Question

Over a 24-hour period, the tide in a harbor can be modeled by one period of asinusoidal function. The tide measures 4.35 ft at midnight, rises to a high of8.3 ft, falls to a low of 0.4 ft, and then rises to 4.35 ft by the next midnight.What is the equation for the sine function f(x), where x represents time inhours since the beginning of the 24-hour period, that models the situation?Enter your answer in the box.f(x) =

Answer 1

Sinus function

y = A • Sin ( X + d)

Maximum = 8.3 ft

Minimum = 0.4 ft

Amplitude = 8.3 - 0.4 = 7.9 ft

Sin (0 + d )•A = 4.35

Sin (0 + d)= 4.35/7.9 = 0.55

Then

Sin d= 0.55

d = 33.36°

THEN equation is

f(x) = 7.9• (Sin( X + 33.36°))