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Home » \( r^3 = 144 \). - RedTag Digital

\( r^3 = 144 \). - RedTag Digital

📅 May 17, 2026 👤 scraface

May 17, 2026

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\theta = 2k\pi
Within $ [0, 2\pi) $, the only solution is $ \theta = 0 $.
Case 2:** $ 3\theta = 2k\pi - 2\theta $
Add $ 2\theta $ to both sides:
5\theta = 2k\pi \quad \Rightarrow \quad \theta = \frac{2k\pi}{5}
We now find all values of $ k $ such that $ 0 \leq \frac{2k\pi}{5} < 2...
Dividing by $ 2\pi $:
\leq \frac{k}{5} < 1 \quad \Rightarrow \quad k = 0, 1, 2, 3, 4
So the solutions are:
\theta = 0, \frac{2\pi}{5}, \frac{4\pi}{5}, \frac{6\pi}{5}, \frac{8\pi...

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