Chapter 6 - The Circular Functions and Their Graphs - 6.3 Graphs of the Sine and Cosine Functions - 6.3 Exercises - Page 602: 45

$y=3\ sin(4x)$

As $f(0)=0$, use the form $y=a\ sin(bx)$. We can identify the period as $p=\frac{\pi}{2}$, thus $\frac{2\pi}{b}=\frac{\pi}{2}$ and $b=4$. We can find the amplitude as $3$, let $a=3$ which is good for $f(\frac{\pi}{8})=3$. The answer is $y=3\ sin(4x)$