Asked Questions
What is cosine?
Cosine is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse in a right triangle. On the unit circle, it represents the x-coordinate of a point.
How do you convert degrees to radians?
To convert degrees to radians, multiply by π/180. For example: 90° = 90 × π/180 = π/2 radians ≈ 1.5708 radians.
What are the common cosine values?
Common cosine values include: cos(0°) = 1, cos(30°) = √3/2 ≈ 0.866, cos(45°) = √2/2 ≈ 0.707, cos(60°) = 1/2 = 0.5, cos(90°) = 0.