مذكرات حساب المثلثات في مثلث قائم

الكاتب: الأستاذ الوافي محمدتاريخ النشر: أغسطس 30, 2025 آخر تحديث: سبتمبر 06, 2026 وقت القراءة:

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حساب المثلثات في مثلث قائم

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مقال

لنسب المثلثية. تهدف المذكرة إلى إكساب الطلاب القدرة على حل مشكلات تتعلق بالأشكال الهندسية المستوية.

المكتسبات القبلية:
معرفة النسب المثلثية لزاوية حادة في مثلث قائم.
معرفة العلاقة بين النسب المثلثية.
التعرف على النسب المثلثية: جيب تمام، جيب، وظل.
الأنشطة والدروس:
النسب المثلثية لزاوية حادة في مثلث قائم: يتم التطرق إلى جيب الزاوية (sin)، جيب تمام الزاوية (cos)، وظل الزاوية (tan).
الخاصية الأساسية: شرح العلاقة الأساسية بين الجيب وجيب التمام (sin²α + cos²α = 1).
تطبيق على النسب: استخدام النسب المثلثية لحساب أطوال الأضلاع والزوايا في مثلث قائم.
الخاصية الأساسية المكملة: شرح العلاقة بين ظل الزاوية وجيبها وجيب تمامها (tanα = sinα / cosα).
تطبيقات وتمارين: تتضمن المذكرة تمارين متنوعة لحساب الأطوال والزوايا، مثل حساب طول ضلع في مثلث قائم، وحل مشكلات هندسية باستخدام النسب المثلثية
التكبير والتصغير: يتم استخدام النسب المثلثية في حالات التكبير والتصغير للمثلثات.

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