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in an arms of an angel - Parker Core Knowledge

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 R \left( \sin(2z)\cos\alpha + \cos(2z)\sin\alpha \right) = R \cos\alpha \sin(2z) + R \sin\alpha \cos(2z)

📌 Matching coefficients:

📌 R \cos\alpha = 1, \quad R \sin\alpha = \sqrt{3}

📌 R^2 = 1^2 + (\sqrt{3})^2 = 4 \Rightarrow R = 2

📌 \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:

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