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. \( \cos \frac{\pi}{2} \)

Below are the evaluated expressions along with brief explanations: 1. cos 2π   = 1   (Completing one full revolution brings you back to the point (1, 0).) 2. sin (3π/2)   = –1   (The sine corresponds to the y-coordinate; at 3π/2, the point is (0, –1).) 3. cos (π/4)   = √2/2   (On a 45° angle, both sine and cosine are √2/2.) 4. sin (π/3)   = √3/2   (The sine of 60° is √3/2.) 5. cos (5π/3)   = 1/2   (5π/3 is a 60° reference angle in the 4th quadrant where cosine is positive.) 6. sin (4π/3)   = –√3/2   (4π/3 is in the 3rd quadrant where sine is negative and the reference angle is π/3.) 7. cos (5π/6)   = –√3/2   (5π/6 has a reference angle of π/6 and lands in the 2nd quadrant where cosine is negative.) 8. sin (7π/6)   = –1/2   (7π/6 is in the 3rd quadrant with a reference angle of π/6, and sine is negative there.) 9. sin (–7π/6)   = 1/2   (Sine is an odd function, so sin(–θ) = –sin θ. Since sin (7π/6) = –1/2, then sin (–7π/6) = 1/2.) 10. cos (–3π/4)   = –√2/2   (Cosine is even, so cos (–3π/4) = cos (3π/4); at 3π/4 the cosine is –√2/2.) 11. cos (π/3)   = 1/2   (The cosine of 60° is 1/2.) 12. sin (2π/3)   = √3/2   (2π/3 is in the 2nd quadrant; its reference angle is π/3 and sine is positive there.) 13. cos (–5π/6)   = –√3/2   (Cosine is an even function; thus, cos (–5π/6) = cos (5π/6) which is –√3/2.) 14. sin (5π/6)   = 1/2   (5π/6 is in the 2nd quadrant; the sine is positive and equals 1/2.) 15. cos (π/2)   = 0   (The cosine of 90° is 0.) These are all the requested values.