A point on the ocean rises and falls as wave pass Suppose that a wave passes every 4 s, and the height of each wave from the crest to the trough in 0.5 m.

a) how do we graph the height of the point relative to tis average height for a complete cycle, starting at the crest of a wave. And how do we make up the equation of the graph?

Just look to any physics text book on simple harmonic motion.I think the average height is given by the Area covered by the curve divided by it's period.you can use a cosine fuction to approximate the motion since at t0(initial) the point is at the crest.Hopes it helps a little.

the answer is...

amp = 0.5
Period ==> 4 = 2pi/k ==> pi/2

if y = a sin(kt), then the equation will be... y = 0.5 sin [(pi/2)*t]

test model: let t = 4 sec

y= 0.5* sin [(pi/2)*(4)] = 0