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

0.000000
sin(0°)
Exact value: 0
Normalized angle:0.000°
Quadrant:1
Reference angle:0.000°
Sign:zero (at 0°, 180°, 360°, etc.)

Unit Circle Position

Red line shows sine value (y-coordinate)

Function Analysis

Domain:All real numbers
Range:[-1, 1]
Period:360° (2π radians)
Amplitude:1
Function type:Periodic, continuous, odd function

Common Sine Values

Angle (degrees)Angle (radians)Exact ValueDecimal
0°000
30°π/61/20.5
45°π/4√2/20.707
60°π/3√3/20.866
90°π/211
120°2π/3√3/20.866
135°3π/4√2/20.707
150°5π/61/20.5
180°π00
270°3π/2-1-1
360°00

Sine Function Properties

1

Periodic

Repeats every 360° (2π rad)

2

Bounded

Always between -1 and 1

3

Odd Function

sin(-x) = -sin(x)

4

Continuous

No breaks or discontinuities

Sine Signs by Quadrant

Quadrant I
0° to 90°
+
Quadrant II
90° to 180°
+
Quadrant III
180° to 270°
-
Quadrant IV
270° to 360°
-

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. 1.Enter any angle value (positive or negative)
  2. 2.Choose your preferred unit (degrees or radians)
  3. 3.View the sine value and angle properties
  4. 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