Answer with explanation:
The Cosine function which represents the tide in Bright Sea is represented as:
[tex]f(t)=4 cos(\frac{\pi}{3t}) + 15 \\\\ f(t)=4 cos(2 k\pi+\frac{\pi}{3t}) + 15[/tex]
Where, k=0,1,2,3,...........
Cos function has a Period of [tex]2\pi[/tex].
Maximum , Cosine of an angle =1
Minimum, Cosine of an Angle = -1
At, t=0, →Maximum ,f(t)= 4 ×1 +15=19 feet
Minimum, f(t)= 4 × (-1) +15=15-4=11 feet
Tide repeats after ,every 6 hours.
After , 6 hours ,the tide function is represented in same way.That is
[tex]f(t)=4 cos(2 k\pi + \frac{\pi}{3t}) + 15[/tex]
Here,k=6 n, where, n=0,1,2,3...
We have to find how tide function is represented after 5 hours.
→ 6 n=5
→[tex]n=\frac{5}{6}[/tex]
[tex]f(t)=4 cos(2\times\frac{5\times\pi}{6} + \frac{\pi}{3\times 5}) + 15\\\\f(t)=4 cos(\frac{5\times\pi}{3}+ \frac{\pi}{15})+15\\\\f(t)=4\times cos(\frac{26\pi}{15})+15\\\\f(t)=4 \times cos 312^{\circ}+15\\\\f(t)=4\times cos 48^{\circ}+15\\\\ f(t)=4 \times 0.6691+15\\\\f(t)=2.6764+15\\\\f(t)=17.68[/tex]
Height of tide after 5 hours = 17.68 feet
