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Consider the position function s(t)=sin((pi)(t)) representing the position of an object moving along a line on the end of a spring. Sketch a graph of s with the secant line passing through (0,s(0)) and (0.5,s(0.5)). Determine the slope of the secant line and its relationship to the moving object.1

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  1. Hmm -- your school subject appears to be math, not chabot college.

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    Ms. Sue
  2. s = sin (pi t) is a sin function starting at (0,0)the period T is when pi t = 2 pi
    or in other words when t = 2

    when t = .5
    s = sin (pi/2) = 1

    at t=0 the slope = cos 0 = 1
    at t = .5 the slope = cos pi/2 = 0
    in other words the function climbs up from (0,0) to a peak at (.5,1) and then heads down

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