Chapter 5 - Trigonometric Functions - Section 5.2 Trigonometric Functions: Unit Circle Approach - 5.2 Assess Your Understanding - Page 402: 35

$\dfrac{1}{2}$

We need to compute $\sin 45^{\circ} \cos 45^{\circ}$. We use the unit circle values (where $\cos{45^{\circ}}=\frac{\sqrt2}{2}$ and $\sin{45^{\circ}}=\frac{\sqrt2}{2}$) to obtain: $\sin 45^{\circ} \cos 45^{\circ} \\ =(\dfrac{\sqrt 2}{2}) \times (\dfrac{\sqrt 2}{2}) \\ =\dfrac{2}{4}\\ =\dfrac{1}{2}$