# General formula for Sine functions?

• Feb 26th 2011, 10:40 AM
Kiriri
General 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 AM
skoker
I believe you solve these to get horizontal shift.

$bx-c=0$

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

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

When $C = \frac{\pi}{2}$ you get cos(x)
• Feb 26th 2011, 10:56 AM
Kiriri
Quote:

Originally Posted by skoker
I believe you solve these to get horizontal shift.

$bx-c=0$

$bx-c=2\pi$

Wait, huh? So if you have b...you just take a random x value to plug in? I don't think that's it....unless I am missing something?
• Feb 26th 2011, 11:25 AM
skoker
you solve for x. and find beginning and end point of period.
• Feb 26th 2011, 11:39 AM
Kiriri
....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 PM
skoker
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 PM
Kiriri
I believe I'm looking for the horizontal shift of the graph, not a value of 0.
• Feb 26th 2011, 12:51 PM
e^(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 $\sin(Bx)$ passes through (0,0) for all B. The value of $\sin(B[x-c])$ can be found by where it intersects the x axis (ie: y=0). For example if C=45 degrees then $\sin(Bx-C)$ will be shifted to the right by 45 degrees compared to $\sin(Bx)$

Post 2 shows the mathematical representation

Edit: In case a picture helps:
• Feb 26th 2011, 01:10 PM
Kiriri
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.