Answer:
The graph of the function is shown below.
Step-by-step explanation:
The given function is
[tex]y=-2\sin(\theta -\frac{\pi}{3})+2[/tex] .... (1)
The general equation of a sine function is
[tex]f(x)=A\sin(Bx+C)+D[/tex] .... (2)
Where, A is amplitude, [tex]\frac{2\pi}{B}[/tex] is period, C is phase shift and 2 is midline or vertical shift.
From (1) and (2), we get
[tex]A=-2, B=1,C=\frac{\pi}{3},D=2[/tex]
The amplitude is -2.
[tex]Period=\frac{2\pi}{1}=2\pi[/tex]
[tex]\text{Phase shift}=-\frac{\pi}{3}[/tex]
It means graph shifts [tex]\frac{\pi}{3}[/tex] units right.
[tex]Midline:y=2[/tex]
The graph shifts 2 units up.
Therefore the graph of the function is shown below.
