Section 2.6 Key points: π π ⎛ ⎞ ⎛ ⎞ ⎛ 5π ⎞ ⎛ 2π ⎞ 6 1. phase shift 3 ,0 ⎟ , ⎜ −3⎟ , , ⎜ ⎟ ⎜ ⎟ ⎜ (π 3 ,0 , 2 ,3 , ,0) ⎝ ⎠ ⎝ ⎠ 2. False ⎝ ⎠ ⎝ ⎠ 3. = 4sin(2 − π) y x Amplitude: = 4 = 4 A Period: = = = π 2π 2π T ω 2 Phase Shift: φ = π ω 2 Interval defining one cycle: φ φ ⎡ , + ⎤ = ⎡π , 3π ⎤ T ω ⎢ω ⎥ ⎢ 2 2 ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: 5. = 2 cos ⎛ 3x + π ⎞ y ⎜ ⎟ 2 ⎝ ⎠ = 2 2 π = T 4 4 A 2π 2π = Amplitude: Key points: = = Period: T ,0 π ⎛ ⎞ (π ,0 , ⎞ −4 ⎞ ⎛ 3π , ,0) , , ⎛ 3π ⎛ 5π ω 3 ⎞ , ⎛ π ⎞ ⎜ 2 ⎟ ⎜ 4 ⎟ ⎜ 4 ⎟ ⎜ 2 ⎟ − ⎝ ⎠ ⎝ ⎠ ⎜ 2 ⎟ π = =− φ ω 3 Phase Shift: ⎝ ⎠ ⎝ ⎠ 6 Interval defining one cycle: φ φ π π ⎡ , + ⎤ = ⎡− , ⎤ T ω ⎢ω ⎥ ⎢ 6 2 ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: π = 2π / 3 = T 4 4 6 Key π ⎛ π ⎞ ⎛ ⎞ ⎛ π ⎞ π ⎛ − ,2 , ,0 (0, −2 , 0) , , , ,2 ⎜ 6 ⎟ ⎜ 6 ⎟ ⎜ 3 ⎟ ⎜ 2 ⎟ = − π) 4. 3sin(3x y
Section 2.6 Key points: ⎛ π ⎞ ⎛ π ⎞ ⎛ 2π ⎞ ⎛ 5π ⎞ 1. phase shift ⎜ 3 ,0 ⎟ , ⎜ 2 ,3 ⎟ , ⎜ 3 ,0 ⎟ , ⎜ , −3⎟ , (π ,0) 6 2. False ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ 3. y = 4sin(2 x − π) Amplitude: A = 4 = 4 Period: T = 2π = 2π = π Phase Shift: ω 2 φ = π ω 2 Interval defining one cycle: ⎡ φ , φ + T ⎤ = ⎡π , 3π ⎤ ⎢ω ω ⎥ ⎢ 2 2 ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: 5. y = 2 cos ⎛ 3x + π ⎞ ⎜ 2 ⎟ ⎝ ⎠ T = π 4 4 Amplitude: A = 2 = 2 2π 2π Key points: Period: T = = ⎛ π ⎞ ,0 , ⎛ 3π ⎞ , (π ,0) , ⎛ 5π , −4 ⎞ , ⎛ 3π ⎞ ,0 ω 3 ⎛ π ⎞ ⎜ 2 ⎟ ⎜ 4 ⎟ ⎜ 4 ⎟ ⎜ 2 ⎟ − ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ Phase Shift: φ ⎜ 2 ⎟ π = =− ω 3 6 Interval defining one cycle: ⎡ φ , φ + T ⎤ = ⎡− π , π ⎤ ⎢ω ω ⎥ ⎢ 6 2 ⎥ ⎣ ⎦ ⎣ ⎦ Subinterval width: T = 2π / 3 = π 4 4 6 Key ⎛ π ⎞ ⎛ π ⎞ ⎛ π ⎞ ⎛ − π ,2 , (0, 0) , , −2 , ,0 , ,2 ⎜ 6 ⎟ ⎜ 6 ⎟ ⎜ 3 ⎟ ⎜ 2 ⎟ 4. y = 3sin(3x − π)