1. What is Phase Shift in Trigonometric Functions?

Phase shift refers to the horizontal displacement of a trigonometric function along the x-axis. It determines how much the graph of the function is shifted left or right from its standard position.

2. How Does the Phase Shift Formula Work?

The calculator uses the phase shift formula:

Where:

• \( \phi \) — Phase shift in radians
• \( T \) — Period of the trigonometric function
• \( \text{shift} \) — Horizontal shift in units
• \( 2\pi \) — Full cycle in radians (approximately 6.2832)

Explanation: The formula converts a horizontal shift in units to the corresponding phase shift in radians, taking into account the period of the function.

3. Importance of Phase Shift Calculation

Details: Phase shift calculation is essential in signal processing, wave analysis, electrical engineering, and physics. It helps determine the timing relationship between different waveforms and is crucial for analyzing periodic phenomena.

4. Using the Calculator

Tips: Enter the period (T) in units and the horizontal shift in units. The period must be greater than zero. The result will be the phase shift in radians.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between phase shift and horizontal shift?
A: Horizontal shift is measured in the same units as the x-axis, while phase shift is measured in radians or degrees and represents the angular displacement.

Q2: Can phase shift be negative?
A: Yes, phase shift can be negative, indicating a shift to the left, or positive, indicating a shift to the right.

Q3: How does period affect phase shift?
A: For the same horizontal shift, a shorter period results in a larger phase shift in radians, while a longer period results in a smaller phase shift.

Q4: What are common applications of phase shift?
A: Phase shift is used in AC circuit analysis, sound wave interference, light wave phenomena, and in the analysis of any periodic signals.

Q5: Can I convert phase shift from radians to degrees?
A: Yes, multiply the phase shift in radians by 180/π (approximately 57.2958) to convert to degrees.