find phase shift in sin graph

[alpine plover]

i wanted to find the sin function from this graph just as practice. i believe i got everything correct in my final answer except the phase shift. can someone please help finding the phase shift?

[alpine plover]

my phase shift is:
pi/2 + 1
because the graphs first maximum is at 1, instead of pi/2

but i seem to be finding that incorrectly

[alpine plover]

i randomly guessed that its actually -1/4 but i dont know why

[crimson schooner]

This only works when the period is 2pi, which it is not here

[alpine plover]

ohhhhh right

so i believe i didnt provied enough information in the graph when i made the question

[crimson schooner]

there's enough information

You need the period first, and from that you can get the phase shift

@alpine plover

[alpine plover]

if i do

2pi/3 * asin(1)

i believe i should get the theta value of the function with no phase shift

and then the desired phase shift would be 1 minus that

lemme check

no

i just have to find what x value yields 1 in sin(2pi/3 x)

sin(2pi/3 x) = 1
2pi/3 x = arcsin(1)
2pi/3 x = pi/2
x = (pi/2)/(2pi/3)
x = (pi/2)(3/2pi)
x = 3pi/4pi
x = 3/4

and we need to shift right by 1 - 3/4

f(x) = 67/56 * sin(2pi/3 * (x - 0.25)) -53/56

amazing

thank you a lot 🎑

[midnight urchin]

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