4sinx-2>0 2tg 2x+8>0 5cos 2 x+2

jabockeez @jabockeez

October 2021 1 8 Report

4sinx-2>0
2tg 2x+8>0
5cos 2 x+2<7
есть ли решение у этих уравнений

Answers & Comments

nKrynka 1) 4sinx > 2
sinx > 1/2
arcsin(1/2) + 2πn < x < π - arcsin(1/2) + 2πn, n∈Z
π/6 + 2πn < x < π - π/6 + 2πn, n∈Z
π/6 + 2πn < x < 5π/6 + 2πn, n∈Z

2) 2tg 2x+ 8> 0
tg2x > - 4
- arctg4 + πk < 2x < π/2 + πk, k∈Z
-(1/2)*arctg4 + (πk)/2 < x < π/4 + (πk)/2, k∈Z,

3) 5cos 2 x+2<7
5 cos2x < 5
cosx < 1
arccos(1) + 2πm < 2x < 2π - arccos(1) + 2πm, m∈Z
0 + 2πm < 2x < 2π - 0 + 2πm, m∈Z
2πm < 2x < 2π + 2πm, m∈Z
πm < x <π + πm, m∈Z

4 votes Thanks 14

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