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

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- moongazer

- schrodinger

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- amistre64

to allow us to determine this from the origin

- amistre64

|dw:1345902565889:dw|

- phi

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"

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## More answers

- amistre64

does this make sense?

- moongazer

I'm still trying to understand it :)

- amistre64

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

- amistre64

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

- amistre64

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

- moongazer

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

- amistre64

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

- amistre64

if x is out of phase by a factor of "c"
then we need to adjust this thing back into place with (x-c)

- amistre64

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

- moongazer

That's what I am thinking with this sine graph
|dw:1345904532767:dw|
you need to subtract pi/3 to make it to the origin

- moongazer

I think what you said:
"then we need to adjust this thing back into place with (x-c)"
explains it

- moongazer

could you also explain why |a| is the amplitude and d is the vertical shift?

- moongazer

I'm just curious how does that work :)

- hartnn

when u write y=a sin (b(x+c))
the maximum value of y is |a|
because the maximum value of sine function is |1|
and the amplitude is the maximum value a function can take....

- hartnn

now consider the equation
y-d=a sin (b(x+c))
this means that all the points with y-coordinate y has now the y coordinate of y-d
this is a vertical shift of the entire function
if d is positive, the entire function shifts down by d units
and if d is negative the entire function shifts up by d units

- hartnn

i hope u got this @moongazer

- amistre64

a is a scalar factor that affects the slope of this thing at any given point.
if we take the sine wave, it only has values from -1 to 1, the "a" part manipulates the slope at every given point to change how high or low the sin function can reach

- amistre64

sin(90) = 1; but lets say the original function is such that sin(90) = 3; multiply both sides by 3
3 sin(90) = 3

- amistre64

hartnn looks to have explained that well

- moongazer

Thanks for the answers. I agree that hartnn explained it well. :)

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