(2x = + π) 6. 3cos y Amplitude: = 3 = 3 A Period: = 2π = 2π = π T ω 2 Phase Shift: φ = −π = − π ω 2 2 Interval defining one cycle: φ φ π π ⎡ , + ⎤ = ⎡− , ⎤ T ω ⎢ω ⎥ ⎢ ⎥ 2 2 ⎣ ⎦ ⎣ ⎦ Subinterval width: 8. = − 2 cos ⎛ 2 − π ⎞ y x ⎜ ⎟ ⎝ ⎠ π = T = − 2 = 2 4 4 A Amplitude: Key points: 2π = 2π = π = T Period: π ⎞ ⎛ ⎞ ⎛ π ⎞ ⎛ π ⎞ ω 2 π ⎛ − ,3 , − , ,3 (0, ,0 , −3) , ,0 ⎜ ⎟ ⎜ ⎟ 2 4 ⎜ ⎟ ⎜ ⎟ π 4 2 ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ Phase Shift: φ = 2 = π ω 2 4 Interval defining one cycle: φ φ ⎡ , + ⎤ = ⎡π , 5π ⎤ T ω ⎢ω ⎥ ⎢ ⎥ 4 4 ⎣ ⎦ ⎣ ⎦ Subinterval width: π = T 4 4 Key points: π π ⎛ −2 ⎞ ⎛ ⎞ , , , ⎛ 5π ⎛ 3π , (π −2 ⎞ , ,0) , ⎞ ⎜ 4 ⎟ ⎜ 2 ⎜ ⎟ 4 ⎟ ⎜ ⎟ 4 7. = −3sin ⎛ 2x + π y ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎞ ⎜ 2 ⎟ ⎝ ⎠ Amplitude:
6. y = 3cos (2x + π) Amplitude: A = 3 = 3 Period: T = 2π = 2π = π ω 2 Phase Shift: φ = −π = − π ω 2 2 Interval defining one cycle: ⎡ φ , φ + T ⎤ = ⎡− π , π ⎤ ⎢ω ω ⎥ ⎢ 2 2 ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: 8. y = − 2 cos ⎛ 2 x − π ⎞ ⎜ ⎟ ⎝ ⎠ T = π 4 4 Amplitude: A = − 2 = 2 Key points: Period: T = 2π = 2π = π ⎞ ⎛ π ⎞ ⎛ π ⎞ ⎛ π ⎞ ω 2 ⎛ − π ,3 , − ,0 , (0, −3) , ,0 , ,3 ⎜ 2 ⎟ ⎜ 4 ⎟ ⎜ 4 ⎟ ⎜ 2 ⎟ π ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ Phase Shift: φ = 2 = π ω 2 4 Interval defining one cycle: ⎡ φ , φ + T ⎤ = ⎡π , 5π ⎤ ⎢ω ω ⎥ ⎢ 4 4 ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: T = π 4 4 Key points: ⎛ π , −2 ⎞ , ⎛ π ⎞ , ⎛ 3π ⎞ , (π ,0) , ⎛ 5π , −2 ⎞ ⎜ 4 ⎟ ⎜ 2 ⎟ ⎜ 4 ⎟ ⎜ 4 ⎟ 7. y = −3sin ⎛ 2x + π ⎞ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎜ 2 ⎟ ⎝ ⎠ Amplitude:
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