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Home » Substituting \( n = 8 \) and \( r = 3 \): - Midis

Substituting \( n = 8 \) and \( r = 3 \): - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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We want to find the **maximum value of $r$** for which this equation h...
Step 1: Solve for $r^2$:
r^2 = \frac{100}{\sin(2\theta)}.
Since $r^2 \geq 0$, we must have $\sin(2\theta) > 0$. The maximum valu...
However, to **maximize $r$**, we must **minimize the denominator** $\s...
Actually, the **maximum finite value of $r$** occurs when $\sin(2\thet...
r^2 \leq \frac{100}{1} = 100 \Rightarrow r \leq 10.
But we must check if this maximum is **attainable**. That is, does the...
Set $\sin(2\theta) = 1 \Rightarrow 2\theta = \frac{\pi}{2} + 2k\pi \Ri...
Try $\theta = \frac{\pi}{4}$:

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