# How do you find the amplitude and period for #y=3sin2 (x-pi/6)#?

##### 1 Answer

Period:

Amplitude:

#### Explanation:

We start analyzing the argument of sin in

If the function was

If we sum anything to the argument (for example like the function

So we can consider a similar function with the same amplitude and period that is easier to study:

**Amplitude**

If we consider that the sine function has a range

What really matters in amplitude is the vertical dilation/compression factor **outside** of sin(x): in this case we would have

**Period**

If we consider the sine function, it has a period of **inside** the argument is a horizontal dilation/compression of the function. We could find the value of the period deviding

**Verify**

As we can see in this graph, the range is [-3,3], and the function is plotted in the interval

graph{3sin(2(x-pi/6)) [0, 3.14, -3, 3]}