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Sinusoidal Expression:
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A sinusoidal expression describes a mathematical function that oscillates in a smooth, repetitive pattern. It's commonly used to model periodic phenomena in physics, engineering, and signal processing.
The calculator uses the sinusoidal expression:
Where:
Explanation: The equation calculates the instantaneous value of a sine wave at a given time, accounting for amplitude, frequency, and phase shift.
Details: Sinusoidal functions are fundamental in analyzing alternating currents, sound waves, light waves, mechanical vibrations, and many other oscillatory systems in science and engineering.
Tips: Enter amplitude in appropriate units, angular frequency in rad/s, time in seconds, and phase angle in radians. All values must be valid real numbers.
Q1: What's the difference between angular frequency and frequency?
A: Angular frequency (ω) is measured in radians per second, while frequency (f) is measured in Hertz (cycles per second). They are related by ω = 2πf.
Q2: How does phase angle affect the waveform?
A: Phase angle determines the horizontal shift of the waveform. A positive phase shifts the wave to the left, while a negative phase shifts it to the right.
Q3: Can this calculator handle cosine functions?
A: While this calculator specifically handles sine functions, cosine can be represented as a sine function with a phase shift of π/2 radians.
Q4: What are typical units for amplitude?
A: Amplitude units depend on the physical context - volts for electrical signals, meters for mechanical waves, or any other relevant unit of measurement.
Q5: How accurate is the calculation?
A: The calculation uses PHP's built-in sin() function, which provides high precision for most practical applications.