2cos(p-2x)>1 помогите пожалуйста. Created by рау01. algebra-ru

2cos(p-2x)>1 помогите пожалуйста...

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2cos(p-2x)>1
cos(pi - 2x) > 1/2
2pk - arccos1/2 < pi - 2x < 2pk + arccos1/2, k∈Z
2pk - pi/3 < pi - 2x < 2pk + pi/3, k∈Z
2pk - pi/3 -pi < - 2x < 2pk + pi/3 - pi, k∈Z
2pk - 4pi/3 < - 2x < 2pk - 2pi/3, k∈Z
-pk + 2pi/3 > x > -pk + pi/3, k∈Z
pi/3 - pik < x < 2pi/3 - pik, k∈Z

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oganesbagoyan

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task/24804493
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решить неравенство 2cos(π-2x) >1 ;
-2cos2x > 1 ;
cos2x < -1/2 ;
(π -π/3) <2x < π+π/3 ;
2π/3 <2x < 4π/3 ;
2πn +2π/3 <2x < 4π/3 +2πn ;
πn +π/3 <x < 2π/3 +πn ; n ∈ Z * * * Z _множество целых чисел * * *

ответ : ∪ ( πn +π/3 ; 2π/3 +πn )
n ∈ Z .
* * * * * * * * * * * * * * * * * * * * * *
k = -n ∈ Z

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