Question

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.

Answer 1

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

Answer 2

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

Answer 3

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)

Answer 4

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.

Answer 5

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.

Answer 6

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 :)

Answer 7

1-5=-4 yes u r right

Answer 8

oops wrong area to post -4 sorry

Answer 9

so the answer ends up being

y= 2sin(2(x+1/(8pi))) +3

Answer 10

I hope it helps :)

Answer 11

thank you so much for all your help!