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mac1147_lecture25_2_c

# mac1147_lecture25_2_c - L25 Graphing General Sinusoidal...

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299 L25 Graphing General Sinusoidal Functions; Graphs of Other Trigonometric Functions 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: Steps in Graphing Sinusoidal Functions : 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. 300 Example : Graph: 3sin 2 1 3 y x π = − + + .

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