Question 974517
For this solution, we're going to use 2 double angle equations:

{{{sin(2x)=2sin(x)cos(x)}}}

and 

{{{cos(2x)=1-2sin^2(x)}}}


{{{sin(4x)=2sin(2x)cos(2x)}}}


{{{2(2sin(x)cos(x))(1-2sin^2(x))}}}


{{{4sin(x)cos(x)-8sin^3(x)cos(x)}}}

and it looks like this

*[illustration sin4x.png].