1. The problem statement, all variables and given/known data y = (4/3)cos(x/2 + pi/6) - (2/3) (0 <= x < 2pi) Find the maximum and minimum values for the trigonometry function without calculus or drawing the graph. Basically in the solution they apply the transformations to the domain given in order to find a new domain and range, so I attempted to do the same. So first I tried to get the new domain, by applying changes to 0 <= x < 2pi 0 <= x < 2pi pi/6 <= x < 2pi/2 + pi/6 pi/6 <= x/2 + pi/6 < 7pi/6 // until this step is correct, no difficulties here Now from the new domain I have to find a new range so I find the cos of the x values of the new domain cos of pi/6 is +(root3)/2 cos of 7pi/6 is +(root3)/2 This is where I am confused because the range is the same value +(root3)/2 <= cosx <= +(root3)/2 However, if I had gotten this step right what I would have done next is apply the transformations from the given function that apply to the y values. Why is the earlier step wrong though? Can some please help?