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Home » \fracVV_k = \frac\frac23 \pi r^3\frac23 \pi k^3 r^3 = \frac1k^3 - Dachbleche24

\fracVV_k = \frac\frac23 \pi r^3\frac23 \pi k^3 r^3 = \frac1k^3 - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 \cos\alpha = \frac{1}{2}, \quad \sin\alpha = \frac{\sqrt{3}}{2} \Rightarrow \alpha = 60^\circ

📌 So the equation becomes:

📌 \sin(2z + 60^\circ) = 1 \Rightarrow \sin(2z + 60^\circ) = \frac{1}{2}

📌 The general solution for $ \sin \theta = \frac{1}{2} $ is:

📌 \theta = 30^\circ + 360^\circ k \quad \text{or} \quad \theta = 150^\circ + 360^\circ k

📌 Let $ \theta = 2z + 60^\circ $, so:

📌 2z + 60^\circ = 30^\circ + 360^\circ k \Rightarrow 2z = -30^\circ + 360^\circ k \Rightarrow z = -15^\circ + 180^\circ k

📌 2z + 60^\circ = 150^\circ + 360^\circ k \Rightarrow 2z = 90^\circ + 360^\circ k \Rightarrow z = 45^\circ + 180^\circ k

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