Answer a question

Please do problems#30, 34, 36, 37, 39, 40, 41, 43, 53, 54, 55, 56

CHAPTER 7 REVIEW 641 For the following exercises, simplify the equation algebraically as much as possible. Then use a calculator to find the solutions on the interval [0, 27). Round to four decimal places. 46. V 3 cot? x + cot x = 1 47. csc2 x - 3csc x - 4=0 For the following exercises, graph each side of the equation to find the zeroes on the interval [0, 27). 48. 20cos2 x + 21cos x + 1 = 0 49. sec2 x - 2sec x = 15 MODELING WITH TRIGONOMETRIC EQUATIONS For the following exercises, graph the points and find a possible formula for the trigonometric values in the given table. 50. 1 2 3 4 5 51. X 2 3 4 5 6 11 6 6 V -2 V 1 -5 -2 1 52. X -3 -2 -1 0 IN y 3+2V2 3 2V2- 1 3 - 2V2 -1- 2V2 53. A man with his eye level 6 feet above the ground 54. Using the ladder from the previous exercise, if a is standing 3 feet away from the base of a 15-foot 6-foot-tall construction worker standing at the vertical ladder. If he looks to the top of the ladder, at top of the ladder looks down at the feet of the what angle above horizontal is he looking? man standing at the bottom, what angle from the horizontal is he looking? For the following exercises, construct functions that model the described behavior. 55. A population of lemmings varies with a yearly low 56. Daily temperatures in the desert can be very of 500 in March. If the average yearly population of extreme. If the temperature varies from 90 F to 30 F lemmings is 950, write a function that models the and the average daily temperature first occurs at 10 population with respect to t, the month. AM, write a function modeling this behavior. For the following exercises, find the amplitude, frequency, and period of the given equations. 57. y = 3cos(XIT) 58. y = -2sin(16x7) For the following exercises, model the described behavior and find requested values. 59. An invasive species of carp is introduced to Lake 60. The native fish population of Lake Freshwater Freshwater. Initially there are 100 carp in the lake averages 2500 fish, varying by 100 fish seasonally. and the population varies by 20 fish seasonally. If by Due to competition for resources from the invasive year 5, there are 625 carp, find a function modeling carp, the native fish population is expected to the population of carp with respect to t, the number decrease by 5% each year. Find a function modeling of years from now. the population of native fish with respect to t, the number of years from now. Also determine how many years it will take for the carp to overtake the native fish population.Math 155 Lab (7.4-7.6).pdf Q SUM-TO-PRODUCT AND PRODUCT-TO-SUM FORMULAS For the following exercises, evaluate the product for the given expression using a sum or difference of two functions. Write the exact answer. 30. cos ( 3 ) sin ( 4 ) 31. 2sin 27 32. 2cos (5 ) cos ( 3 ) For the following exercises, evaluate the sum by using a product formula. Write the exact answer. 33. sin - sinn 34. cos + cos (17 ) For the following exercises, change the functions from a product to a sum or a sum to a product. 35. sin(9x)cos(3x) 36. cos(7x) cos(12x) 37. sin(1 1x) + sin(2x) 38. cos(6x) + cos(5x) SOLVING TRIGONOMETRIC EQUATIONS For the following exercises, find all exact solutions on the interval [0, 27). 39. tan x + 1 = 0 40. 2sin(2x) + V2 =0 For the following exercises, find all exact solutions on the interval [0, 27). 41. 2sin' x - sin x = 0 42. cos' x - cos x - 1 = 0 43. 2sin' x + 5 sin x + 3 = 0 44. cos x - 5sin(2x) = 0 45. 1 sec2 x + 2 + sin' x + 4cos' x = 0