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Home » Number of doubling periods: $ 10 / 2 = 5 $. - Veritas Home Health

Number of doubling periods: $ 10 / 2 = 5 $. - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 السؤال: أوجد جميع الزوايا $z \in [0^\circ, 360^\circ]$ التي تحقق المعادلة $\cos 2z = \sin z$.

📌 \cos 2z = \sin z

📌 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 $\sin z = \frac{1}{2}$:

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