# pre calc, sinusoidal equations

If the sea level decreases leaving the seabed exposed (normally $30$ feet below sea level), then it rises a equal distance above sea level. waves have a maximum height of $38.9$ meters. the cycle of rise and fall took between $26$-$35$ minutes. assuming the waves follow a sine curve, (height $Y$ of the wave varies sinusoidally with time $t$)

• use $f(t)=A\sin b(t)+k$ to find a an equation that fits best
• what does $A, b$ and $K$ stand for?
• how long was the seabed exposed at the shortest period of 26 minutes?
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## 1 Answer

How can sea level rise above sea level?

$b$ is the angular frequency, about $0.0034s^{-1}$ and $k$ is the mean sea level. The time the seabed was exposed for is the distance between nearest intersection points of $y=-30x$ and the sine wave. $\frac{26(\tau-2sin^{-1}(\frac{30\times 12}{38.9\times 39.37}))}{\tau}$ where $\tau=2\pi$.

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hi Angela, i rewrote the question on this link, the full problem and what i was able to work out. can you please provide me with any tips on if im going in the right direction and wether if the answers are correct or not. thank you math.stackexchange.com/questions/249775/sinusoidal-word-problem –  kelz Dec 5 '12 at 3:56
hi Angela, i rewrote the question on this link, the full problem and what i was able to work out. can you please provide me with any tips on if im going in the right direction and wether if the answers are correct or not. thank you math.stackexchange.com/questions/249775/sinusoidal-word-problem –  kelz Dec 5 '12 at 3:57