Answer with explanation:
The given trigonometric function is
[tex]y= -2 \sin (\Theta -\frac{\pi}{3})+2\\\\y= -[-2 \sin (\frac{\pi}{3}-\Theta)]+2\\\\ y=2 \sin (\frac{\pi}{3}-\Theta)+2[/tex]
The sine function has maximum and minimum are 1 and -1, which it will achieve at ,
[tex]\Theta =\pm(2k+1)\frac{\pi}{2}[/tex]
So, the given function will attain maximum and minimum at,
[tex] =\pm(2k+1)\frac{\pi}{2}-\frac{\pi}{3}[/tex]
for different values of k.
