Решите тригонометрические неравенства.(c помощью единичной окружности)
а)tgx >1
б)сos x≤0
в)ctgx <1
г)sinx ≥0
а)tgx >1
б)сos x≤0
в)ctgx <1
г)sinx ≥0
More Questions From This User See All
Copyright © 2025 SCHOLAR.TIPS - All rights reserved.
Answers & Comments
Verified answer
a) tgx >1πn +π/4 < x < π/2 + πn , n ∈ Z.
---------------------------------------------------------------
x ∈ об единение интервалов ( πn +π/4 ; π/2 +πn );
*****************************************************************
π/4 < x < π/2 ;
2πk+π/4 < x < π/2 + 2πk ;
2k*π+ π/4 < x < π/2 + 2k*π (1)
2k _четное число .
-------------------------------------------
π+ π/4 < x <3π/2 ;
π+ π/4 < x < π/2 + π ;
2πk+π+ π/4 < x < π/2 + π +2πk ;
(2k+1)π + π/4 < x < π/2 + (2k+1)π (2)
(2k+1)__нечетное число .
πn +π/4 < x < π/2 + πn , n ∈ Z.
******************************************************************
б) сos x≤0 .
2πk + π/2 ≤ x ≤ 3π/2 +2πk , k∈ Z.
в) ctgx <1.
πk+ π/4 < x < π +πk
г) sinx ≥0 .
πk ≤ x ≤ (2k +1)π ; k∈ Z
---------------------------------------------
2πk+0 ≤ x ≤ π + 2πk ; k∈ Z.
2πk ≤ x ≤ π + 2πk ; k∈ Z.
2πk ≤ x ≤ (2k +1)π ; k∈ Z
---------------------------------------