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fomenkoasya
@fomenkoasya
October 2021
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решите 2 , 3 и 5 тригонометрические неравенства, срочно пожалуйста
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oganesbagoyan
Verified answer
2)
tqx ≥ -1;
-
π/4
≤ x <
π/2
;
πn -π/4 ≤ x < π/2 +πn ;n∈Z
x ∈ [ -π/4 +πn ;π/2 +πn] ,n∈ Z
3)
2sinx -1 >0 ;
sinx >1/2 ;
π/6
< x <
π -π/6;
π/6
< x < 5
π/6;
π/6 +2πn < x < 5π/6+2πn ,n∈ Z.
5)
-√3 ≤ 3ctq(2x+π/5) ≤1;
-1/√3 ≤ ctq(2x+π/5) ≤1/3;
arcctq1/3≤ 2x+π/5 ≤ 2π/3 ;
-π/5 +arcctq1/3≤ 2x ≤ 7π/15 ;
-π/5 +arcctq1/3 +πn ≤ 2x ≤ 7π/15+πn;
-π/10 +1/2*arcctq1/3 +π/2*n ≤ x ≤ 7π/30+π/2*n ; n∈Z.
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Answers & Comments
Verified answer
2) tqx ≥ -1;-π/4 ≤ x < π/2;
πn -π/4 ≤ x < π/2 +πn ;n∈Z
x ∈ [ -π/4 +πn ;π/2 +πn] ,n∈ Z
3) 2sinx -1 >0 ;
sinx >1/2 ;
π/6 < x < π -π/6;
π/6 < x < 5π/6;
π/6 +2πn < x < 5π/6+2πn ,n∈ Z.
5) -√3 ≤ 3ctq(2x+π/5) ≤1;
-1/√3 ≤ ctq(2x+π/5) ≤1/3;
arcctq1/3≤ 2x+π/5 ≤ 2π/3 ;
-π/5 +arcctq1/3≤ 2x ≤ 7π/15 ;
-π/5 +arcctq1/3 +πn ≤ 2x ≤ 7π/15+πn;
-π/10 +1/2*arcctq1/3 +π/2*n ≤ x ≤ 7π/30+π/2*n ; n∈Z.