moongazer 3 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

1. amistre64

to allow us to determine this from the origin

2. amistre64

|dw:1345902565889:dw|

3. 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"

4. amistre64

does this make sense?

5. moongazer

I'm still trying to understand it :)

6. amistre64

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

7. amistre64

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

8. 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

9. moongazer

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

10. 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

11. 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)

12. amistre64

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

13. 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

14. moongazer

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

15. moongazer

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

16. moongazer

I'm just curious how does that work :)

17. 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....

18. 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

19. hartnn

i hope u got this @moongazer

20. 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

21. 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

22. amistre64

hartnn looks to have explained that well

23. moongazer

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