graph one complete period of the given sine or cosine curve. (check your answer with your graphing…

Explanation:

Step1: Find the amplitude

For the function (y = A\sin(x - C)+D), the amplitude is (|A|). In (f(x)=-2+\sin x) (which can be written as (f(x)=\sin x - 2) or (y = 1\times\sin(x-0)-2)), (A = 1). So, the amplitude (|A|=|1| = 1).

Step2: Find the period

The period of the function (y=\sin(Bx - C)+D) is (T=\frac{2\pi}{|B|}). In (f(x)=\sin x-2), (B = 1). So, the period (T=\frac{2\pi}{|1|}=2\pi).

Step3: Find the phase - shift

The phase - shift of the function (y=\sin(Bx - C)+D) is given by (\frac{C}{B}). In (f(x)=\sin(x - 0)-2), (C = 0) and (B = 1). So, the phase - shift (\frac{C}{B}=\frac{0}{1}=0).

Answer:

Amplitude (=1), Period (=2\pi), Phase Shift (=0)