How to Identify Amplitude, Period, Phase Shift, and Vertical Shift in Trig Functions Definition, Types, Examples & Uses

How to Identify Amplitude, Period, Phase Shift, and Vertical Shift in Trig Functions

Subject: Mathematics

Book: Maths Mastery

For y=A sin(Bx–C)+D or y=A cos(Bx–C)+D:
• Amplitude = |A|, the peak displacement.
• Period = 2π/B for sine/cosine (π/B for tangent).
• Phase Shift = C/B, horizontally shifting the graph.
• Vertical Shift = D, moving it up or down.
Example: y=3 sin(2x–π)+1 has amplitude 3, period π, phase shift π/2, vertical shift 1. Understanding these parameters is pivotal in wave analysis (light, sound, tides), engineering vibrations, or cyclical data modeling. Mastery brings clarity to transformations and deeper intuition for describing recurring phenomena mathematically.