Question

the oscillation of tides in Laguna Beach, California can be modeled with a sinusoidal function. The difference between the highest and lowest point is 7.4 and the period is 12.8 hours. What function represents the position D of the tides of time t.

Answer 1

the amplitude should be half of \(7.4\) which is \(3.7\)

Answer 2

it doesn't say whether to use sine or cosine, so lets use sine

Answer 3

all of the options of cosine

Answer 4

the period is given at \(12.8\) ok so use \(3.7\cos(bt)\)

Answer 5

to find \(b\) the period is \(\frac{2\pi}{b}\) so set
\[\frac{2\pi}{b}=12.8\]and solve for \(b\)

Answer 6

you get \(b=\frac{2\pi}{12.8}\) or \(b=\frac{\pi}{6.4}\) unless you want a decimal

Answer 7

i don't know what your choices are but it should look something like
\[3.7\cos(\frac{\pi t}{6.4})\]

Answer 8

yeah thats the answer. thanks a lot...:D

Answer 9

yw