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The way you find the period is to know the fact that
sin (x) has a period of 2pi.

Given y=sin(ax-b), the period is 2pi/a and the phase shift is b

1-5=-4 yes u r right

oops wrong area to post -4 sorry

so the answer ends up being
y= 2sin(2(x+1/(8pi))) +3

I hope it helps :)

thank you so much for all your help!