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Консультация № 197189
24.11.2019, 10:24
0.00 руб.
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3
1
Здравствуйте! Прошу помощи в следующем вопросе:
Вычислите:
sinα+cosα/sinα-cosα, если tgα/2=1/2
Вычислите:
sinα+cosα/sinα-cosα, если tgα/2=1/2
Обсуждение
24.11.2019, 11:57
общий
Адресаты:
Ваше тяп-ляп-написанное условие можно толковать 2*2 способами :
sinα + (cosα/sinα) - cosα либо (sinα + cosα) / (sinα - cosα) ?
tg(α/2) либо tg(α)/2 ?
На Ваши мутно-двусмысленные Вопросы Вы будете получать такие же несоответствующие Ответы. Надо стараться продумывать свои Вопросы.
На Портале есть Редактор формул Использование формул и Тестовая страница rfpro.ru/forum/20/273/last , где Вы можете потренироваться в написании формул и удалить свои неудачные опыты.
sinα + (cosα/sinα) - cosα либо (sinα + cosα) / (sinα - cosα) ?
tg(α/2) либо tg(α)/2 ?
На Ваши мутно-двусмысленные Вопросы Вы будете получать такие же несоответствующие Ответы. Надо стараться продумывать свои Вопросы.
На Портале есть Редактор формул Использование формул и Тестовая страница rfpro.ru/forum/20/273/last , где Вы можете потренироваться в написании формул и удалить свои неудачные опыты.
24.11.2019, 12:16
общий
Адресаты:
Извините.
Не получается освоить этот "Редактор формул" пока. Вот так выглядит задача точнее
Вычислите:
(sinα + cosα) / (sinα - cosα), если tg(α/2)=1/2
Не получается освоить этот "Редактор формул" пока. Вот так выглядит задача точнее
Вычислите:
(sinα + cosα) / (sinα - cosα), если tg(α/2)=1/2
Прикрепленные файлы:
25.11.2019, 14:03
общий
это ответ
Здравствуйте, zhaizhbekowa!
Дано : tg([$945$]/2) = 1/2
Вычислить
Решение : Проще всего решить эту задачу в каком-нибудь вычислителе (Windows-калькуляторе или приложении Маткад) :
[$945$]/2 = arctg(1/2) = 0,464 рад
[$945$] = 2·([$945$]/2) = 0,927 рад = 53,13°
Тогда sin([$945$]) = 0,8 , cos([$945$]) = 0,6
Искомое отношение [sin([$945$]) + cos([$945$])] / [sin([$945$]) - cos([$945$])] = (0,8 + 0,6) / (0,8 - 0,6) = 1,4 / 0,2 = 7
Однако, я догадываюсь, будто преподаватель, предложивший Вам эту задачу , хочет проверить Ваши знания тригонометрии?
Вспоминаем школьную математику или ищем в учебниках / интернет-справочниках тему Тригонометрия \ Формулы двойных углов :
В нашем случае 2·х = [$945$] , tg([$945$]/2) = tg(x) = 1/2
Заменим tg([$945$]/2) = 1/2 на t = 1/2 для упрощения выкладок. Получим :
Ответ : Искомое отношение
Дано : tg([$945$]/2) = 1/2
Вычислить
Решение : Проще всего решить эту задачу в каком-нибудь вычислителе (Windows-калькуляторе или приложении Маткад) :
[$945$]/2 = arctg(1/2) = 0,464 рад
[$945$] = 2·([$945$]/2) = 0,927 рад = 53,13°
Тогда sin([$945$]) = 0,8 , cos([$945$]) = 0,6
Искомое отношение [sin([$945$]) + cos([$945$])] / [sin([$945$]) - cos([$945$])] = (0,8 + 0,6) / (0,8 - 0,6) = 1,4 / 0,2 = 7
Однако, я догадываюсь, будто преподаватель, предложивший Вам эту задачу , хочет проверить Ваши знания тригонометрии?
Вспоминаем школьную математику или ищем в учебниках / интернет-справочниках тему Тригонометрия \ Формулы двойных углов :
В нашем случае 2·х = [$945$] , tg([$945$]/2) = tg(x) = 1/2
Заменим tg([$945$]/2) = 1/2 на t = 1/2 для упрощения выкладок. Получим :
Ответ : Искомое отношение
5
Спасибо огромное Вам
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