решить уравнение 5sin^2 x+6cosx-6=0. Created by Wasted23. matematika-ru

решить уравнение 5sin^2 x+6cosx-6=0...

June 2022 1 36 Report

решить уравнение
5sin^2 x+6cosx-6=0

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Graver9062 5sin²x +6cosx-6=0
5-5cos²x+6cosx-6=0
5cos²-6cosx+1=0
Пусть cos x =t; |t|≤0
5t²-6t+1=0
D=36-20=16
√D=4
t=1
t=0,4

cos x=1
x=π+2πk

cos x =0,4
x= ± arccos0,4+2πk
Ответ: {π+2πk; ±arccos0,4+2πk | k€Z}

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