the ones w the pink dot, make sure to show work equal arcs, corresponding to t-values of43. The number of hours of daylight, H, on day 1 of any given year(on January 1,1 = 1) in Fairbanks, Alaska, can be modeled bythe function5m 37 77and 27.4 2 44 2 427H() = 12 + 8.3 sin365 (- )a. Use the (x, y) coordinates in the figure to find the value ofthe trigonometric function.b. Use periodic properties and your answer from part (a) tofind the value of the same trigonometric function at thea. March 21, the 80th day of the year, is the spring equinox.Find the number of hours of daylight in Fairbanks on thisday.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 hoursof daylight in Fairbanks on this day.c. December 21, the 355th day of the year, is the wintersolstice, the day with the minimum number of hours ofdaylight. Find, to the nearest tenth of an hour, the numberof 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 givenyear (on January 1, 1 = 1) in San Diego, California, can bemodeled by the function(0, -1)H() = 12 + 2.4 sin365(08 – 1)3a. March 21, the 80th day of the year, is the spring equinox.Find the number of hours of daylight in San Diego on thisday.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 hours25. a. sin26. a. cos411b. sin4117b. cos27. a. cos28. a. sinof daylight in San Diego on this day.c. December 21, the 355th day of the year, is the wintersolstice, the day with the minimum number of hours ofdaylight. To the nearest tenth of an hour, find the numberof hours of daylight in San Diego on this day.b. cos97b. sin229. a. tan 730. a. cotb. tan 177157b. cot -45. People who believe in biorhythms claim that there are threecycles that rule our behavior-the physical, emotional, andmental. Each is a sine function of a certain period. Thefunction for our emotional fluctuations is31. a. sin32. a. cos477b. sin47b. cos4E = sin t,14where t is measured in days starting at birth. Emotionalfluctuations, E, are measured from -1 to 1, inclusive, with1 representing peak emotional well-being. -1 representingthe low for emotional well-being, and0 representing feelingneither emotionally high nor low.a. Find E corresponding to t = 7, 14,21,28, and 35. Describewhat you observe.b. What is the period of the emotional cycle?Practice PlusIn Exercises 33-42, letsin i = a, cos t = b, and tan i = c.Write each expression in terms of a, b, and c.33. sin(-1) – sin t34. tan(-r) – tan t36. 3 cos(-1) – cos t35. 4 cos(-1) – cos I37. sin(t + 27) – cos(t + 47) + tan(t + 7)46. The height of the water, H, in feet, at a boat dock t hours after6 A.M. is given by38. sin(t + 27) + cos(t + 47) – tan(t + #)H = 10 + 4 sin t.39. sin(-t – 27) – cos(-1 – 47) – tan(-t – 7)40. sin(-1 - 27) + cos(-1 - 47) – tan(-t - 7)41. cos t + cos(t + 10007) - tan t -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 thismean about the tides?tan(t + 9997) – sin t +4 sin(t – 10007)42. -cos t + 7 cos(t + 10007) + tan t + tan(t + 9997) +sin t + sin(t - 10007)

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Answered: 25. a. sin 11m b. sin

25. a. sin 11m b. sin

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.2: Trigonometric Functions Of Angles

Problem 92E