Amplitude, Period, and Phase Shift

Calculus Readiness · Axiom Academy

LESSON Amplitude, Period & Phase Shift The four numbers in — and how each one reshapes the wave you can see. The amplitude is the distance from the midline to a peak (and the same distance down to a trough). The parent graphs and have amplitude 1 . Multiply by A and the whole wave stretches vertically — watch the peaks and troughs ride the lines as A grows. amplitude is the absolute value of A the wave lives between these two heights For , the amplitude is 3 , so the graph oscillates between -3 and 3 . For , the amplitude is ; the negative sign flips the graph upside-down so it starts at instead of . The parent sine and cosine complete one full cycle every units. Multiply the input by B and you speed the wave up or slow it down. As B grows, the wave compresses — more cycles squeeze into the same width, and the length of one cycle (the period ) shrinks. Example 2 — Finding the period (a) has period — the wave completes twice as fast. (b) has period — the wave stretches out. (c) has period — handy when the input is in seconds. 3. Phase Shift C — Slide Sideways The phase shift slides the whole graph horizontally. The tricky part: it is measured in x , not in Bx . In , a positive C slides the wave right ; a negative C slides it left . Watch the faint parent stay put while the live wave slides by C . Example 3 — Phase shift by factoring Factor the B out of the argument: . So the phase shift is units to the right, and the period is . 4. Vertical Shift D — The Midline

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