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Консультация № 145548
30.09.2008, 18:51
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здравствуйте.помогите пожалуйста по заданному значению функции найти сos [$223$]/4,если cos[$223$]=-7/25,180градусов[$8804$][$223$][$8804$]270 градусов
Обсуждение
Неизвестный
30.09.2008, 19:56
общий
это ответ
Здравствуйте, G-buck!
1)cosß=2*cos(ß/2)^2-1
Следоват. cos(ß/2)=(+/-)(корень(cosß+1)/2)=(+/-)(3/5)
Т.к. 90>(ß/2)>135, то cos(ß/2)=-3/5
2)cos(ß/2)=2*cos(ß/4)^2-1
Следоват. cos(ß/4)=(+/-)(корень(cos(ß/2)+1)/2)=(+/-)(1/корень(5))
Т.к. 45>(ß/2)>67,5, то cos(ß/4)=-1/корень(5)
ОТВЕТ: cos(ß/4)=-1/корень(5)
1)cosß=2*cos(ß/2)^2-1
Следоват. cos(ß/2)=(+/-)(корень(cosß+1)/2)=(+/-)(3/5)
Т.к. 90>(ß/2)>135, то cos(ß/2)=-3/5
2)cos(ß/2)=2*cos(ß/4)^2-1
Следоват. cos(ß/4)=(+/-)(корень(cos(ß/2)+1)/2)=(+/-)(1/корень(5))
Т.к. 45>(ß/2)>67,5, то cos(ß/4)=-1/корень(5)
ОТВЕТ: cos(ß/4)=-1/корень(5)
Неизвестный
01.10.2008, 09:08
общий
это ответ
Здравствуйте, G-buck!
Будем использовать формулу для половинного аргумента
cosα/2 = ±√((1+cosα)/2) (знак зависит от положения угла α/2
Два раза применим формулу получим:
Cosβ/4 = ±√((1+cosβ/2)/2)
cosβ/2 = ±√((1+cosβ)/2)
при этом имеем ввиду что cosβ < 0, cosβ/2 < 0, cosβ/4 > 0
В итоге получаем
Cosβ/4 = √((1 – (√((1 – 7/25)/2)))/2) = 1/√5 ≈ 0,45
Формулы приведения половинных аргументов :
http://www.pm298.ru/trigon5.shtml
Будем использовать формулу для половинного аргумента
cosα/2 = ±√((1+cosα)/2) (знак зависит от положения угла α/2
Два раза применим формулу получим:
Cosβ/4 = ±√((1+cosβ/2)/2)
cosβ/2 = ±√((1+cosβ)/2)
при этом имеем ввиду что cosβ < 0, cosβ/2 < 0, cosβ/4 > 0
В итоге получаем
Cosβ/4 = √((1 – (√((1 – 7/25)/2)))/2) = 1/√5 ≈ 0,45
Формулы приведения половинных аргументов :
http://www.pm298.ru/trigon5.shtml
Форма ответа
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