ACT-Style: Finding Period from a Graph

ACT Math · Axiom Academy

EXAMPLE ACT-Style Finding Period from a Graph Read the period straight off a graph, then turn it into the equation of the wave. The graph below is one of the form . Find its period , then use the period to determine B , read off the amplitude, and write the equation of the graph. Consecutive peaks sit at x = 0 and ; the peak value is 3 and the midline is y = 0 . Nice work — you turned a picture of a wave into its exact equation by reading the period first. Period from a graph: the horizontal distance between two consecutive peaks (or troughs, or any two matching points) is the period. Period gives B : since , a shorter period means a larger B . Here period . Peak at x = 0 means cosine: starting at a maximum picks over ; the amplitude is the peak-to-midline distance. Result: period , amplitude = 3 , so . On the ACT, lock down the period first — it hands you B , and the rest of the equation falls out from the amplitude and where the curve starts.

This is the written version of the interactive lesson above. See the full ACT Math course.