Sine Function Calculator
Calculate sine values, explore the sine function properties, and visualize the sine wave
Calculate Sine Function
Enter any angle value (positive or negative)
Sine Function Results
Unit Circle Position
Function Analysis
Common Sine Values
Angle (degrees) | Angle (radians) | Exact Value | Decimal |
---|---|---|---|
0° | 0 | 0 | 0 |
30° | π/6 | 1/2 | 0.5 |
45° | π/4 | √2/2 | 0.707 |
60° | π/3 | √3/2 | 0.866 |
90° | π/2 | 1 | 1 |
120° | 2π/3 | √3/2 | 0.866 |
135° | 3π/4 | √2/2 | 0.707 |
150° | 5π/6 | 1/2 | 0.5 |
180° | π | 0 | 0 |
270° | 3π/2 | -1 | -1 |
360° | 2π | 0 | 0 |
Sine Function Properties
Periodic
Repeats every 360° (2π rad)
Bounded
Always between -1 and 1
Odd Function
sin(-x) = -sin(x)
Continuous
No breaks or discontinuities
Sine Signs by Quadrant
Key Points
sin(0°) = 0 (x-axis intersections)
sin(90°) = 1 (maximum value)
sin(180°) = 0 (x-axis intersections)
sin(270°) = -1 (minimum value)
sin(360°) = 0 (completes one cycle)
Understanding the Sine Function
What is the Sine Function?
The sine function is a fundamental trigonometric function that represents the y-coordinate of a point on the unit circle as it moves around the circle. For any angle θ, sin(θ) gives the vertical projection of the radius when the radius makes angle θ with the positive x-axis.
Key Properties
- •Domain: All real numbers (-∞, ∞)
- •Range: [-1, 1]
- •Period: 360° or 2π radians
- •Amplitude: 1 (maximum distance from x-axis)
How to Use This Calculator
- 1.Enter any angle value (positive or negative)
- 2.Choose your preferred unit (degrees or radians)
- 3.View the sine value and angle properties
- 4.Optionally enable graph data points for visualization
Tip: The calculator shows exact values for common angles like 30°, 45°, 60°, etc.
Applications of the Sine Function
Physics
Wave motion, oscillations, simple harmonic motion, AC circuits
Engineering
Signal processing, structural analysis, vibration analysis
Navigation
GPS systems, astronomy, surveying, maritime navigation