Find the value of each expression. Try not to look back at the Unit Circle for help. 1. \( \cos 2 \pi \) 2. \( \sin \frac{3 \pi}{2} \) 3. \( \cos \frac{\pi}{4} \) 4. \( \sin \frac{\pi}{3} \) 5. \( \cos \frac{5 \pi}{3} \) 6. \( \sin \frac{4 \pi}{3} \) 7. \( \cos \frac{5 \pi}{6} \) 8. \( \sin \frac{7 \pi}{6} \) 9. \( \sin \left(-\frac{7 \pi}{6}\right) \) 10. \( \cos \left(-\frac{3 \pi}{4}\right) \) 11. \( \cos \frac{\pi}{3} \) 12. \( \sin \frac{2 \pi}{3} \) 13. \( \cos \left(-\frac{5 \pi}{6}\right) \) 14. \( \sin \frac{5 \pi}{6} \) 15. \( \cos \frac{\pi}{2} \)

1. \( \cos 2 \pi = 1 \) 2. \( \sin \frac{3 \pi}{2} = -1 \) 3. \( \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2} \) 4. \( \sin \frac{\pi}{3} = \frac{\sqrt{3}}{2} \) 5. \( \cos \frac{5 \pi}{3} = \frac{1}{2} \) 6. \( \sin \frac{4 \pi}{3} = -\frac{\sqrt{3}}{2} \) 7. \( \cos \frac{5 \pi}{6} = -\frac{\sqrt{3}}{2} \) 8. \( \sin \frac{7 \pi}{6} = -\frac{1}{2} \) 9. \( \sin \left(-\frac{7 \pi}{6}\right) = \frac{1}{2} \) 10. \( \cos \left(-\frac{3 \pi}{4}\right) = -\frac{\sqrt{2}}{2} \) 11. \( \cos \frac{\pi}{3} = \frac{1}{2} \) 12. \( \sin \frac{2 \pi}{3} = \frac{\sqrt{3}}{2} \) 13. \( \cos \left(-\frac{5 \pi}{6}\right) = -\frac{\sqrt{3}}{2} \) 14. \( \sin \frac{5 \pi}{6} = \frac{1}{2} \) 15. \( \cos \frac{\pi}{2} = 0 \) To spice things up, let’s peek into some fascinating trivia! Did you know that the origins of trigonometric functions can be traced back to ancient civilizations? The Babylonians and Egyptians used simple forms of geometry and ratios to solve practical problems, and these intuitive concepts laid the groundwork for the trigonometric functions we utilize today! Also, in real life, knowing these trigonometric values can help in various fields such as architecture, engineering, and even navigation! For instance, architects use angles and sine/cosine functions to ensure buildings are structurally sound. Next time you look at a skyline, remember there's trigonometry behind that beauty!