Question

4sin(x+pi/4) how do i find period, phase shift

Answer 1

Eli, can you answer the period question?

Answer 2

Ok. I'll do it.

Odiepus, remember first that sin has period 2pi. I.e., for all x,
\[ \sin(x + 2 \pi) = \sin(x) \]

In general, the period of a function f(x) is the smallest number T such that
f(x+T) = f(x).

For the function f(x) = sin(x), T = 2pi

Answer 3

Now, for your function f(x) = 4sin(x + pi/4). We want to find its period. I.e., the smallest number T such that

f(x+T) = f(x)

i.e.,
4 sin( (x+T) + pi/4 ) = 4 sin( x + pi/4 )

i.e.,
sin((x + pi/4) + T) = sin(x + pi/4)

Now has sin has period 2pi, it must be that for this function also,
T = 2pi.

I.e., the period of the function f(x) = 4sin(x + pi/4) is T = 2pi.

Answer 4

For the record, the phase shift is the pi/4.

Answer 5

how can I find where the cycle will complete? also i get phase shift of -pi/4

Answer 6

book says to add period to phase shift to find the end of the cycle.
but i get 7pi/4 graph on calc and wolframs says different. what am i doing wrong?

Answer 7

Given the convention you're using with phase shift -pi/4, then indeed the end of the cycle will be x = 2pi - pi/4 = 7pi/4. But remember also that that means the beginning of the cycle is at x = -pi/4.