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z1 ЖКарты бұрь ріндер: a) \( \sin ^{2} 6 \alpha \); ә) \( \cos ^{2} 4 \alpha \);

Ask by Edwards Franklin. in Kazakhstan
Feb 18,2025

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Answer

а) \( \sin^{2} 6\alpha = \frac{1 - \cos 12\alpha}{2} \) ә) \( \cos^{2} 4\alpha = \frac{1 + \cos 8\alpha}{2} \)

Solution

Найдем эквивалентные выражения для заданных тригонометрических функций, используя следующие стандартные тригонометрические тождества: 1. sin²θ = (1 – cos2θ)/2 2. cos²θ = (1 + cos2θ)/2 а) Пусть θ = 6α. Тогда:   sin²6α = (1 – cos(2·6α))/2 = (1 – cos12α)/2. ә) Пусть θ = 4α. Тогда:   cos²4α = (1 + cos(2·4α))/2 = (1 + cos8α)/2. Ответ: а) sin²6α = (1 – cos12α)/2 ә) cos²4α = (1 + cos8α)/2

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Синус және косинус функциялары тригонометрияда әртүрлі бұрыштардың қатынастарын зерттеуге көмектеседі. \( \sin^{2} 6\alpha \) және \( \cos^{2} 4\alpha \) формулалары бұрыштарды жалпылай қарастыруда тиімді. Мысалы, тригонометриялық идентичностарды қолдана отырып, \( \sin^2 \) және \( \cos^2 \) функцияларын квадраттық немесе мультипликативтік формаларға ауыстыруға болады. Практикалық жағынан, бұл функцияларды пайдалана отырып, біздің күнделікті өмірімізде қолданылатын деректерді және бұрыштарды визуализациялауға көмектеседі. Мысалы, сәулетшілер ғимараттарды жобалау кезінде бұрыштарды қамтамасыз ету үшін тригонометриялық функцияларды пайдаланады. Бұрыштардың дұрыс есептелуі – жобаның сенімділігі мен эстетикалық көрінісі үшін маңызды!

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