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pviolao
@pviolao
July 2022
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Тригонометрическое уравнение, помогите решить 7cos^2 x + 8cosx - 8 = 0
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CatSimon
Sin^2x=1-cos^2x
7-7cos^2x+8cosx-8=0
7cos^2x-8cosx+1=0 пусть cosx=t tприн [-1; 1]
7t^2-8t+1=0
t=(4+-3)/7
t1=1
t2=1/7
2) cosx=1, x=2
n
cosx=1/7, x=+-arccos(1/7) + 2
n
1 votes
Thanks 3
CatSimon
n принадлежит Z
pviolao
спасибо)
CatSimon
Рад помочь)
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Answers & Comments
7-7cos^2x+8cosx-8=0
7cos^2x-8cosx+1=0 пусть cosx=t tприн [-1; 1]
7t^2-8t+1=0
t=(4+-3)/7
t1=1
t2=1/7
2) cosx=1, x=2n
cosx=1/7, x=+-arccos(1/7) + 2n