Graphing y = A sin(Bx)

Pre-Calculus · Axiom Academy

Work through amplitude, period, the five key points, and the curve for one specific sine. Graph one complete period of . Find the amplitude and period, locate the five key points across one period, then sketch the curve. Amplitude 2 (peaks at +2, troughs at −2); one full cycle finishes at x = 2π/3. The five orange dots are the key points, evenly spaced a quarter-period apart. Nicely done. You graphed the same way you can graph any : read off A and B, get the amplitude and period, then place five evenly spaced key points. Amplitude: the height is |a| , so here |2| = 2 — the curve runs from -2 to 2 . Period: one cycle takes , so — a larger b compresses the wave horizontally. Key points: split one period into quarters ; the heights cycle . Master these five points and you can sketch any sine of the form — and the same recipe carries straight over to cosine.

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