Sin Theta Calculator
Calculate sine of any angle (θ) in degrees, radians, or π radians with detailed analysis
Calculate sin(θ)
Enter any angle value (positive or negative)
sin(θ) Results
Unit Circle Position
Related Trigonometric Values
Common Sine Values
| Angle (degrees) | Angle (radians) | sin(θ) - Exact | sin(θ) - Decimal |
|---|---|---|---|
| 0° | 0 | 0 | 0.0000 |
| 30° | π/6 | 1/2 | 0.5000 |
| 45° | π/4 | √2/2 | 0.7071 |
| 60° | π/3 | √3/2 | 0.8660 |
| 90° | π/2 | 1 | 1.0000 |
| 120° | 2π/3 | √3/2 | 0.8660 |
| 135° | 3π/4 | √2/2 | 0.7071 |
| 150° | 5π/6 | 1/2 | 0.5000 |
| 180° | π | 0 | 0.0000 |
| 270° | 3π/2 | -1 | -1.0000 |
| 360° | 2π | 0 | 0.0000 |
Sine Signs by Quadrant
Sine Function Properties
Periodic
Period = 360° (2π rad)
Range
-1 ≤ sin(θ) ≤ 1
Odd Function
sin(-θ) = -sin(θ)
Unit Circle
y-coordinate on unit circle
Quick Tips
sin(0°) = 0, sin(90°) = 1, sin(180°) = 0, sin(270°) = -1
Sine is positive in quadrants I and II
sin(θ + 360°) = sin(θ) for any angle
sin²(θ) + cos²(θ) = 1 (Pythagorean identity)
Understanding the Sine Function
What is sin(θ)?
The sine function (sin) is one of the fundamental trigonometric functions. For any angle θ, sin(θ) represents the y-coordinate of the point where the terminal side of the angle intersects the unit circle (a circle with radius 1 centered at the origin).
Unit Circle Definition
On the unit circle, if we draw a line from the origin at angle θ from the positive x-axis, the sine of θ equals the y-coordinate of where this line meets the circle. This geometric interpretation helps us understand why sine values range from -1 to 1.
Key Properties
- •Domain: All real numbers
- •Range: [-1, 1]
- •Period: 360° or 2π radians
- •Symmetry: Odd function (sin(-θ) = -sin(θ))
Remember: Sine is positive in quadrants I and II, negative in quadrants III and IV.
Applications of sin(θ)
Physics
Wave motion, oscillations, alternating current, projectile motion
Engineering
Signal processing, structural analysis, electrical engineering
Navigation
GPS calculations, astronomy, surveying, maritime navigation