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Home » Is Xbox Down? The Shocking Truth Behind the Outage That’s Breaking Gamers! - Aurero

Is Xbox Down? The Shocking Truth Behind the Outage That’s Breaking Gamers! - Aurero

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Actually, the **maximum finite value of $r$** occurs when $\sin(2\theta)$ is at its **maximum**, because $r^2 = \frac{100}{\sin(2\theta)}$, and $\sin(2\theta) \leq 1$.

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

📌 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.

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