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mac1147_lecture19_2_b - L19 Graphing General Sinusoidal...

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266 L19 Graphing General Sinusoidal Functions; Graphs of Other Trigonometric Functions Graphing General Sinusoidal Functions ( ) sin sin y A x B A x B φ ω φ ω ω = + = + , 0 ω > ( ) cos cos y A x B A x B φ ω φ ω ω = + = + , 0 ω > Amplitude: Period: Phase shift: Vertical shift: 1. Determine the amplitude A and period 2 T π ω = . 2. Find the x -coordinate of the starting key point of one cycle , φ ω (phase shift), and the ending point, T φ ω + . 3. Divide the period T by 4: 4 T . 4. Find the x -coordinates of the other 3 key points: 4 T φ ω + , 4 4 T T φ ω + + , 4 4 4 T T T φ ω + + + . 5. Find the y -coordinates of the five key points. 6. Plot the five key points in the coordinate system. 7. Fill in one cycle of the graph. 8. Continue the graph periodically to make it complete. 267 Example : Graph: 3sin 2 1 3 y x π = − + + .
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