# 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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$b$ 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 $\tau=2\pi$.