mac1147_lecture19_1_b

mac1147_lecture19_1_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 yA x BA x B φ ωφ ω ⎛⎞ =− + = + ⎜⎟ ⎝⎠ , 0 ω> cos cos x x B + = + , 0 Amplitude: Period: Phase shift: Vertical shift: 1. Determine the amplitude A and period 2 T π = . 2. Find the x -coordinate of the starting key point of one cycle , (phase shift), and the ending point, T + . 3. Divide the period T by 4: 4 T . 4. Find the x -coordinates of the other 3 key points: 4 T + , 44 TT + + , 444 TTT + ++ . 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.
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267 Example : Graph: 3sin 2 1 3 yx π ⎛⎞ = −+ + ⎜⎟ ⎝⎠ .
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268 Example : Find the sinusoidal function ( ) sin yA x B ω φ = −+ from the graph given below. Note : Amplitude: maximum value - minimum value 2 A = Vertical shift: maxumum value + minimum value 2 B =
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269 Blood Pressure 8 100 20cos 5 P t π =−
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mac1147_lecture19_1_b - L19 Graphing General Sinusoidal...

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