A point on the ocean rises and falls as waves pass. Suppose that a wave passes every 4s, and the height of each wave from the crest to the trough is 0.5 m.
a) Sketch a graph to model the height of the point relative to its average height for a complete cycle, starting at the crest of a wave.
b) Use exact values to write an equation of the form h(t) = a cos(kt) to model the height of the point, h(t) metres, relative to its average height, as a function of time, t seconds.
c) If the times on the f-axis were changed from seconds to minutes, what would be the transformational effect on the graph, and what would be the new equation?