= ⎛ − π ⎞ 220 sin 60π , t 28. c. ≥ 0 t (t ) I ⎜ 6 ⎟ ⎝ ⎠ Period: = 2π = 2π T = 1 ω 60π 30 Amplitude: π = 220 A = 220 Phase Shift: (0.517 φ = − + = = d. 15.62 sin 2 .096) 40.377 6 1 y x ω 60π 360 e. 60 29. a. 0 13 20 30. a. b. Amplitude: = 56.0 − 24.2 = 31.8 = A 80.0 − 34.6 45.4 15.9 2 2 Shift: b. Amplitude: = A = = 22.7 = = 56.0+24.2 80.2 40.1 2 2 2 2 80.0+34.6 114.6 ω = = π 2π = = 57.3 Vertical Shift: 12 6 2 2 Phase shift (use = 24 .2, = y x ω = 2π = π 1): 12 6 φ 24.2 = 15.9 sin ⎛ π ⋅1 − ⎞ + 40.1 Phase shift (use = 34.6, = 1): y x ⎜ ⎟ 6 ⎝ ⎠ −15.9 = ⎛ π − φ 15.9 sin ⎞ 34.6 = 22.7 sin ⎛ π ⎝ 6
28. I (t ) = 220 sin ⎛ 60π t − π ⎞ , c. t ≥ 0 ⎜ 6 ⎟ Period: ⎝ ⎠ T = 2π = 2π = 1 ω 60π 30 Amplitude: A = 220 π = 220 Phase Shift: φ = 6 = 1 d. y = 15.62 sin (0.517 x − 2 .096) + 40.377 ω 60π 360 e. 60 29. a. 0 13 20 30. a. b. Amplitude: A = 56.0 − 24.2 = 31.8 = 15.9 2 2 80.0 − 34.6 45.4 Shift: 56.0+24.2 = 80.2 = 40.1 b. Amplitude: A = = = 22.7 2 2 2 2 80.0+34.6 114.6 ω = 2π = π 12 6 Phase shift (use y = 24 .2, x = 1): Vertical Shift: ω = 2π = π 12 6 = = 57.3 2 2 24.2 = 15.9 sin ⎛ π ⋅1 − φ ⎞ + 40.1 Phase shift (use y = 34.6, x = 1): ⎜ 6 ⎟ ⎝ ⎠ −15.9 = 15.9 sin ⎛ π − φ ⎞ 34.6 = 22.7 sin ⎛ π ⎝ 6
62514-0132318806_ISM_02-1.docx