Simplify each expression. See Example 4.
⅛ sin 29.5° cos 29.5°

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Recognize that the expression involves the product of sine and cosine of the same angle: \(\frac{1}{8} \sin 29.5^\circ \cos 29.5^\circ\).

Recall the double-angle identity for sine: \(\sin 2\theta = 2 \sin \theta \cos \theta\). This allows us to rewrite the product \(\sin \theta \cos \theta\) as \(\frac{1}{2} \sin 2\theta\).

Apply this identity to the expression: replace \(\sin 29.5^\circ \cos 29.5^\circ\) with \(\frac{1}{2} \sin (2 \times 29.5^\circ)\), which simplifies to \(\frac{1}{2} \sin 59^\circ\).

Substitute back into the original expression: \(\frac{1}{8} \times \frac{1}{2} \sin 59^\circ\).

Combine the constants: multiply \(\frac{1}{8}\) and \(\frac{1}{2}\) to get \(\frac{1}{16}\), so the simplified expression is \(\frac{1}{16} \sin 59^\circ\).

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