# Demonstrate that T = 4pie is period of y = sin x+|sin2x|?

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### 1 Answer

To determine the period of the function `y=sinx+|sin2x|` , we need to determine how long it takes for the function to repeat.

Given the function

`f(x)=sinkx`

its period is `T={2pi}/k` .

This means that `sinx` has a period of `2pi` and `|sin2x|` has a period of `{2pi}/2=pi` .

Now when two functions are added together, the period of the functions is the longer period of the two functions.

**This means that the period of `y=sinx+|sin2x|` is `2pi` , not `4pi` as stated in the question.**