# Thread: Deriving an equation from a sin graph.

1. ## Deriving an equation from a sin graph.

Here is the picture: 2011-11-15_11-07-53_425.jpg picture by Bashyboy - Photobucket

The amplitude is easy enough to find--it is 3, and since it is a reflection, it is therefore -3--, but what I can't find is the coefficient for x, which is b. I understand the period to be 2pi/b, and in the answer key they are utilizing in this way: 2pi/b = pi. I don't understand, is pi the period? And if so, how am I able to deduce this from the graph?

Thank you

2. ## Re: Deriving an equation from a sin graph.

Not entirely sure what you are referring to, it is something like a general formula:

$y=asin(bx+c)$?

Here, we have:

$y=-3sin(bx+c)$
We deduce the value for b from the number of 'loops' of the graph - and as you say, this can be calculated through knowing the period. $sin(x)$ is periodic in that it repeats itself every $2\pi$ radians. This means that:
$sin(x)$ has one full 'loop' between $x=0$ and $x=2\pi$ Here, there are two full loops, so $b=2$

The way your text describes it:

$\frac{2\pi}{b}=\pi$

$b=\frac{2\pi}{\pi}=2$

3. ## Re: Deriving an equation from a sin graph.

Yes, I am referring to that general formula. Now, how do I find the horizontal translation (denoted by c) mathematically?

4. ## Re: Deriving an equation from a sin graph.

By looking at the $x$-intercepts, I would think. Compare where the graph cuts the x-axis of this graph with where it cuts the x axis of $sin(x)$

5. ## Re: Deriving an equation from a sin graph.

I am terribly sorry, I meant algebraically; but your method seems quite sensible. Thank you.