Cosine Calculator
Calculate cosine values with detailed step-by-step solutions for angles in degrees or radians, including special angle recognition.
Enter Angle
• Common angles: 0°, 30°, 45°, 60°, 90°
• Cosine is maximum (1) at 0° and 360°
Result
Enter an angle to calculate its cosine value
Unit Circle & Cosine
On the unit circle, cosine represents the x-coordinate of the point where the angle intersects the circle.
cos(θ) = x-coordinate on unit circle
Special Angles
| Degrees | Radians | Cosine (Exact) | Cosine (Decimal) |
|---|---|---|---|
| 0° | 0 | 1 | 1 |
| 30° | π/6 | √3/2 | 0.8660 |
| 45° | π/4 | √2/2 | 0.7071 |
| 60° | π/3 | 1/2 | 0.5 |
| 90° | π/2 | 0 | 0 |
| 180° | π | -1 | -1 |
| 270° | 3π/2 | 0 | 0 |
| 360° | 2π | 1 | 1 |
Cosine Function Properties
Domain & Range
Domain: All real numbers
Range: [-1, 1]
Periodicity
Period: 2π radians (360°)
cos(x + 2π) = cos(x)
Symmetry
Even function: cos(-x) = cos(x)
Symmetric about y-axis
Key Values
Maximum: 1 (at 0°, 360°, ...)
Minimum: -1 (at 180°, 540°, ...)
Important Cosine Identities
cos²(x) + sin²(x) = 1
Pythagorean Identity
cos(90° - x) = sin(x)
Cofunction Identity
cos(2x) = cos²(x) - sin²(x)
Double Angle Formula
cos(x + y) = cos(x)cos(y) - sin(x)sin(y)
Addition Formula
Frequently Asked Questions
The cosine function (cos) is a trigonometric function that relates an angle in a right triangle to the ratio of the adjacent side to the hypotenuse. On the unit circle, it represents the x-coordinate.