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Home » Top 10 Reasons the Superior Spiderman Is Breaking Records in Cinematic History! - Leaselab

Top 10 Reasons the Superior Spiderman Is Breaking Records in Cinematic History! - Leaselab

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 عندما يصبح الباقي صفرًا، فإن القاسم المشترك الأكبر هو آخر باقي غير صفري، وهو $15$.

📌 إذن، $\gcd(105, 165) = \boxed{15}$.السؤال: أوجد مجموع جميع الزوايا $z \in [0^\circ, 360^\circ]$ التي تحقق $\sin(2z) = \frac{\sqrt{3}}{2}$.

📌 الحل: لحل المعادلة $\sin(2z) = \frac{\sqrt{3}}{2}$، نحدد أولاً الزوايا التي تساوي فيها دالة الجيب $\frac{\sqrt{3}}{2}$. هذه الزوايا في الربعين الأول والثاني ضمن الفترة $[0^\circ, 360^\circ]$ هي $60^\circ$ و $120^\circ$. بما أن وسيط دالة الجيب ضمن المعادلة هو $2z$، فإننا نحل لإيجاد $2z$:

📌 2z = 60^\circ \quad \text{أو} \quad 2z = 120^\circ

📌 بالقسمة على 2، نحصل على:

📌 z = 30^\circ \quad \text{أو} \quad z = 60^\circ

📌 بعد ذلك، نأخذ في الاعتبار دورية دالة الجيب. الحلول العامة لـ $2z$ هي:

📌 2z = 60^\circ + 360^\circ k \quad \text{و} \quad 2z = 120^\circ + 360^\circ k \quad \text{لـ } k \text{ عدد صحيح}

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