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Graphing Sinusoids

Master the skill of graphing sinusoids with this detailed tutorial. Begin by identifying the midline (d) and amplitude (a), then calculate the period and determine the phase shift. Follow clear steps to graph your function: sketch the midline, draw parallel lines based on amplitude, mark hash points for one full period, and use dashed lines for preliminary curves. Learn through examples and visualize shifts in maximum, minimum, and midline points due to phase shifts. This guide ensures accurate and confident sinusoid graphing for all learners.

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Graphing Sinusoids

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  1. Mr. Schaefer’s little tutorial Graphing Sinusoids

  2. Steps To Successful Graphing Before graphing • Identify the midline ("d") • Identify the amplitude ("a": is it negative?) • Calculate the period. • Determine phase shift . How to graph • Sketch the midline (unless it's the x-axis) • Use the amplitude "a" to sketch 2 parallel lines. "a" units above the midline and "a" units below the midline. • Make 4 evenly spaced hash marks on the midline to mark one full period. • Use a dashed line to sketch the curve prior to the phase shift (if there is one). If "a" is negative, reflect curve over midline. • Use the phase shift calculation and mark places on the graph where each max., min., and midline point will shift to. • Make a final sketch of the curve after the phase shift.

  3. Example: Graphing • Identify the midline ("d") • Identify the amplitude ("a": is it negative?) • Calculate the period. • Determine phase shift. The horizontal line y = - 3 Amplitude = 2

  4. Example: Graphing “d” y = -3, “a” = 2, per = 4π, p.s. = 2π π 2π 3π 4π 5π 6π - 1 - 3 - 5

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