# Thread: General formula for Sine functions?

1. ## 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?

2. I believe you solve these to get horizontal shift.

$\displaystyle bx-c=0$

$\displaystyle bx-c=2\pi$

3. 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)

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

$\displaystyle bx-c=0$

$\displaystyle bx-c=2\pi$
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?

5. you solve for x. and find beginning and end point of period.

6. ....huh? I thought we're finding c. o_o. So if my C is x now, what's the c in your formula then...?

7. 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?

8. I believe I'm looking for the horizontal shift of the graph, not a value of 0.

9. 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:

10. 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.

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### general formula of sin function

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