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Консультация № 177252
14.03.2010, 20:16
0.00 руб.
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1
Здравствуйте, уважаемые эксперты! Помогите, пожалуйста, решить уравнение:
cos6x+sin(3x/2)=3-|cosx|
cos6x+sin(3x/2)=3-|cosx|
Обсуждение
Неизвестный
14.03.2010, 23:49
общий
16.03.2010, 16:24
это ответ
Здравствуйте, Болдырев Тимофей.
Рассмотрим отдельно левую и правую части уравнения
cos6x+sin(3x/2)<=2
причем cos6x+sin(3x/2)=2 если cos6x=sin(3x/2)=1
|6*x=2Pi*n (n-целое)
|3*x/2=Pi/2+2Pi*n (n-целое)
получится x=Pi/3+(4/3)*Pi*n (n-целое)
Теперь рассмотрим правую часть
минимум достигается при |cos(x)|=1, значит x=Pi*n (n-целое)
Pi/3+(4/3)*Pi*n=Pi*n
4*n+1=3*n
n=-1
Получили один из корней x= -Pi
Период составит 4*Pi
Ответ: -Pi+4*Pi*n (n-целое)
График, корни в точках пересечения
Рассмотрим отдельно левую и правую части уравнения
cos6x+sin(3x/2)<=2
причем cos6x+sin(3x/2)=2 если cos6x=sin(3x/2)=1
|6*x=2Pi*n (n-целое)
|3*x/2=Pi/2+2Pi*n (n-целое)
получится x=Pi/3+(4/3)*Pi*n (n-целое)
Теперь рассмотрим правую часть
минимум достигается при |cos(x)|=1, значит x=Pi*n (n-целое)
Pi/3+(4/3)*Pi*n=Pi*n
4*n+1=3*n
n=-1
Получили один из корней x= -Pi
Период составит 4*Pi
Ответ: -Pi+4*Pi*n (n-целое)
График, корни в точках пересечения
5
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