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moongazer

  • 2 years ago

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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  1. amistre64
    • 2 years ago
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    to allow us to determine this from the origin

  2. amistre64
    • 2 years ago
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    |dw:1345902565889:dw|

  3. phi
    • 2 years ago
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    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"

  4. amistre64
    • 2 years ago
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    does this make sense?

  5. moongazer
    • 2 years ago
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    I'm still trying to understand it :)

  6. amistre64
    • 2 years ago
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    evaluating things that are at the origin, is by far simpler than trying to evaluate them at a distance.

  7. amistre64
    • 2 years ago
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    since moving an object doesnt change its inherent structure; we move it to the origin to study it

  8. amistre64
    • 2 years ago
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    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

  9. moongazer
    • 2 years ago
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    I think I understood it now with the explanation of phi.

  10. amistre64
    • 2 years ago
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    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

  11. amistre64
    • 2 years ago
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    if x is out of phase by a factor of "c" then we need to adjust this thing back into place with (x-c)

  12. amistre64
    • 2 years ago
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    i think factor is a bad term there, but you know .....

  13. moongazer
    • 2 years ago
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    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

  14. moongazer
    • 2 years ago
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    I think what you said: "then we need to adjust this thing back into place with (x-c)" explains it

  15. moongazer
    • 2 years ago
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    could you also explain why |a| is the amplitude and d is the vertical shift?

  16. moongazer
    • 2 years ago
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    I'm just curious how does that work :)

  17. hartnn
    • 2 years ago
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    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....

  18. hartnn
    • 2 years ago
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    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

  19. hartnn
    • 2 years ago
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    i hope u got this @moongazer

  20. amistre64
    • 2 years ago
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    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

  21. amistre64
    • 2 years ago
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    sin(90) = 1; but lets say the original function is such that sin(90) = 3; multiply both sides by 3 3 sin(90) = 3

  22. amistre64
    • 2 years ago
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    hartnn looks to have explained that well

  23. moongazer
    • 2 years ago
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    Thanks for the answers. I agree that hartnn explained it well. :)

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