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16 questions
tgx≤3\ tgx\le\sqrt{3} tgx≤3
[π3+πn;π2+πn]\left[\frac{\pi}{3}+\pi n;\frac{\pi}{2}+\pi n\right][3π+πn;2π+πn]
[π3+πn;π2+πn)\left[\frac{\pi}{3}+\pi n;\frac{\pi}{2}+\pi n\right)[3π+πn;2π+πn)
[−π2+πn;π3+πn)\left[-\frac{\pi}{2}+\pi n;\frac{\pi}{3}+\pi n\right)[−2π+πn;3π+πn)
(−π2+πn;π3+πn]\left(-\frac{\pi}{2}+\pi n;\frac{\pi}{3}+\pi n\right](−2π+πn;3π+πn]
sin3x≥12\sin3x\ge\frac{1}{\sqrt{2}}sin3x≥21
[π12+2πn3;π4+2πn3;]\left[\frac{\pi}{12}+\frac{2\pi n}{3};\frac{\pi}{4}+\frac{2\pi n}{3};\right][12π+32πn;4π+32πn;]
[π4+2πn;3π4+2πn;]\left[\frac{\pi}{4}+2\pi n;\frac{3\pi}{4}+2\pi n;\right][4π+2πn;43π+2πn;]
[−π12+2πn;π4+2πn;]\left[-\frac{\pi}{12}+2\pi n;\frac{\pi}{4}+2\pi n;\right][−12π+2πn;4π+2πn;]
[3π4+6πn;π4+6πn;]\left[\frac{3\pi}{4}+6\pi n;\frac{\pi}{4}+6\pi n;\right][43π+6πn;4π+6πn;]
cos2x>−32\cos2x>-\frac{\sqrt{3}}{2}cos2x>−23
(−5π12+2πn2;5π4+2πn2;)\left(-\frac{5\pi}{12}+\frac{2\pi n}{2};\frac{5\pi}{4}+\frac{2\pi n}{2};\right)(−125π+22πn;45π+22πn;)
(−5π12+2πn2;5π12+2πn2;)\left(-\frac{5\pi}{12}+\frac{2\pi n}{2};\frac{5\pi}{12}+\frac{2\pi n}{2};\right)(−125π+22πn;125π+22πn;)
(−π12+2πn;π4+2πn;)\left(-\frac{\pi}{12}+2\pi n;\frac{\pi}{4}+2\pi n;\right)(−12π+2πn;4π+2πn;)
(−2π3+2πn2;2π3+2πn2;)\left(-\frac{2\pi}{3}+\frac{2\pi n}{2};\frac{2\pi}{3}+\frac{2\pi n}{2};\right)(−32π+22πn;32π+22πn;)
ctg(x3+π6)≤−3\operatorname{ctg}\left(\frac{x}{3}+\frac{\pi}{6}\right)\le-\sqrt{3}ctg(3x+6π)≤−3
[−2π+3πk; 2.5π+3πk]\left[-2\pi+3\pi k;\ 2.5\pi+3\pi k\right][−2π+3πk; 2.5π+3πk]
(2π+3πk; 2.5π+3πk)\left(2\pi+3\pi k;\ 2.5\pi+3\pi k\right)(2π+3πk; 2.5π+3πk)
[2π+3πk; 53π+3πk)\left[2\pi+3\pi k;\ \frac{5}{3}\pi+3\pi k\right)[2π+3πk; 35π+3πk)
2tg(x−π6)−3≤−12tg\left(x-\frac{\pi}{6}\right)-3\le-12tg(x−6π)−3≤−1
(−4π3+πk; 5π12+πk)\left(-\frac{4\pi}{3}+\pi k;\ \frac{5\pi}{12}+\pi k\right)(−34π+πk; 125π+πk)
(−2π3+πk; 5π12+πk]\left(-\frac{2\pi}{3}+\pi k;\ \frac{5\pi}{12}+\pi k\right](−32π+πk; 125π+πk]
(−π3+πk; 5π12+πk)\left(-\frac{\pi}{3}+\pi k;\ \frac{5\pi}{12}+\pi k\right)(−3π+πk; 125π+πk)
(−π3+πk; 5π12+πk]\left(-\frac{\pi}{3}+\pi k;\ \frac{5\pi}{12}+\pi k\right](−3π+πk; 125π+πk]
3tg(−4x−π3)−3<03tg\left(-4x-\frac{\pi}{3}\right)-3<03tg(−4x−3π)−3<0
[−7π48+πk4;π24+πk4]\left[\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{\pi}{24}+\frac{\pi k}{4}\right][48−7π+4πk;24π+4πk]
(−7π48+πk4;5π24+πk4)\left(\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{5\pi}{24}+\frac{\pi k}{4}\right)(48−7π+4πk;245π+4πk)
(−7π48+πk4;π24+πk4)\left(\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{\pi}{24}+\frac{\pi k}{4}\right)(48−7π+4πk;24π+4πk)
(−7π48+πk4;π24+πk4]\left(\frac{-7\pi}{48}+\frac{\pi k}{4};\frac{\pi}{24}+\frac{\pi k}{4}\right](48−7π+4πk;24π+4πk]
2ctg( x3−π6)+12≥02\operatorname{ctg}(\ \frac{x}{3}-\frac{\pi}{6})+\sqrt{12}\ge02ctg( 3x−6π)+12≥0
(−π2+3πk;3π+3πk)\left(-\frac{\pi}{2}+3\pi k;3\pi+3\pi k\right)(−2π+3πk;3π+3πk)
(π2+3πk;3π+3πk]\left(\frac{\pi}{2}+3\pi k;3\pi+3\pi k\right](2π+3πk;3π+3πk]
(π4+3πk;π+3πk]\left(\frac{\pi}{4}+3\pi k;\pi+3\pi k\right](4π+3πk;π+3πk]
(π8+3πk;2π+3πk)\left(\frac{\pi}{8}+3\pi k;2\pi+3\pi k\right)(8π+3πk;2π+3πk)
9ctg(6x−π3)−33≤09\operatorname{ctg}\left(6x-\frac{\pi}{3}\right)-3\sqrt{3}\le09ctg(6x−3π)−33≤0
[−π9+πk9;2π9+πk9)\left[-\frac{\pi}{9}+\frac{\pi k}{9};\frac{2\pi}{9}+\frac{\pi k}{9}\right)[−9π+9πk;92π+9πk)
[π9+πk9;2π9+πk9]\left[\frac{\pi}{9}+\frac{\pi k}{9};\frac{2\pi}{9}+\frac{\pi k}{9}\right][9π+9πk;92π+9πk]
[π9+πk9;2π9+πk9)\left[\frac{\pi}{9}+\frac{\pi k}{9};\frac{2\pi}{9}+\frac{\pi k}{9}\right)[9π+9πk;92π+9πk)
[−π9+πk9;2π9+πk9]\left[-\frac{\pi}{9}+\frac{\pi k}{9};\frac{2\pi}{9}+\frac{\pi k}{9}\right][−9π+9πk;92π+9πk]
sinx×cosx\sin x\times\cos xsinx×cosx
sin2x2\frac{\sin2x}{2}2sin2x
cos2x2\frac{\cos2x}{2}2cos2x
tg2x2\frac{tg2x}{2}2tg2x
ctg2x2\frac{\operatorname{ctg}2x}{2}2ctg2x
sin2x−cos2x=\sin^2x-\cos^2x=sin2x−cos2x=
−sin2x-\sin2x−sin2x
sin2x\sin2xsin2x
cos2x\cos2xcos2x
−cos2x-\cos2x−cos2x
cos2x−sin2x=\cos^2x-\sin^2x=cos2x−sin2x=
5π6\frac{5\pi}{6}65π радианды градусқа айналдыр
150
300
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180
градусты радианға айналдыр 315°315\degree315°
3π4\frac{3\pi}{4}43π
5π4\frac{5\pi}{4}45π
7π4\frac{7\pi}{4}47π
cos2x
2sin2x−12\sin^2x-12sin2x−1
2cos2x−12\cos^2x-12cos2x−1
sin2x−cos2x\sin^2x-\cos^2xsin2x−cos2x
cos2x−sin2x\cos^2x-\sin^2xcos2x−sin2x
(tgx×cosx)2+cos2x\left(tgx\times\cos x\right)^2+\cos^2x(tgx×cosx)2+cos2x
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cosx=0.5
±arccos0.5+2πn\pm\arccos0.5+2\pi n±arccos0.5+2πn
±π3+2πn\pm\frac{\pi}{3}+2\pi n±3π+2πn
±arccos0.5+πn\pm\arccos0.5+\pi n±arccos0.5+πn
±π3+πn\pm\frac{\pi}{3}+\pi n±3π+πn
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