How do I find the period of the graph, f(x)=sqrt(sin^2(x/4)f(x)=√sin2(x4), without graphing?
f(x)=sqrt(sin^2(x/4)f(x)=√sin2(x4)
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