To answer this question we need to remember that in a function of the form:
[tex]y=A\sin (B(\theta+C))+D[/tex]
we have that:
• The amplitude is A
,
• The period is
[tex]\frac{2\pi}{B}[/tex]
• The phase shift is C (here if C>0 the shift is to the left, otherwise is to the right).
,
• The midline is
[tex]y=D[/tex]
Now that we know this we need to determine the values of each constant, comparing the function given by the general expression above we have:
[tex]\begin{gathered} A=2 \\ B=1 \\ C=-\pi \\ D=1 \end{gathered}[/tex]
Using the definitions given above we have that:
[tex]\text{Midline }y=1[/tex]
[tex]\text{Amplitude 2}[/tex][tex]\text{ Period }2\pi[/tex][tex]\text{ Phase shift }-\pi[/tex]
The graph of the function is:
