Question

graph one complete period of the given sine or cosine curve. (check your answer with your graphing calculator!) f(x)=-2+sin x amplitude = _ period = _ phase shift = ___

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 \(=0\)