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Консультация № 198173
08.04.2020, 00:15
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу помощи в решении следующих заданий:
Прикрепленные файлы:
Обсуждение
12.04.2020, 18:50
общий
это ответ
Здравствуйте, pilot!
1. Так как cos (-x) = cos x и sin (-x) = - sin x, то
и f(-x) [$8800$] f(x), f(-x) [$8800$] -f(x), то есть функция f(x) не является ни чётной, ни нечётной.
2. Да, например функции cos x и sin x имеют период 2[$960$], а их произведение sin x cos x = 1/2 sin 2x имеет период [$960$], то есть вдвое меньший.
3. Так как sin([$945$]+[$946$]) = sin [$945$] cos [$946$] + cos [$945$] sin [$946$], и при [$945$], [$946$] [$8712$] (0, [$960$]/2) имеем 0 < cos [$945$], cos [$946$] < 1, то sin [$945$] cos [$946$] < sin [$945$] и cos [$945$] sin [$946$] < sin [$946$], откуда sin [$945$] cos [$946$] + cos [$945$] sin [$946$] < sin [$945$] + sin [$946$], то есть sin ([$945$]+[$946$]) < sin [$945$] + sin [$946$].
4. Так как
то наименьшее значение достигается при sin 2[$945$] = [$177$]1, то есть при 2[$945$] = [$960$]/2 + [$960$]k или при [$945$] = [$960$]/4 + [$960$]k/2.
5. Раскрывая скобки, получаем
Выражение, стоящее слева в последнем равенстве, тождественно равно tg (x+y), следовательно, tg (x+y) = 1, откуда x+y = [$960$]/4 + [$960$]k, k [$8712$] Z и наименьшим положительным значением x+y будет [$960$]/4.
1. Так как cos (-x) = cos x и sin (-x) = - sin x, то
и f(-x) [$8800$] f(x), f(-x) [$8800$] -f(x), то есть функция f(x) не является ни чётной, ни нечётной.
2. Да, например функции cos x и sin x имеют период 2[$960$], а их произведение sin x cos x = 1/2 sin 2x имеет период [$960$], то есть вдвое меньший.
3. Так как sin([$945$]+[$946$]) = sin [$945$] cos [$946$] + cos [$945$] sin [$946$], и при [$945$], [$946$] [$8712$] (0, [$960$]/2) имеем 0 < cos [$945$], cos [$946$] < 1, то sin [$945$] cos [$946$] < sin [$945$] и cos [$945$] sin [$946$] < sin [$946$], откуда sin [$945$] cos [$946$] + cos [$945$] sin [$946$] < sin [$945$] + sin [$946$], то есть sin ([$945$]+[$946$]) < sin [$945$] + sin [$946$].
4. Так как
то наименьшее значение достигается при sin 2[$945$] = [$177$]1, то есть при 2[$945$] = [$960$]/2 + [$960$]k или при [$945$] = [$960$]/4 + [$960$]k/2.
5. Раскрывая скобки, получаем
Выражение, стоящее слева в последнем равенстве, тождественно равно tg (x+y), следовательно, tg (x+y) = 1, откуда x+y = [$960$]/4 + [$960$]k, k [$8712$] Z и наименьшим положительным значением x+y будет [$960$]/4.
5
Форма ответа
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