Sine Calculator
Calculate sine values for any angle in degrees, radians, or gradians. Our free online tool provides precise results instantly.
How to Use:
- Enter the angle value in the input field
- Select the unit of measurement (degrees, radians, or gradians)
- Choose the decimal precision for the result
- Click "Calculate Sine"
- View the result and copy it if needed
Understanding the Sine Function
What is Sine?
In trigonometry, the sine of an angle in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. Along with cosine and tangent, it's one of the three primary trigonometric functions.
Sine Graph
The sine function produces a smooth, periodic wave (sine wave) when graphed. It has a period of 2π radians (360°), an amplitude of 1, and ranges between -1 and 1. The graph starts at (0,0) for angle 0.
Common Sine Values
- sin(0°) = 0
- sin(30°) = 0.5
- sin(45°) = √2/2 ≈ 0.7071
- sin(60°) = √3/2 ≈ 0.8660
- sin(90°) = 1
Applications of Sine
Sine is fundamental in physics for wave mechanics, in engineering for signal processing, in acoustics for sound waves, in electrical engineering for alternating current, and in many other fields involving periodic phenomena.
Key Properties of the Sine Function
Periodicity
The sine function is periodic with a period of 2π radians (360°). This means sin(θ) = sin(θ + 2πn) for any integer n. The function repeats its values every full rotation.
Symmetry
Sine is an odd function, meaning sin(-θ) = -sin(θ). Graphically, this means the sine wave is symmetric about the origin (point symmetry).
Range and Amplitude
The sine function always returns values between -1 and 1, inclusive. The amplitude (height from center line to peak) is always 1 for the basic sine function.
Phase Shift
The sine function can be shifted horizontally (phase shift) or vertically, and its period or amplitude can be modified to model various real-world periodic phenomena.
Why Use Our Sine Calculator?
Practical Applications of Sine
Physics
Used to describe simple harmonic motion, wave propagation, and alternating current in electricity. The sine function models many natural periodic phenomena.
Engineering
Essential in signal processing, audio engineering, and telecommunications. Sine waves form the basis for Fourier analysis of complex signals.
Computer Graphics
Used to create smooth animations, circular motion, and wave effects. Sine functions help simulate natural movements and transitions.
Navigation
Critical in GPS technology and celestial navigation. Sine functions help calculate positions based on angles and distances.
Calculate Sine Values with Confidence
Whether you're solving trigonometry problems, working on engineering projects, or studying wave phenomena, our sine calculator provides accurate results instantly. Bookmark this tool for all your sine calculation needs!