# Thread: Deriving cosine equation from a chart

1. ## Deriving cosine equation from a chart

I've been given the following information:

x = y
1 = 9.08
2 = 9.95
3 = 11.20
4 = 12.73
5 = 14.10
6 = 15.13
7 = 15.32
8 = 14.52
9 = 13.18
10 = 11.75
11 = 10.30
12 = 9.25
First, I was asked to derive a sine function to model the data, which I got as: Y=3.12sin[pi/6(x-4)]+12.2

Now, I need to get a cosine function to model it. This is where I'm stuck; the sine curve has one maximum, as does the data, so I was easily able to figure out the phase shift. But a cosine curve has two maximums so I'm having a little trouble figuring out a cosine equation.

I decided to check the back of the book and see the answer as y=3.11cos[0.51(m-6.71)]+12.14

At this point, I'm completely lost

Could anyone point me into the right direction as to how I'd be able to derive a cosine function from the above data?

2. Originally Posted by youngb11
I've been given the following information:

First, I was asked to derive a sine function to model the data, which I got as: Y=3.12sin[pi/6(x-4)]+12.2

Now, I need to get a cosine function to model it. This is where I'm stuck; the sine curve has one maximum, as does the data, so I was easily able to figure out the phase shift. But a cosine curve has two maximums so I'm having a little trouble figuring out a cosine equation.

I decided to check the back of the book and see the answer as y=3.11cos[0.51(m-6.71)]+12.14

At this point, I'm completely lost

Could anyone point me into the right direction as to how I'd be able to derive a cosine function from the above data?

Were you given a method to use? I suspect that the book answer comes from a least-squares fit, while yours comes from inspecting the data.

To convert you answer to a cosine answer, recognize that you can obtain the graph of
$\displaystyle y=\sin(x)$ by shifting the graph of $\displaystyle y=\cos(x)$ by $\displaystyle \pi/2$ units to the right.

So, $\displaystyle y=3.12\sin[(\pi/6)(x-4)]+12.2$ is equivalent to $\displaystyle y=3.12\cos[(\pi/6)(x-4)-(\pi/2)]+12.2$.

Do some algebra to compare. I'm puzzled by the variable m in the cosine expression the "book" gave.