Question

Determine the period of this Function.

Answer 1

Answer:

4p

Step-by-step explanation:

The period is basically the difference in x from one "peak" to the other "peak".

The peaks are the highest points of a sinosodial function, and the figure them out, use the formula:

$|peak_1-peak_2|=period$

We know the first peak is at about x=0$\pi$

We know the second peak is at about x=4$\pi$

So plugging this in:

$|0-4\pi |=4\pi$

So the period is $4\pi$

I am assuming "p" stands for $\pi$, so the answer should be 4p.

There are other ways to find the period, for instance if you are given a sinusodial function in writing instead of a graph.

Here is an example:

5sin(5x+2)+3

If we want to find period, we need to find what we call "b"

b is the number in front of x, which we can identify as bx, which in this case is 5x above.

Now what do we do with this "b"?

This is the value we need to find our period.

If you know b, you can use this formula to find the period:

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

And when we plug in b:

$\frac{2\pi }{5}$

=

1.257, which would be your period.

THis can also be reworked so that you can find b:

If the formula for period is $\frac{2\pi }{b}=p$, then the opposite formula would be $\frac{2\pi }{ p}=b$

And when you plug the period you have in:

$\frac{2\pi }{1.257}$

=

5

Anyway, your answer is 4p.

Hope this helps!