y = AsinB(x-C) +D.

I know that A (amplitude) can be found by getting (max-min )/2, B = 2pi / current period, and D = average of max and min y.

But how do you find C, once you've found those 3?

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- Feb 26th 2011, 10:40 AMKiririGeneral formula for Sine functions?
y = AsinB(x-C) +D.

I know that A (amplitude) can be found by getting (max-min )/2, B = 2pi / current period, and D = average of max and min y.

But how do you find C, once you've found those 3? - Feb 26th 2011, 10:47 AMskoker
I believe you solve these to get horizontal shift.

$\displaystyle bx-c=0$

$\displaystyle bx-c=2\pi$ - Feb 26th 2011, 10:48 AMe^(i*pi)
C is the phase shift.

Since $\displaystyle \sin(x)$ passes through the origin, the value of C is the distance from the origin.

When $\displaystyle C = \frac{\pi}{2}$ you get cos(x) - Feb 26th 2011, 10:56 AMKiriri
- Feb 26th 2011, 11:25 AMskoker
you solve for x. and find beginning and end point of period.

- Feb 26th 2011, 11:39 AMKiriri
....huh? I thought we're finding c. o_o. So if my C is x now, what's the c in your formula then...?

- Feb 26th 2011, 12:29 PMskoker
are you looking for the value of 0? or are you trying to find the critical points of a sine function with a phase/horizontal shift?

- Feb 26th 2011, 12:43 PMKiriri
I believe I'm looking for the horizontal shift of the graph, not a value of 0.

- Feb 26th 2011, 12:51 PMe^(i*pi)
C

*is*the horizontal shift of sin(B[x-c]) compared to sin(Bx)

you can calculate it most easily at the origin because $\displaystyle \sin(Bx)$ passes through (0,0) for all B. The value of $\displaystyle \sin(B[x-c])$ can be found by where it intersects the x axis (ie: y=0). For example if C=45 degrees then $\displaystyle \sin(Bx-C)$ will be shifted to the right by 45 degrees compared to $\displaystyle \sin(Bx)$

Post 2 shows the mathematical representation

Edit: In case a picture helps: - Feb 26th 2011, 01:10 PMKiriri
Ah, I see. So the easiest way would be to find where the point that passed the origin is, and see how far has it gone from origin after all the shifts. Thank you.