Chapter 6 - The Circular Functions and Their Graphs - 6.4 Translations of the Graphs of the Sine and Cosine Functions - 6.4 Exercises - Page 613: 22

A

Comparing $y=-2\sin(4x-3)$ to $y=A\sin(\omega x-\phi)$, note that $A=-2$, $\omega=4$, and $\phi=3$. Amplitude=$|A|=2$ Period $T=\frac{2\pi}{\omega}=\frac{2\pi}{4}=\frac{\pi}{2}$ and Phase shift = $\frac{\phi}{\omega}=\frac{3}{4}$ Option A is the correct match.