1. What is the Sine Function?

The sine function is a fundamental trigonometric function that describes a smooth periodic oscillation. It's widely used in mathematics, physics, engineering, and signal processing to model periodic phenomena.

2. How Does the Calculator Work?

The calculator uses the sine function formula:

Where:

• \( a \) — Amplitude (height of the wave)
• \( b \) — Frequency (how many cycles occur in 2π units)
• \( c \) — Phase shift (horizontal shift)
• \( d \) — Vertical shift
• \( x \) — Input value (angle in radians)
• \( y \) — Output value

Explanation: The equation describes a sinusoidal wave with adjustable amplitude, frequency, and phase characteristics.

3. Importance of Sine Function

Details: Sine waves are essential in physics for describing wave motion, in electrical engineering for AC current, in sound engineering for audio signals, and in many other applications involving periodic behavior.

4. Using the Calculator

Tips: Enter the parameters a, b, c, and d to define your sine function. Optionally enter an x value to calculate the corresponding y value. All parameters accept decimal values.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for x?
A: The calculator uses radians by default. If you have degrees, convert them to radians first (multiply by π/180).

Q2: What does a negative amplitude mean?
A: A negative amplitude flips the wave upside down while maintaining the same shape.

Q3: How does frequency affect the graph?
A: Higher frequency values create more oscillations in the same x-range, making the wave appear "compressed" horizontally.

Q4: What's the difference between phase shift and vertical shift?
A: Phase shift moves the wave left or right, while vertical shift moves it up or down.

Q5: Can I graph the function with this calculator?
A: This calculator computes specific values. For graphing, you would need to plot multiple points or use graphing software.