We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# ​ 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

+1
260
1

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? Apr 11, 2018

### 1+0 Answers

#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   Apr 11, 2018