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fantastic four film 2015 cast - Professionaloutdoormedia

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 But we must check if this maximum is **attainable**. That is, does there exist a $\theta$ such that $\sin(2\theta) = 1$ and $r = 10$?

📌 Set $\sin(2\theta) = 1 \Rightarrow 2\theta = \frac{\pi}{2} + 2k\pi \Rightarrow \theta = \frac{\pi}{4} + k\pi$.

📌 Try $\theta = \frac{\pi}{4}$:

📌 Then $r^2 = \frac{100}{1} = 100 \Rightarrow r = 10$.

📌 Check if this point lies within the circular region:

📌 The circle has radius 10, so $r = 10$ is on the boundary — valid.

📌 Thus, the **maximum possible value of $r$** is:

📌 \boxed{10}

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