SOLUTION: Dear Sir/Madam, I am confronted with the following problem: "Which of the following are true of the function f(x) = -7sin(x/2 - pi/3)? I. The maximum value of the function f

Question 6724: Dear Sir/Madam,
I am confronted with the following problem:
"Which of the following are true of the function 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."
I figured out that the first one by looking at the first derivative, but the other two I couldn't figure out (at least not without the use of a graphing calculator). And what is meant by a phase shift?
Thanks in advance.
Regards,
-Mike
Answer by khwang(438) (Show Source):
You can put this solution on YOUR website!
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