Chapter 7 - Applications of Trigonometric Functions - Section 7.3 The Law of Cosines - 7.3 Assess Your Understanding - Page 561: 67

$y=-3\sin(4x)$

1. We can identify the given graph resembles $y=-sin(x)$, thus we can assume a general form $y=-A\ sin(kx)$ 2. We can find the amplitude $A=3$ 3. We can find the period $\frac{2\pi}{k}=\frac{\pi}{2}$, thus $k=4$ 4. Thus the equation is $y=-3sin(4x)$