# How do I find the period of the graph, #f(x)=sqrt(sin^2(x/4)#, without graphing?

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#f(x)=sqrt(sin^2(x/4)#

##### 1 Answer

The period of

#### Explanation:

Let

We ask what is the period of:

Basically, this means solving the equality below for

If

**1.**

#sin(x/4+rho_0/4) = sin(x/4)#

#sin(x/4)cos(rho_0/4)+cos(x/4)sin(rho_0/4)=sin(x/4)#

With lowest positive value

**2.**

#sin(x/4)cos(rho_0/4)+cos(x/4)sin(rho_0/4)=-sin(x/4)#

This time, the lowest positive value is

As such, the principal period is actually

With the set of periods