On a particular summer day at 7:00 a.m. in California, high tide was measured at 13 feet above sea level.

Question

On a particular summer day at 7:00 a.m. in California, high tide was measured at 13 feet above sea level. At 1:00 pm the same day, low tide was measured at 9 feet above sea level. Assume that the tide models a sinusoidal graph which can be expressed in the form h(t) = asin[b(t – c)] + d where t is the hours after midnight and h is in feet above sea level. The period of the graph is _____h and the phase shift of the sine curve (a > 0) is ____h. 

Answer 1

h(t) = asin[b(t - c)] + d; a = (13 - 9)/2 = 2 ft; d = (13 + 9)/2 = 11 ft

b = 2π/24 = π/12; sinb(7 - c) = 1; b(7 - c) = π/2; sinb(13 - c) = - 1; b(13 - c) = 3π/2;

7b - bc = π/2; 13b - bc = 13π/2; 6b = 6π; b = π; 7π - πc = π/2; c = 13/2

So, h(t) = 2sin[π(t - 13/2)] + 11