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 phenomena in physics, engineering, and other sciences. The general form is y = A × sin(ωt + φ), where A is amplitude, ω is angular frequency, t is time, and φ is phase angle.

2. How Does the Calculator Work?

The calculator uses the sinusoidal function equation:

Where:

• \( A \) — Amplitude (peak deviation from zero)
• \( \omega \) — Angular frequency (radians per second)
• \( t \) — Time (seconds)
• \( \phi \) — Phase angle (radians)

Explanation: The function calculates the instantaneous value of a sine wave at a specific time, accounting for amplitude, frequency, and phase shift.

3. Applications of Sinusoidal Functions

Details: Sinusoidal functions are fundamental in describing alternating current (AC) circuits, sound waves, light waves, mechanical vibrations, and many other periodic phenomena in nature and technology.

4. Using the Calculator

Tips: Enter all parameters in their respective units. The phase angle should be in radians (π radians = 180°). The calculator will compute the instantaneous value of the sinusoidal function at the specified time.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert frequency from Hz to rad/s?
A: Multiply by 2π (ω = 2πf). For example, 1 Hz = 6.283 rad/s.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. For example, 90° = π/2 ≈ 1.5708 radians.

Q3: What does a negative amplitude mean?
A: It indicates the wave is inverted (180° phase shift) compared to the standard sine wave.

Q4: Can this calculator handle cosine functions?
A: Yes, by setting the phase angle to π/2 (90°), as cos(θ) = sin(θ + π/2).

Q5: What's the difference between angular frequency and regular frequency?
A: Angular frequency (ω) is measured in radians per second, while regular frequency (f) is in Hertz (cycles per second). They're related by ω = 2πf.