Question

What is the formula to determine the phase shift of a function?

Answer 1

of a sine function?

Answer 2

any

Answer 3

phase shift of
\[\sin(bx+c)\] is \(-\frac{c}{b}\)

Answer 4

if you want a non memorization way of finding it, set \(bx+c=0\) and solve for \(x\)

Answer 5

for example if you have
\[\sin(3x+\pi)\] then set
\[3x+\pi=0\] and solve to get
\[x=\frac{-\pi}{3}\] as the phase shift

Answer 6

isnt it if at the last number it has a plus, then the direction goes to the left and if its a minus, then the direction goes to the right?

Answer 7

yes, that is true
that is why the phase shift in my example above is \(-\frac{\pi}{3}\) the graph moves \(\frac{\pi}{3}\) units to the left

Answer 8

this makes sense if you think about what you are doing
you know \(\sin(0)=0\) i.e. you are at the origin
if instead you have \(\sin(3x+\pi)\) then it will give you zero is \(3x+\pi=0\) in other words if \(x=-\frac{\pi}{3}\)

Answer 9

here is a graph of \(y=\sin(3x+\pi)\) you can see it looks like a sine curve, but shifted left \(\frac{\pi}{3}\) units
http://www.wolframalpha.com/input/?i=sin%283x%2Bpi%29