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Pre-Calc Exam Notes 117

Pre-Calc Exam Notes 117 - y =− 2 sin 3 x π 2 Solution...

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Properties of Graphs of Trigonometric Functions Section 5.2 117 The phase shift is defined similarly for the other trigonometric functions. Example5.11 Find the amplitude, period, and phase shift of y = 3 cos (2 x π ). Solution: The amplitude is 3, the period is 2 π 2 = π , and the phase shift is π 2 . The graph is shown in Figure 5.2.12: x y 0 3 2 1 1 2 3 π 2 π 3 π 2 2 π period = π phase shift = π 2 amplitude = 3 Figure 5.2.12 y = 3 cos (2 x π ) Notice that the graph is the same as the graph of y = 3 cos 2 x shifted to the right by π 2 , the amount of the phase shift. Example5.12 Find the amplitude, period, and phase shift of
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Unformatted text preview: y =− 2 sin ( 3 x + π 2 ) . Solution: The amplitude is 2, the period is 2 π 3 , and the phase shift is − π 2 3 =− π 6 . Notice the negative sign in the phase shift, since 3 x + π = 3 x − ( − π ) is in the form ω x − φ . The graph is shown in ±igure 5.2.13: x y − 2 − 1 1 2 − π 6 π 6 π 3 π 2 2 π 3 5 π 6 π 7 π 6 4 π 3 period = 2 π 3 phase shift =− π 6 amplitude = 2 Figure 5.2.13 y =− 2 sin ( 3 x + π 2 )...
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