Question 6724
 f(x) = -7sin(x/2 - pi/3)? 
I. The maximum value of the function f is 7 and occurs when x = pi/2.
II. The period of the function is 4pi.
III. The phase shift of f is 2pi/3." 

 This a period function 
 f(x) = -7sin(x/2 - pi/3) = -7 sin[(x - 2pi/3)/2]

 you see f(2pi/3) = 0 but f(x) = 0 for f(x) = A sin x.

 In general, as a standard form f(x) = A sin(x -delta)/T 
 where A means the amplitude, period is 2piT,delta is the phase shift
(gemetrically it means translation.)

 Start from x--> A sin x --> A sin (x/T) --> A sin ((x- delta)/T) 
             (P=2pi,shift=0) (P=2piT,shift=0)  (P=2piT,shift=delta) 

 It came from the wave function in physics.
 [same case for cos function)

 Kenny