Pre-Calc Exam Notes 118

Pre-Calc Exam Notes 118 - 118 Chapter 5 Graphing and...

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118 Chapter 5 Graphing and Inverse Functions §5.2 In engineering two periodic functions with the same period are said to be out of phase if their phase shifts differ. For example, sin ( x π 6 ) and sin x would be π 6 radians (or 30 ) out of phase, and sin x would be said to lag sin ( x π 6 ) by π 6 radians, while sin ( x π 6 ) leads sin x by π 6 radians. Periodic functions with the same period and the same phase shift are in phase . The following is a summary of the properties of trigonometric graphs: For any constants A negationslash= 0, ω negationslash= 0, and φ : y = A sin ( ω x φ ) has amplitude | A | , period 2 π ω , and phase shift φ ω y = A cos ( ω x φ ) has amplitude | A | , period 2 π ω , and phase shift φ ω y = A tan ( ω x φ ) has undefined amplitude, period π ω , and phase shift φ ω y = A csc ( ω x φ ) has undefined amplitude, period 2 π ω , and phase shift φ ω y = A sec ( ω x φ ) has undefined amplitude, period 2 π ω , and phase shift φ ω y = A cot ( ω x φ
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