find the period, amplitude, and phase shift of the function.\n\n$y = \\frac{1}{2}\\sin(\\pi x…

find the period, amplitude, and phase shift of the function.\n\n$y = \\frac{1}{2}\\sin(\\pi x - \\frac{\\pi}{2}) - 2$\n\ngive the exact values, not decimal approximations.\n\nperiod: \n\namplitude: \n\nphase shift:

find the period, amplitude, and phase shift of the function.\n\n$y = \\frac{1}{2}\\sin(\\pi x - \\frac{\\pi}{2}) - 2$\n\ngive the exact values, not decimal approximations.\n\nperiod: \n\namplitude: \n\nphase shift:

Answer

Explanation:

Step1: Recall the general form of a sine function

The general form of a sine function is (y = A\sin(Bx - C)+D). For the given function (y=\frac{1}{2}\sin(\pi x-\frac{\pi}{2})-2), we have (A = \frac{1}{2}), (B=\pi), (C=\frac{\pi}{2}), (D = - 2).

Step2: Calculate the amplitude

The amplitude of (y = A\sin(Bx - C)+D) is given by (|A|). Substituting (A=\frac{1}{2}), we get (|A|=\frac{1}{2}).

Step3: Calculate the period

The period of (y = A\sin(Bx - C)+D) is (T=\frac{2\pi}{|B|}). Substituting (B = \pi), we have (T=\frac{2\pi}{\pi}=2).

Step4: Calculate the phase - shift

The phase - shift of (y = A\sin(Bx - C)+D) is (\frac{C}{B}). Substituting (C=\frac{\pi}{2}) and (B=\pi), we get (\frac{C}{B}=\frac{\frac{\pi}{2}}{\pi}=\frac{1}{2}).

Answer:

Period: (2) Amplitude: (\frac{1}{2}) Phase shift: (\frac{1}{2})