c. y c. y 80 9 70 7 60 50 5 x 3 2 4 6 8 12 1 0 1 2 3 4 5 6 7 8 9 101112 20 = − + d. 22.46 sin(0.506 2.060) y x 54.35 (16.1333) = ⎛ − ⎞ + d. 4.4 sin 4π 0.2555 y 3.8 ⎜ 25 ⎟ ⎝ ⎠ ≈ 8.2 feet 34. a. 8.1833 + 12.5 = 20.6833 hours which is at 8:41 PM. e. 80 13.2 − 2.2 11 b. Amplitude: = = = 5.5 A 2 2 + = = Vertical Shift: 13.2 2.2 15.4 7.7 2 2 0 13 ω = = π = 2π 4π 20 Phase shift (use = 13.2, = 8.1833): y x 3.6333 + 12.5 = 16.1333 hours which is at 33. a. = ⎛ ⋅ − φ ⎞ + 13.2 5.5 sin 4π 8.1833 7.7 4:08 PM. 12.5 6.25 25 = 8 .2 − (− 0.6) = 8 .8 = ⎜ 25 ⎟ A b. Amplitude: 4.4 ⎝ ⎠ 2 2 ⎛ 4π ⎞ ⎝ ⎠ φ 1 = sin ⎛ 32.7332π − Vertical Shift: 5.5 = 5.5 ⎞ sin ⎜ ⋅ φ 8.1833 − 8.2 + ( − 0.6) = 7.6 = 3.8 ⎟ 2 2 ω = 2π = π = 4π ⎜ ⎟ 12.5 6.25 25 ⎝ 25 ⎠ = = Phase shift (use 8.2, 3.6333) y x φ π = 32.7332π − : 2 25 = ⎛ ⋅ − φ ⎞ + 8.2 4.4 sin 4π 3.6333 3.8 ⎜ 25 ⎟ φ ≈ 2.5426 ⎝ ⎠ ⎛ 4π ⎞ 4.4 = 4.4 sin ⎛ 4π ⋅ 3.6333 − φ ⎞ Thus, = 5.5 sin ⎜ 25 − 2.5426 ⎟ + 7.7 y x or ⎜ 25 ⎟ ⎝ ⎠
c. y 80 70 60 50 20 0 1 2 3 4 5 6 7 8 9 101112 c. y 9 7 5 3 1 x 2 4 6 8 12 d. y = 22.46 sin(0.506 x − 2.060) + 54.35 d. y = 4.4 sin ⎛ 4π (16.1333) − 0.2555 ⎞ + 3.8 ⎜ 25 ⎟ ⎝ ⎠ ≈ 8.2 feet e. 80 34. a. 8.1833 + 12.5 = 20.6833 hours which is at 8:41 PM. 13.2 − 2.2 11 b. Amplitude: A = = = 5.5 2 2 Vertical Shift: 13.2 + 2.2 = 15.4 = 7.7 2 2 0 13 ω = 2π = π = 4π 20 33. a. 3.6333 + 12.5 = 16.1333 hours which is at 4:08 PM. 12.5 6.25 25 Phase shift (use y = 13.2, x = 8.1833): 13.2 = 5.5 sin ⎛ 4π ⋅ 8.1833 − φ ⎞ + 7.7 b. Amplitude: A = 8 .2 − (− 0.6) = 8 .8 = 4.4 ⎜ 25 ⎟ ⎝ ⎠ 2 2 ⎛ 4π ⎞ Vertical Shift: 8.2 + ( − 0.6) = 7.6 = 3.8 2 2 5.5 = 5.5 sin ⎜ ⋅ 8.1833 − φ ⎟ ⎝ ⎠ 1 = sin ⎛ 32.7332π − φ ⎞ ω = 2π = π = 4π ⎜ ⎟ 12.5 6.25 25 Phase shift (use y = 8.2, x = 3.6333) : 8.2 = 4.4 sin ⎛ 4π ⋅ 3.6333 − φ ⎞ + 3.8 ⎝ 25 ⎠ π = 32.7332π − φ 2 25 ⎜ 25 ⎟ φ ≈ 2.5426 ⎝ ⎠ ⎛ 4π ⎞ 4.4 = 4.4 sin ⎛ 4π ⋅ 3.6333 − φ ⎞ Thus, y = 5.5 sin ⎜ 25 x − 2.5426 ⎟ + 7.7 or ⎜ 25 ⎟ ⎝ ⎠
62514-0132318806_ISM_02-1.docx