\begin{tabular}{l} What is the exact value of \( \cos 60^{\circ} \) ? \\ Oo \\ \hline\( \frac{1}{2} \) \\ \hline\( \frac{\sqrt{3}}{2} \) \\ \hline\end{tabular}

Did you know that \( \cos 60^{\circ} \) comes straight from the special triangles? If you take an equilateral triangle (where all angles are \(60^\circ\)) and draw a height, you create two right triangles—each has a base of \( \frac{1}{2} \) and a hypotenuse of \(1\). Using the definition of cosine (adjacent over hypotenuse), you find \( \cos 60^\circ = \frac{1}{2} \). Thinking practically, the cosine function helps us find values related to angles in real-world scenarios like architecture and engineering. For example, if you're figuring out how high a ladder leans against a wall, you can find the angle of the ladder and use \( \cos \) to calculate the height it reaches, ensuring you build safely and effectively.