Graphing Transformed Trig Functions

Pre-Calculus · Axiom Academy

EXAMPLE Graphing Transformed Trig Functions Graphing y = A·sin(B(x − C)) + D with all four transformations — amplitude, period, phase shift, and vertical shift. Graph one complete period of . Find its amplitude, period, phase shift, and midline, locate the five key points, and sketch the curve. You worked every transformation in and graphed it from its five key points. Factor B before reading the phase shift: rewrite as , so the shift is , not . Amplitude and period from |A| and |B|: amplitude = | -2 | = 2 , period . Midline is the vertical shift: D = -1 , so the wave oscillates between -3 and 1 . A negative A flips the wave: instead of up first, it goes down first — the pattern becomes zero → min → zero → max → zero. Master and any sine or cosine — stretched, squeezed, slid, or flipped — graphs from the same four numbers.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.