We are given that
[tex]y=-2+2\cos (2x-\frac{\pi}{3})[/tex]
Note: Given the cosine function
[tex]y=a\cos (bx-c)+d[/tex]
then
[tex]\begin{gathered} Amplitude=a \\ Period=\frac{2\pi}{b} \\ PhaseShift=\frac{c}{b} \\ VerticalShift=d \end{gathered}[/tex]
Comparing the question with what is written in the note
We have
[tex]\begin{gathered} a=2 \\ b=2 \\ c=\frac{\pi}{3} \\ d=-2 \end{gathered}[/tex]
We want to find
(a). Amplitude
From the given question, the amplitude (a) is
[tex]\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}[/tex]
(b).Period
From the given question, the period is
[tex]\begin{gathered} Period=\frac{2\pi}{b} \\ Period=\frac{2\pi}{2} \\ Period=\pi \end{gathered}[/tex]
(c). Phase Shift
From the given question, the phase shift is
[tex]\begin{gathered} PhaseShift=\frac{c}{b} \\ PhaseShift=\frac{\pi}{3}\times\frac{1}{2} \\ PhaseShift=\frac{\pi}{6} \end{gathered}[/tex]
