We know,
sin(x) and cos(x) have minimum value equal to -1 and maximum value is 1.
Maximum value of sin(x) is 1
So we replace sin by 1 in our given equation
[tex]y=-2+5sin(\frac{\pi }{12}(x-2))[/tex]
When we replace sin by 1 we will get
[tex]y=-2+5(1))[/tex]
y= -2+5 = 3
So maximum value is 3
