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Home » You Won’t Believe How Shel Silverstein’s Poems Changed Childhood Forever! - Upplift

You Won’t Believe How Shel Silverstein’s Poems Changed Childhood Forever! - Upplift

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 To find the maximum height of the tide, we rewrite the function in the form $ R\sin\left(\frac{\pi}{6}t + \phi\right) $, where $ R $ is the amplitude and gives the maximum height.

📌 h(t) = 4\sin\left(\frac{\pi}{6}t\right) + 3\cos\left(\frac{\pi}{6}t\right)

📌 This can be expressed as:

📌 h(t) = R\sin\left(\frac{\pi}{6}t + \phi\right)

📌 where $ R = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 $

📌 So the maximum height is $ \boxed{5} $.

📌 To find the time at which this maximum occurs, we use:

📌 \tan\phi = \frac{3}{4} \Rightarrow \phi = \arctan\left(\frac{3}{4}\right)

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