1. What is a Sinusoidal Function?

A sinusoidal function is a mathematical function that describes a smooth periodic oscillation. It's commonly used to model wave patterns, circular motion, alternating current, and many other periodic phenomena in physics, engineering, and mathematics.

2. How Does the Calculator Work?

The calculator uses the standard sinusoidal function equation:

Where:

• \( A \) — Amplitude (peak deviation from the center)
• \( B \) — Frequency (how many oscillations occur per unit)
• \( C \) — Phase shift (horizontal displacement)
• \( D \) — Vertical shift (up/down displacement)
• \( x \) — Input value
• \( y \) — Output value

Explanation: The function calculates the y-value of a sine wave at a given x-value with specified parameters.

3. Parameters Explained

Amplitude (A): Determines the height of the wave peaks (absolute value).
Frequency (B): Controls how many complete cycles occur per unit (2π/B gives the period).
Phase Shift (C): Moves the wave left or right (positive values shift left).
Vertical Shift (D): Moves the entire wave up or down.

4. Using the Calculator

Tips: Enter all parameters as real numbers. Phase shift is in radians (π radians = 180°). The calculator will compute the y-value for your given x-value.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between sine and cosine functions?
A: They're phase-shifted versions of each other: cos(x) = sin(x + π/2).

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. Most programming languages use radians by default.

Q3: What does a negative amplitude mean?
A: It inverts the wave vertically (flips it upside down).

Q4: Can I model damped oscillations with this?
A: No, this models a perfect, undamped sine wave. Damped oscillations require additional terms.

Q5: What's the range of possible output values?
A: The output ranges from (D - |A|) to (D + |A|), since sine oscillates between -1 and 1.