equal arcs, corresponding to t-values of 43. The number of hours of daylight, H, on day r of any given year 3m 5m 3m 7m 0.7 T2 4 (on January 1,1 = 1) in Fairbanks, Alaska, can be modeled by the function and 2m. 2m a. Use the (x. y) coordinates in the figure to find the value of the trigonometric function. b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the H() = 12 + 8.3 sin - 80). a. March 21, the 80th day of the year, is the spring equinox. Find the number of hours of daylight in Fairbanks on this day. b. June 21, the 172nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in Fairbanks on this day. c. December 21, the 355th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. Find, to the nearest tenth of an hour, the number of hours of daylight in Fairbanks on this day. indicated real number. (0, 1) (-1,0) (1,0) 44. The number of hours of daylight, H, on day t of any given year (on January 1, 1 = 1) in San Diego, California, can be modeled by the function (0.-1) H() = 12 + 2.4 sin 2 365 - 80) a. March 21, the 80th day of the year, is the spring equinox. Find the number of hours of daylight in San Diego on this day. b. June 21, the 172nd day of the year, is the summer solstice, the day with the maximum number of hours of daylight. Find, to the nearest tenth of an hour, the number of hours of daylight in San Diego on this day. c. December 21, the 355th day of the year, is the winter solstice, the day with the minimum number of hours of daylight. To the nearest tenth of an hour, find the number of hours of daylight in San Diego on this day. 3m 25. a. sin 26. a. cos b. sin 11 11 b. cos 27. a. cos 28. a. sin 9m b. cos b. 29, a. tan b. tan 17 30. a. cot b. cot 15л 45. People who believe in biorhythms claim that there are three cycles that rule our behavior-the physical, emotional, and mental. Each is a sine function of a certain period. The function for our emotional fluctuations is 31. a. sin 32. a. COST 7 47 b. sin 47 b. cos E - sin t. where t is measured in days starting at birth. Emotional fluctuations, E, are measured from -1 to 1, inclusive, with 1 representing peak emotional well-being. -1 representing the low for emotional well-being, and 0 representing feeling neither emotionally high nor low. a. Find E corresponding to t = 7,14,21,28, and 35. Describe what you observe. b. What is the period of the emotional cycle? Practice Plus In Exercises 33-42, let sin t = a, cos t = b, and tan i = c. Write each expression in terms of a, b, and c. 33. sin(-1) – sin t 34. tan(-1) – tan i 35. 4 cos(-1) - cos t 37. sin(t + 27) – cos(t + 4) + tan(t + #) 38. sin(t + 27) + cos(t + 4) - tan(t + ) 39. sin(-t - 27) - cos(-1 - 4) – tan(-r - =) 36. 3 cos(-1) – cos t 46. The height of the water, H, in feet, at a boat dock r hours after 6 A.M. is given by H = 10 + 4 sin t. 40. sin(-t - 2=) + cos(-1 - 47) – tan(-r - =) 41. cost + cos(t + 1000m) – tan t - tan(t + 999m) – sin t+ 4 sin(t - 1000) 42. -cost + 7 cos(t + 1000m) + tan i + tan(t + 999) + sin t + sin(t - 1000) a. Find the height of the water at the dock at 6 A.M., 9 A.M., noon, 6 P.M., midnight, and 3 A.M. b. When is low tide and when is high tide? c. What is the period of this function and what does this mean about the tides?