Chapter 7 - Analytic Trigonometry - 7.1 The Inverse Sine, Cosine, and Tangent Functions - 7.1 Assess Your Understanding - Page 453: 90

$\frac{\sqrt 3}{4}$

Step 1. For angle $\theta=\frac{\pi}{3}$, the corresponding point on a unit circle is $(\frac{1}{2},\frac{\sqrt 3}{2})$. Step 2. Thus we have $sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$ and $cos\frac{\pi}{3}=\frac{1}{2}$. Step 3. Thus $sin\frac{\pi}{3}cos\frac{\pi}{3}=\frac{\sqrt 3}{4}$