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KitNoir
@KitNoir
July 2022
1
13
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а) Решите уравнение 15
cosx
= 3 cosx
· 5 sinx
.
б) Найдите все корни этого уравнения, принадлежащие отрезку [ 5π ; 13π/
2
]
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finka
A)15cosx=3cosx*5sinx
15cosx/cosx=3cosx/cosx*5sinx/cosx
15=3*5tgx
5tgx=5
tgx=1
x=П/4+Пn
б)5П<П/4+Пn<13П/2
5П-П/4<П/4+Пn-П/4<13P/2-П/4
10P/4-P/4<Pn<26P/4-P/4
9P/4<Pn<25P/4
2,25<n<6,25
n=3,4,5,6
8 votes
Thanks 5
Ksenia56
а)15cosx=3cosx*5sinx
15cosx/cosx=3cosx/cosx*5sinx/cosx
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Answers & Comments
15cosx/cosx=3cosx/cosx*5sinx/cosx
15=3*5tgx
5tgx=5
tgx=1
x=П/4+Пn
б)5П<П/4+Пn<13П/2
5П-П/4<П/4+Пn-П/4<13P/2-П/4
10P/4-P/4<Pn<26P/4-P/4
9P/4<Pn<25P/4
2,25<n<6,25
n=3,4,5,6
15cosx/cosx=3cosx/cosx*5sinx/cosx