Over a 24 hour period, the tide in a harbour can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at midnight, rises to a high of 10.2 ft, falls to a low of 0.1 ft, and then rises to 5.15 ft by the next midnight.
What is the equation for the sine function f(x), Where x represents time in hours since the beginning of the 24 hour period, that models the situation?
We have the form
f(x) = A sin (Bx) + D
A = the amplitude = [ highest point - lowest point] / 2 = [ 10.2 - .1] / 2 = 10.1/2 = 5.05
The period is 24
B = 2pi / period = 2pi /24 = pi/12
D = the midline = (highest point + lowest point] ) / 2 = (10.2 + 0.1) / 2 = 10.3 /2 = 5.15
So....the equation is
f(x) = 5.05sin [ (pi/12) x ] + 5.15