Write the sine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2; period: π; phase shift: -1/8π ; vertical shift:3 I know this is how it starts f(t) =2sin. And I know that it ends with +3 but I don't know how to do the middle part.

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Write the sine function with the given amplitude, period, phase shift, and vertical shift. amplitude: 2; period: π; phase shift: -1/8π ; vertical shift:3 I know this is how it starts f(t) =2sin. And I know that it ends with +3 but I don't know how to do the middle part.

Mathematics
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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
so if the period is half of that, it means that the input is moving as twice as faster, so it would look like sin (2x)

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exactly what Xavier said, so if you have other problems like this one you can use the formula period = 2pi/a so if it is pi. pi = 2pi/a <=> a = 2.
The phase shift is the toughest among all of the numbers. Remember that f(x-c) shifts the graph horizontally and f(ax) compresses the graph horizontally ? When both of these happen, you have to write it in the form f(a(x-c)) which is horizontally shifted AND compressed.
so since the phase shift is -1/(8pi), it is very tempting to write the answer as sin(2x+1/(8pi)) however, the actual answer is sin(2(x+1/(8pi)) I like to leave it like this, but if you need to follow the form y = sin(ax+b) then sin(2(x+1/(8pi)) = sin(2x+1/(4pi)). Just follow your instructions :)
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!

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