# How do you calculate amplitude and period of #y = -0.3 cos (2x)#?

##### 1 Answer

In this problem we deal with a type of function *sinusoidal*.

These functions have a *period*, that is there exists a real value

These functions also have a characteristic called an *amplitude* - the maximum deviation from zero occurred on any interval of at least a size of a period

If function *period* *period* of

This fact follows from a simple chain of equalities:

(since

We have proven that

which means that *period*.

If a function *amplitude* *amplitude*

Indeed, let's consider that the maximum deviation of

Then *amplitude* of

Obviously, changes in *period* and *altitude* of a sinusoidal function are independent of each other and can be evaluated separately.

Using the above theoretical consideration, we see in our case for a function *period* equals to *period* of a function *altitude* equals to

We know that the *period* of a function *period* of a function

The *amplitude* of a function *amplitude* of