y = sin (x - Pi sign)
amplitude:
period:
phase shift:
To find the amplitude, period, and phase shift of the given function y = sin (x - Pi), we can use the standard form of a sine function: y = A * sin(Bx - C) + D. Here's how to do it:
1. Amplitude:
The amplitude (A) represents the maximum displacement or the highest point of the function from the x-axis. In this case, the coefficient of sin(x - Pi) is 1, so the amplitude is 1. The amplitude is always positive.
2. Period:
The period (P) represents the distance between two consecutive peaks or troughs of the function. The period can be calculated using the formula:
P = 2π / |B|
In the given function, the coefficient of x is 1 (B = 1). So, the period is:
P = 2π / |1| = 2π
Therefore, the period of the given function is 2π.
3. Phase Shift:
The phase shift (C) represents the horizontal shift or the displacement from the origin. It can be calculated using the formula:
C = h / B
Where h is the given constant term in the argument of sin(x - Pi). In this case, -Pi is the constant term. So, the phase shift is:
C = -Pi / 1 = -Pi
Therefore, the phase shift of the given function is -Pi.
To summarize:
Amplitude: 1
Period: 2π
Phase Shift: -Pi