Phase Shift

[lunar lava]

Can someone explain phase shift for trig. functions, and how finding the phase shift differs between sine and cosine?

[cedar dust]

if you have any function f(x)

if you replace f(x) with f(x-a) where a is a constan

this will shift the function by 'a' units to the right

you can check with something like (x)^2 + 3 vs (x-3)^2 +3

the second one will be shifted to the right 3 units

so for f(x) = sin(3x)

sin(3(x-2)) = f(x-2), so the graph of sin3x will be shifted 2 units to the right

if 'a' is negative, the graph will shift to the right