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Консультация № 194115
06.12.2018, 18:04
0.00 руб.
1
5
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Объяснить, почему.
Объяснить, почему.
Прикрепленные файлы:
Обсуждение
06.12.2018, 23:32
общий
06.12.2018, 23:32
По определению арккосинуса?
Учтите, однако, что арккосинус имеет область значений от [tnr]0[/tnr] до [tnr][$960$][/tnr] и только на этой области выполняется [tnr]arccos(cos x) = x[/tnr]
в общем виде, для целого [tnr]k[/tnr] и [tnr]t[$8712$][0; [$960$]][/tnr]
[tnr]arccos(cos(2[$960$]k+t)) = t[/tnr]
[tnr]arccos(cos((2k+1)[$960$]+t) = [$960$]-t[/tnr]
Учтите, однако, что арккосинус имеет область значений от [tnr]0[/tnr] до [tnr][$960$][/tnr] и только на этой области выполняется [tnr]arccos(cos x) = x[/tnr]
в общем виде, для целого [tnr]k[/tnr] и [tnr]t[$8712$][0; [$960$]][/tnr]
[tnr]arccos(cos(2[$960$]k+t)) = t[/tnr]
[tnr]arccos(cos((2k+1)[$960$]+t) = [$960$]-t[/tnr]
07.12.2018, 00:18
общий
Адресаты:
воспользуйтесь тем, что
[tnr]cos([$960$]+x)=cos([$960$]-x)[/tnr]
Ещё более удачный вариант выражения в общем виде:
для целого [tnr]k[/tnr] и [tnr]t[$8712$][-[$960$]; [$960$]][/tnr]
[tnr]arccos(cos(2[$960$]k+t)) = |t|[/tnr]
[tnr]cos([$960$]+x)=cos([$960$]-x)[/tnr]
Ещё более удачный вариант выражения в общем виде:
для целого [tnr]k[/tnr] и [tnr]t[$8712$][-[$960$]; [$960$]][/tnr]
[tnr]arccos(cos(2[$960$]k+t)) = |t|[/tnr]
07.12.2018, 14:13
общий
Адресаты:
"Объяснить, почему" - потому что по определению arccos(x) - это угол, косинус которого = x.
arccos(cos(3)) cначала преобразовали из формы угла в тригонометрию, а потом обратно. Поэтому и должно получиться исходное значение. С учётом ограничений, которые Вам уже рассказал уважаемый Roman Chaplinsky .
Если снова непонятно, то простая аналогия : перевод слова с русского языка на немецкий и обратно должен возвратить исходный смысл.
arccos(cos(3)) cначала преобразовали из формы угла в тригонометрию, а потом обратно. Поэтому и должно получиться исходное значение. С учётом ограничений, которые Вам уже рассказал уважаемый Roman Chaplinsky .
Если снова непонятно, то простая аналогия : перевод слова с русского языка на немецкий и обратно должен возвратить исходный смысл.
09.12.2018, 19:40
общий
это ответ
Здравствуйте, svrvsvrv!
Поскольку
постольку
согласно определению арккосинуса.
Поскольку
постольку
согласно определению арккосинуса.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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