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Home » The Hidden Power of ‘Thought’ Thoughts You Never Knew Exist! - Carbonext

The Hidden Power of ‘Thought’ Thoughts You Never Knew Exist! - Carbonext

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Thus, the largest possible value of \( y \) is \(\boxed{20}\).**Question:** A linguist studying phonetic transformations models a sound wave as \( f(x) = a \sin(bx + c) + d \). Given that the maximum amplitude is 3, the period is \( \pi \), and the wave passes through the origin, find the values of \( a, b, c, \) and \( d \).

📌 The general form of the sinusoidal function is \( f(x) = a \sin(bx + c) + d \).

📌 The amplitude \( a \) is given as 3.

📌 The period \( T \) is \( \pi \). For a sine function, the period is \( \frac{2\pi}{b} \), so:

📌 \frac{2\pi}{b} = \pi \implies b = 2

📌 The wave passes through the origin, so \( f(0) = 0 \):

📌 f(0) = a \sin(c) + d = 0

📌 Since the maximum amplitude is 3, the midline is likely centered at 0 (symmetric about \( y = 0 \)), so \( d = 0 \). Then:

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