Sine Calculator
Calculate sine 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°
• π rad = 180°, π/2 rad = 90°
Result
Enter an angle to calculate its sine value
Unit Circle & Sine
On the unit circle, sine represents the y-coordinate of the point where the angle intersects the circle.
sin(θ) = y-coordinate on unit circle
Special Angles
| Degrees | Radians | Sine (Exact) | Sine (Decimal) |
|---|---|---|---|
| 0° | 0 | 0 | 0 |
| 30° | π/6 | 1/2 | 0.5 |
| 45° | π/4 | √2/2 | 0.7071 |
| 60° | π/3 | √3/2 | 0.8660 |
| 90° | π/2 | 1 | 1 |
| 180° | π | 0 | 0 |
| 270° | 3π/2 | -1 | -1 |
| 360° | 2π | 0 | 0 |
Sine Function Properties
Domain & Range
Domain: All real numbers
Range: [-1, 1]
Periodicity
Period: 2π radians (360°)
sin(x + 2π) = sin(x)
Symmetry
Odd function: sin(-x) = -sin(x)
Point symmetric about origin
Key Values
Maximum: 1 (at 90°, 450°, ...)
Minimum: -1 (at 270°, 630°, ...)
Frequently Asked Questions
The sine function (sin) is a trigonometric function that relates an angle in a right triangle to the ratio of the opposite side to the hypotenuse. It's also defined using the unit circle.