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Консультация № 198311
20.04.2020, 12:57
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Здравствуйте! Прошу помощи в следующем вопросе:
как решить пример по алгебре 3 sin a + 4 cos a /разделить на 4 cos a - 3 sin a, если ctg a =2/3
как решить пример по алгебре 3 sin a + 4 cos a /разделить на 4 cos a - 3 sin a, если ctg a =2/3
Обсуждение
22.04.2020, 02:59
общий
это ответ
Здравствуйте, galya.stolyarova1!
Дано : ctg([$945$]) =2/3
Вычислить F([$945$]) = [3·sin([$945$]) + 4 cos([$945$])] / [4·cos([$945$]) - 3·sin([$945$])]
Решение : Разделим делимое и делитель на sin([$945$]) . Получим:
F([$945$]) = [3 + 4 cos([$945$]) / sin([$945$])] / [4·cos([$945$]) / sin([$945$]) - 3] = [3 + 4·ctg([$945$])] / [4·ctg([$945$]) - 3] потому что ctg([$945$]) = cos([$945$]) / sin([$945$])
Заменяем ctg([$945$]) на его значение 2/3 :
F([$945$]) = [3 + 4·ctg([$945$])] / [4·ctg([$945$]) - 3] = [3 + 4·(2/3)] / [4·(2/3) - 3] = (3 + 8/3) / (8/3 - 3) = (9+8) / (8-9) = 17 / (-1) = -17
Ответ : -17
Проверяем Ответ в каком-нибудь инженерном калькуляторе или вычислитель-приложении.
Маткад-скриншот прилагаю ниже.
Проверка успешна.
Дано : ctg([$945$]) =2/3
Вычислить F([$945$]) = [3·sin([$945$]) + 4 cos([$945$])] / [4·cos([$945$]) - 3·sin([$945$])]
Решение : Разделим делимое и делитель на sin([$945$]) . Получим:
F([$945$]) = [3 + 4 cos([$945$]) / sin([$945$])] / [4·cos([$945$]) / sin([$945$]) - 3] = [3 + 4·ctg([$945$])] / [4·ctg([$945$]) - 3] потому что ctg([$945$]) = cos([$945$]) / sin([$945$])
Заменяем ctg([$945$]) на его значение 2/3 :
F([$945$]) = [3 + 4·ctg([$945$])] / [4·ctg([$945$]) - 3] = [3 + 4·(2/3)] / [4·(2/3) - 3] = (3 + 8/3) / (8/3 - 3) = (9+8) / (8-9) = 17 / (-1) = -17
Ответ : -17
Проверяем Ответ в каком-нибудь инженерном калькуляторе или вычислитель-приложении.
Маткад-скриншот прилагаю ниже.
Проверка успешна.
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