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Консультация № 145345
28.09.2008, 19:47
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Доброе здоровьице уважаемые експерты!Прошу помочь мне в решении нескольких задач!Сам я дурак и не могу их решить!Заранее решившему паклон!
6)по данному значению найти ctg(альфа/4),если cos(альфа)=-3/5, 450˚<альфа<540˚
6)по данному значению найти ctg(альфа/4),если cos(альфа)=-3/5, 450˚<альфа<540˚
Обсуждение
29.09.2008, 00:21
общий
это ответ
Здравствуйте, Бортников Артём Михайлович!
Решение.
Поскольку 450[$186$] = 360[$186$] + 90[$186$], 540[$186$] = 360[$186$] + 180[$186$], то угол [$945$] расположен во второй четверти координатной плоскости, в которой sin [$945$] положителен. Следовательно,
sin [$945$] = +[$8730$](1 - (cos [$945$])^2) = +[$8730$](1 - (-3/5)^2) = +[$8730$](16/25) = 4/5,
ctg [$945$] = (cos [$945$])/(sin [$945$]) = (-3/5)/(4/5) = -3/4,
[$945$] = -arcctg (3/4) + 180[$186$] = -53[$186$]8' + 180[$186$] = 126[$186$]52',
[$945$]/4 = 126[$186$]52'/4 = 31[$186$]43',
ctg ([$945$]/4) = ctg 31[$186$]43' = 1,618.
Ответ: 1,618.
Решение.
Поскольку 450[$186$] = 360[$186$] + 90[$186$], 540[$186$] = 360[$186$] + 180[$186$], то угол [$945$] расположен во второй четверти координатной плоскости, в которой sin [$945$] положителен. Следовательно,
sin [$945$] = +[$8730$](1 - (cos [$945$])^2) = +[$8730$](1 - (-3/5)^2) = +[$8730$](16/25) = 4/5,
ctg [$945$] = (cos [$945$])/(sin [$945$]) = (-3/5)/(4/5) = -3/4,
[$945$] = -arcctg (3/4) + 180[$186$] = -53[$186$]8' + 180[$186$] = 126[$186$]52',
[$945$]/4 = 126[$186$]52'/4 = 31[$186$]43',
ctg ([$945$]/4) = ctg 31[$186$]43' = 1,618.
Ответ: 1,618.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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