77. The graph is a reflected sine graph with 81. The graph is a sine graph with amplitude 3 amplitude 1 and period 4π . and period 4. 3 ω Find : 4π = 2π ω Find : = 4 2π ω ω = 3 4ω 2π = 4πω 6π ω = 6π = ω = 2π = π 3 4 2 4π 2 = 3sin ⎛ π ⎞ . y x The equation is: The equation is: ⎝ 2 ⎠ = − sin ⎛ 3 ⎞ . y x ⎜ 2 ⎟ ⎝ ⎠ 82. The graph is a reflected cosine graph 78. The graph is a reflected cosine graph with with amplitude 2 and period 2. amplitude and period π 2π. ω Find : 2 = 2π ω 2πω = ω Find : 2π = 2ω 2π ω = 2π = ω = 2π =π 2π= 2π 1 2 ω 2π The equation is: = − 2 cos(π . y x) reflected cosine graph with The equation is: 83. The = −π cos . graph is a y x 79. The graph is a reflected cosine graph, shifted up 1 unit, with amplitude 1 and period 3 . amplitude 4 and period 2π . 2 3 ω Find : 2π = 2π ω ω Find : 3 = 2π 3 ω 2 2πω = 6π 3ω = 4π ω = 4π ω = 6π = 3 2π (3x ) The equation is: = − 4 cos . 3 y The equation is: = − cos ⎛ 4π ⎞ + y x 1 . ⎜ ⎟ 3 84. The graph is a sine graph with amplitude 4 and ⎝ ⎠
77. The graph is a reflected sine graph with amplitude 1 and period 4π . 81. The graph is a sine graph with amplitude 3 and period 4. 3 Find ω : 4π = 2π Find ω : 4 = 2π ω 3 ω 4ω = 2π 4πω = 6π ω = 6π = 3 ω = 2π = π 4 2 4π 2 The equation is: y = 3sin ⎛ π x ⎞ . The equation is: y = − sin ⎛ 3 x ⎞ . ⎝ 2 ⎠ ⎜ 2 ⎟ ⎝ ⎠ 78. The graph is a reflected cosine graph with 82. The graph is a reflected cosine graph with amplitude 2 and period 2. amplitude π and period 2π. Find ω : 2 = 2π ω Find ω : 2π= 2π ω 2πω = 2π ω = 2π = 1 2ω = 2π ω = 2π =π 2 2π The equation is: y = − 2 cos(π x) . The equation is: y = −π cos x . 83. The graph is a reflected cosine graph with 79. The graph is a reflected cosine graph, shifted up 1 unit, with amplitude 1 and period 3 . 2 amplitude 4 and period 2π . 3 Find ω : 2π = 2π Find ω : 3 = 2π 3 ω 2 ω 2πω = 6π 3ω = 4π ω = 4π ω = 6π = 3 2π The equation is: 3 y = − cos ⎛ 4π x ⎞ + 1 . The equation is: y = − 4 cos (3x ) . ⎜ 3 ⎟ 84. The graph is a sine graph with amplitude 4 and ⎝ ⎠
62514-0132318806_ISM_02-1.docx