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Консультация № 68946
28.12.2006, 17:42
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Здравствуйте! Помогите пожалуйста в решении простейших тригонометрических уравнений(привести до стандартного вида, используя обычные формулы преобразования, я в 10 классе), сам я не успеваю, а от этого зависит четвертная.
cos(2x/3)+5sin(x/3)+2=0
cos2x-4sqrt(2)cosx+4=0
3cosx+sinx=0
sin(60+x)=sin3x
sqr(sinx)-sqr(sin2x)-sqr(sin3x)-sqr(sin4x)=0
cos^3+sin^4=1
cos2x+cos5x=-2
Спасибо.
cos(2x/3)+5sin(x/3)+2=0
cos2x-4sqrt(2)cosx+4=0
3cosx+sinx=0
sin(60+x)=sin3x
sqr(sinx)-sqr(sin2x)-sqr(sin3x)-sqr(sin4x)=0
cos^3+sin^4=1
cos2x+cos5x=-2
Спасибо.
Обсуждение
Неизвестный
28.12.2006, 19:24
общий
это ответ
Здравствуйте, KrocoDIL!
1)cos(2x/3)+5sin(x/3)+2=0
Расписываем cos(2x/3) по формуле двойного угла cos(2x/3) = 1 - 2*(sin(x/3))^2 Получаем квадратное уравнение относительно синуса.
2)cos2x-4sqrt(2)cosx+4=0 То же самое cos2x = 2*(cosx)^2 - 1. Уравнение относительно косинуса.
3)3cosx+sinx=0 Приводим к тангенсу или котангенсу:
4)3 + tgx = 0. cosx не равно 0, т.к. в противном случае и синус был бы равен 0.
5)sin(60+x)=sin3x Расписываем sin(60+x) = cos(60)sinx + sin(60)cosx; sin3x = 3sinx - 4*(sinx)^3. (sinx)^2 = 1/(1+(ctgx)^2). Получаем
0.5sinx + 1/sqrt(2) cosx = 3sinx - 4sinx / (1 + (ctgx)^2). Все делим на sinx и получаем уравнение относительно tgx (или ctgx).
6)затрудняюсь ответить, но видно, что sqr(sinx) легко выносится за скобку.
7,8) к сожалению ничем тут помочь не могу
Возможно, решения не самые оптимальные, но это тоже решения.
1)cos(2x/3)+5sin(x/3)+2=0
Расписываем cos(2x/3) по формуле двойного угла cos(2x/3) = 1 - 2*(sin(x/3))^2 Получаем квадратное уравнение относительно синуса.
2)cos2x-4sqrt(2)cosx+4=0 То же самое cos2x = 2*(cosx)^2 - 1. Уравнение относительно косинуса.
3)3cosx+sinx=0 Приводим к тангенсу или котангенсу:
4)3 + tgx = 0. cosx не равно 0, т.к. в противном случае и синус был бы равен 0.
5)sin(60+x)=sin3x Расписываем sin(60+x) = cos(60)sinx + sin(60)cosx; sin3x = 3sinx - 4*(sinx)^3. (sinx)^2 = 1/(1+(ctgx)^2). Получаем
0.5sinx + 1/sqrt(2) cosx = 3sinx - 4sinx / (1 + (ctgx)^2). Все делим на sinx и получаем уравнение относительно tgx (или ctgx).
6)затрудняюсь ответить, но видно, что sqr(sinx) легко выносится за скобку.
7,8) к сожалению ничем тут помочь не могу
Возможно, решения не самые оптимальные, но это тоже решения.
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