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Home » For the sphere with radius \(3\) units: - Blask

For the sphere with radius \(3\) units: - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 باستخدام متطابقة الزاوية المزدوجة، $\cos 2z = 1 - 2\sin^2 z$, تصبح المعادلة:

📌 - 2\sin^2 z = \sin z \implies 2\sin^2 z + \sin z - 1 = 0

📌 لنفترض $u = \sin z$, إذن:

📌 2u^2 + u - 1 = 0 \implies u = \frac{-1 \pm \sqrt{1 + 8}}{4} = \frac{-1 \pm 3}{4}

📌 إذن، $u = \frac{1}{2}$ أو $u = -1$.

📌 لـ $\sin z = \frac{1}{2}$:

📌 z = 30^\circ \quad \text{أو} \quad z = 150^\circ

📌 لـ $\sin z = -1$:

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