# Math Help - Find formula from table?

1. ## Find formula from table?

Alright so I found the mid line to be 15 and amp to be 3.
The formula I got is f(t) = 3 sin ((pi/10)x) + 15
However according to the back of the book it got;
f(t) = 3 sin ((pi/6)(t - 74) + 15

My question is how did they got that formula from? How did they get a B of pi/6? I am really confused about that part. Everything else on the formula I am ok with. Please help me!

2. Originally Posted by krzyrice

Alright so I found the mid line to be 15 and amp to be 3.
The formula I got is f(t) = 3 sin ((pi/10)x) + 15
However according to the back of the book it got;
f(t) = 3 sin ((pi/6)(t - 74) + 15

My question is how did they got that formula from? How did they get a B of pi/6? I am really confused about that part. Everything else on the formula I am ok with. Please help me!
What you are calling "B" is $\frac{2\pi}{\text{period}}$

If you look at the table you will notice that the P-values go above the principal axis for a while, then below, and finally come back to 14 at t=86. That point would be the start of the next period, so you would define the first period from t=73 to t=85.

So, the period is $85-73 = 12$

$\therefore b=\frac{2\pi}{12} = \frac{\pi}{6}$

Hope that helps

Mathemagister