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?

AngelRay
Apr 11, 2018

#1**+1 **

This one is a little difficult......

Here's the form of the function that we need :

f(x) = Asin (Bx) + C

The amplitude, A, can be determined by taking the [high point - the midline point ] =

8.3 - 4.35 = 3.95

"C" will be the midline point = 4.3

B" is the harder to determine.....we want to divide 2pi by 24 = pi / 12 = B

So our function is

f(x) = 3.95sin [ pi/12 * x ] + 4.35

Here's the graph :

https://www.desmos.com/calculator/1ox0tmscf7

Note that at = 0 [ midnight ] we are at 4.35 ft

At x = 6 [ 6AM] we are at high tide = 8.3 ft

At x = 12 [noon] we are back to 4.35 ft

At x = 18 [ 6PM] we are at low tide = 0.4 ft

At x = 24 [ midnight, again ] we are back to the midline

CPhill
Apr 11, 2018