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Home » The Fastest Yard Casino: Most Rushing Yards Ever—See Who Shocked the League! - Simpleprint

The Fastest Yard Casino: Most Rushing Yards Ever—See Who Shocked the League! - Simpleprint

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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📌 = 2\sin^2 x + 2\cos^2 x = 2(\sin^2 x + \cos^2 x)

📌 Using the Pythagorean identity \(\sin^2 x + \cos^2 x = 1\):

📌 = 2 \times 1 = 2

📌 Therefore, the maximum value is \(\boxed{2}\).

📌 Find the value of \(x\) such that the vectors \(\begin{pmatrix} \sin x \\ \cos x \end{pmatrix}\) and \(\begin{pmatrix} \cos x \\ -\sin x \end{pmatrix}\) are orthogonal.

📌 Two vectors are orthogonal if their dot product is zero. Let’s compute the dot product:

📌 \begin{pmatrix} \sin x \\ \cos x \end{pmatrix} \cdot \begin{pmatrix} \cos x \\ -\sin x \end{pmatrix} = \sin x \cos x + \cos x (-\sin x) = \sin x \cos x - \sin x \cos x = 0

📌 The dot product is always zero, regardless of \(x\). Hence, the vectors are orthogonal for all \(x\).

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