f. \( \cos \frac{9 \pi}{4} \)

To find \( \cos \frac{9 \pi}{4} \), we can first simplify the angle by noting that angles in trigonometry are periodic. Since the cosine function has a period of \( 2\pi \), we can subtract \( 2\pi \) (or \( \frac{8\pi}{4} \)) to bring the angle within the standard range of \( [0, 2\pi) \). So, \( \frac{9 \pi}{4} - \frac{8 \pi}{4} = \frac{\pi}{4} \). Now, we can find \( \cos \frac{\pi}{4} \), which is \( \frac{\sqrt{2}}{2} \). Therefore, \( \cos \frac{9 \pi}{4} = \frac{\sqrt{2}}{2} \). By the way, did you know that the unit circle is not just a tool for finding angles and values for trigonometric functions? It also provides a visual representation of how these values transform as you move around the circle. Imagining the circle can help reinforce your understanding of why certain angles produce the same values! Now, if you ever find yourself confused with trigonometric identities or angle reductions, a common mistake is forgetting to reduce angles properly. Always remember to subtract \( 2\pi \) or \( \pi \) as needed to find equivalent angles, and keep an eye on those quadrants to confirm the signs of your sine and cosine values!