<p>For a sinusoidal model with maximum \(M\), minimum \(m\) and period \(T\):</p>
<div class="content-box-placement content-box-placement--full content-box-placement--align-center" style="display:flex;justify-content:stretch;max-width:100%"><div class="content-box content-box--emphasis" data-content-box-preset="emphasis" style="box-sizing:border-box;border-color:var(--content-box-border, #1E6FBA);border-style:solid;border-width:0px;border-radius:0px;background-color:var(--content-box-background, #F5F8FC);color:var(--content-box-foreground, #111827);padding:12px 16px;font-family:'EB Garamond', serif;font-size:16px;line-height:1.35;width:100%;max-width:100%;border-left-width:3px"><p style="text-align: center">\(\text{Amplitude}=\dfrac{M-m}{2}\qquad c=\dfrac{M+m}{2}\qquad b=\dfrac{2\pi}{T}\)</p></div></div>
<p>Use \(b=360^\circ/T\) for degrees. Choose sine or cosine and the sign to match the starting value and direction.</p>
<p class="paragraph-header">Tide model: \(h=3\sin\dfrac{\pi t}{6}+5\), \(0\le t\le24\)</p>
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<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 540px;"><colgroup><col style="width: 50.0000%;"><col style="width: 50.0000%;"></colgroup><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Feature</strong></th><th style="text-align: center; --cell-justify: center"><strong>Value</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Mean depth</td><td style="text-align: center; --cell-justify: center">5 m</td></tr><tr><td style="text-align: center; --cell-justify: center">Amplitude</td><td style="text-align: center; --cell-justify: center">3 m</td></tr><tr><td style="text-align: center; --cell-justify: center">Period</td><td style="text-align: center; --cell-justify: center">12 hours</td></tr><tr><td style="text-align: center; --cell-justify: center">High tide</td><td style="text-align: center; --cell-justify: center">8 m at \(t=3,15\)</td></tr><tr><td style="text-align: center; --cell-justify: center">Low tide</td><td style="text-align: center; --cell-justify: center">2 m at \(t=9,21\)</td></tr></tbody></table></div></div>
<p>Substitute a time to find the value, or solve the trigonometric equation to find every time in the given interval. State units.</p>

For a sinusoidal model with maximum \(M\), minimum \(m\) and period \(T\):

\(\text{Amplitude}=\dfrac{M-m}{2}\qquad c=\dfrac{M+m}{2}\qquad b=\dfrac{2\pi}{T}\)

Use \(b=360^\circ/T\) for degrees. Choose sine or cosine and the sign to match the starting value and direction.

Tide model: \(h=3\sin\dfrac{\pi t}{6}+5\), \(0\le t\le24\)

Substitute a time to find the value, or solve the trigonometric equation to find every time in the given interval. State units.

Modelling Periodic Phenomena

Modelling Periodic Phenomena

Feature	Value
Mean depth	5 m
Amplitude	3 m
Period	12 hours
High tide	8 m at \(t=3,15\)
Low tide	2 m at \(t=9,21\)