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Консультация № 70755
13.01.2007, 16:08
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Уважаемые эксперты, у меня вопрос: как вычислить значение выражения
|tg(cosП)|/tg(cosП)+2*|cos(sin5)|/cos(sin5)+4*|ctg(cos4)|/ctg(cos4)?
Спасибо большое.
|tg(cosП)|/tg(cosП)+2*|cos(sin5)|/cos(sin5)+4*|ctg(cos4)|/ctg(cos4)?
Спасибо большое.
Обсуждение
Неизвестный
13.01.2007, 16:46
общий
это ответ
Здравствуйте, KISS-KA!
Вообще, выражение |X| / X можео принимать два значения: 1 при X>0 и -1 при X<0.
Так что надо определить знаки tg(cos pi), cos(sin 5) и ctg(cos 4).
cos pi = -1; tg (-1) < 0 т.к. -pi/2<-1<0.
3pi/2 < 5 < 2pi => -1 < sin 5 < 0 => -pi/2 < sin 5 < 0 => cos(sin 5) > 0.
pi < 4 < 3pi/2 => cos 4 < 0 => sin(cos 4) < 0.
Итого: -1+2*1+4*(-1) = -3.
В расчётах мог и ошибиться, но идея правильная.
Удачи!
Вообще, выражение |X| / X можео принимать два значения: 1 при X>0 и -1 при X<0.
Так что надо определить знаки tg(cos pi), cos(sin 5) и ctg(cos 4).
cos pi = -1; tg (-1) < 0 т.к. -pi/2<-1<0.
3pi/2 < 5 < 2pi => -1 < sin 5 < 0 => -pi/2 < sin 5 < 0 => cos(sin 5) > 0.
pi < 4 < 3pi/2 => cos 4 < 0 => sin(cos 4) < 0.
Итого: -1+2*1+4*(-1) = -3.
В расчётах мог и ошибиться, но идея правильная.
Удачи!
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