Phase Shift Calculator
Calculate and visualize phase shifts in trigonometric functions.
Function Plot
Phase Shift Formulas
The general form of a trigonometric function with phase shift is:
\[ f(x) = A\sin(\omega x + \phi) \]
\[ f(x) = A\cos(\omega x + \phi) \]
\[ f(x) = A\tan(\omega x + \phi) \]
Where:
- A is the amplitude
- ω (omega) is the angular frequency
- φ (phi) is the phase shift
- x is the independent variable
Properties:
- Amplitude (A): Maximum displacement from the mean position
- Frequency (ω): Number of cycles per unit time
- Phase Shift (φ): Horizontal displacement of the function
- Period: \[ T = \frac{2\pi}{\omega} \]
Applications:
- Signal processing
- Wave analysis
- Electrical engineering
- Physics (wave motion)
- Music and sound analysis
Common Phase Shifts:
- \[ \sin(x + \frac{\pi}{2}) = \cos(x) \]
- \[ \sin(x + \pi) = -\sin(x) \]
- \[ \sin(x + \frac{3\pi}{2}) = -\cos(x) \]
- \[ \sin(x + 2\pi) = \sin(x) \]