1. **State the problem:** We want to analyze the function $$y = \sin(3x) \cos(2x)$$ and understand its behavior. 2. **Formula and identities:** We can use the product-to-sum identity for sine and cosine: $$\sin A \cos B = \frac{1}{2} [\sin(A+B) + \sin(A-B)]$$ 3. **Apply the identity:** Letting $A=3x$ and $B=2x$, we get: $$y = \sin(3x) \cos(2x) = \frac{1}{2} [\sin(3x+2x) + \sin(3x-2x)] = \frac{1}{2} [\sin(5x) + \sin(x)]$$ 4. **Interpretation:** This shows the function is a sum of two sine waves with frequencies 5 and 1, scaled by $\frac{1}{2}$. 5. **Graph features:** The function oscillates between $-1$ and $1$ because sine functions have range $[-1,1]$ and the factor $\frac{1}{2}$ scales the amplitude to $[-1,1]$. 6. **Summary:** The function $y=\sin(3x)\cos(2x)$ can be rewritten as: $$y = \frac{1}{2} \sin(5x) + \frac{1}{2} \sin(x)$$ which is easier to analyze and graph.