Question

The function f(t) = 4 cos(pi over 3t) + 15 represents the tide in Bright Sea. It has a maximum of 19 feet when time (t) is 0 and a minimum of 11 feet. The sea repeats this cycle every 6 hours. After five hours, how high is the tide?

Answer 1

F(5)=4 cos( 5π3)+ 15=17

Hope this helps

Tide is 17 ft

Answer 2

Answer with explanation:

The Cosine function which represents the tide in Bright Sea is represented as:

    $f(t)=4 cos(\frac{\pi}{3t}) + 15 \\\\ f(t)=4 cos(2 k\pi+\frac{\pi}{3t}) + 15$

Where, k=0,1,2,3,...........

Cos function has a Period of $2\pi$.

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

$f(t)=4 cos(2 k\pi + \frac{\pi}{3t}) + 15$

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

→$n=\frac{5}{6}$

$f(t)=4 cos(2\times\frac{5\times\pi}{6} + \frac{\pi}{3\times 5}) + 15\\\\f(t)=4 cos(\frac{5\times\pi}{3}+ \frac{\pi}{15})+15\\\\f(t)=4\times cos(\frac{26\pi}{15})+15\\\\f(t)=4 \times cos 312^{\circ}+15\\\\f(t)=4\times cos 48^{\circ}+15\\\\ f(t)=4 \times 0.6691+15\\\\f(t)=2.6764+15\\\\f(t)=17.68$

Height of tide after 5 hours = 17.68 feet