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Консультация № 145346
28.09.2008, 19:48
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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!
7)преобразовать в произведение 1-cos(альфа)+sin(альфа)
7)преобразовать в произведение 1-cos(альфа)+sin(альфа)
Обсуждение
28.09.2008, 21:32
общий
это ответ
Здравствуйте, Бортников Артём Михайлович!
Решение.
1 - cos [$945$] + sin [$945$] = 2(sin [$945$]/2)^2 + 2(sin [$945$]/2)(cos [$945$]/2) = 2(sin [$945$]/2)(1 + (cos [$945$]/2)) =
= 2(sin [$945$]/2)2(cos [$945$]/4)^2 = 4(sin [$945$]/2)(cos [$945$]/4)^2.
ответ: 4(sin [$945$]/2)(cos [$945$]/4)^2.
Решение.
1 - cos [$945$] + sin [$945$] = 2(sin [$945$]/2)^2 + 2(sin [$945$]/2)(cos [$945$]/2) = 2(sin [$945$]/2)(1 + (cos [$945$]/2)) =
= 2(sin [$945$]/2)2(cos [$945$]/4)^2 = 4(sin [$945$]/2)(cos [$945$]/4)^2.
ответ: 4(sin [$945$]/2)(cos [$945$]/4)^2.
Об авторе:
Facta loquuntur.
Facta loquuntur.
Неизвестный
29.09.2008, 01:43
общий
это ответ
Здравствуйте, Бортников Артём Михайлович! Порадуйте преподавателя ещё 1 способом , через редкоиспользуемую формулу a*sin(alfa)+b*cos(alfa) = +(sqrt((a^2)+(b^2)))*sin(alfa+fi) ,
sin(fi) = b/(+sqrt((a^2)+(b^2))) , cos(fi) = a/(+sqrt((a^2)+(b^2))) .
{ a=1 , b=-1 , sin(fi)=-1/sqrt(2) , cos(fi)=1/sqrt(2) } -> fi=-Pi/4 или -45 градусов .
1+sin(alfa)-cos(alfa) = 1+(sqrt2)*sin(alfa-45) = (sqrt2)*(sin(45)+sin(alfa-45)) =
= 2*(sqrt2)*(sin(alfa/2))*(cos(45-(alfa/2)) = 2*(sqrt2)*(sin(alfa/2))*(sin(45+(alfa/2))) .
sin(fi) = b/(+sqrt((a^2)+(b^2))) , cos(fi) = a/(+sqrt((a^2)+(b^2))) .
{ a=1 , b=-1 , sin(fi)=-1/sqrt(2) , cos(fi)=1/sqrt(2) } -> fi=-Pi/4 или -45 градусов .
1+sin(alfa)-cos(alfa) = 1+(sqrt2)*sin(alfa-45) = (sqrt2)*(sin(45)+sin(alfa-45)) =
= 2*(sqrt2)*(sin(alfa/2))*(cos(45-(alfa/2)) = 2*(sqrt2)*(sin(alfa/2))*(sin(45+(alfa/2))) .
Форма ответа
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