Question

In graphing trigonometric functions why is it the phase shift of
y = a sin b(x+c) + d .
when c < 0 is to the right and when c > 0 is to the left ??
also for other trigo functions

Answer 1

to allow us to determine this from the origin

Answer 2

the same reason that f(x-1) is shifted to the right. When x is 0, you plot a value taken from the function to the left of zero. You have "moved the point on the left to the right"

Answer 3

does this make sense?

Answer 4

I'm still trying to understand it :)

Answer 5

evaluating things that are at the origin, is by far simpler than trying to evaluate them at a distance.

Answer 6

since moving an object doesnt change its inherent structure; we move it to the origin to study it

Answer 7

we account for the movement in the equation such that if we move the center to the origin; all the points related to the function move in the same manner

Answer 8

I think I understood it now with the explanation of phi.

Answer 9

if we want to study a parabola: y = (x)^2 ; such that the vertex is x = 5, y=3 it is better to study this when the vertex is at the origin so we move it by -5, -3 to get it to (0,0)

y-3 = (x-5)^2

y = (x-5)^2 + 3

Answer 10

if x is out of phase by a factor of "c"

then we need to adjust this thing back into place with (x-c)

Answer 11

i think factor is a bad term there, but you know .....

Answer 12

That's what I am thinking with this sine graph

you need to subtract pi/3 to make it to the origin