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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

Mathematics
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to allow us to determine this from the origin
|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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Other answers:

does this make sense?
I'm still trying to understand it :)
evaluating things that are at the origin, is by far simpler than trying to evaluate them at a distance.
since moving an object doesnt change its inherent structure; we move it to the origin to study it
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
I think I understood it now with the explanation of phi.
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
if x is out of phase by a factor of "c" then we need to adjust this thing back into place with (x-c)
i think factor is a bad term there, but you know .....
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
I think what you said: "then we need to adjust this thing back into place with (x-c)" explains it
could you also explain why |a| is the amplitude and d is the vertical shift?
I'm just curious how does that work :)
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....
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
i hope u got this @moongazer
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
sin(90) = 1; but lets say the original function is such that sin(90) = 3; multiply both sides by 3 3 sin(90) = 3
hartnn looks to have explained that well
Thanks for the answers. I agree that hartnn explained it well. :)

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