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Popular Trigonometry Problems

sin(x)>= 1/2 ,0<= x<= 2pi	\sin(x)\ge\:\frac{1}{2},0\le\:x\le\:2π
2cos(x)+2>= 2	2\cos(x)+2\ge\:2
(2*cos(x)-3)/(sin(x))>= 0	\frac{2\cdot\:\cos(x)-3}{\sin(x)}\ge\:0
cos^3(x^2)-3>0	\cos^{3}(x^{2})-3>0
sin(4x)>cos(2x)	\sin(4x)>\cos(2x)
cos(2x)>= 1/2	\cos(2x)\ge\:\frac{1}{2}
1/(sin(2x))< 1/(sin(x))	\frac{1}{\sin(2x)}<\frac{1}{\sin(x)}
1-4sin^2(x)>0	1-4\sin^{2}(x)>0
tan(x)>=-sqrt(3)	\tan(x)\ge\:-\sqrt{3}
cos(θ)>0,sin(θ)<0	\cos(θ)>0,\sin(θ)<0
tan(x)> 1/(sqrt(3))	\tan(x)>\frac{1}{\sqrt{3}}
tan(2x)>1	\tan(2x)>1
sin^2(x)>-1	\sin^{2}(x)>-1
tan(pi-2x)>= sqrt(3)	\tan(π-2x)\ge\:\sqrt{3}
solvefor x,cos(x)<= 1	solvefor\:x,\cos(x)\le\:1
cos(x)+cos(2x)>0	\cos(x)+\cos(2x)>0
solvefor x,sin(x)=-1/2-pi<= x<= pi	solvefor\:x,\sin(x)=-\frac{1}{2}-π\le\:x\le\:π
0.86<= cos^{2(10)}((68)/n)	0.86\le\:\cos^{2(10)}(\frac{68}{n})
pi/2 cos((pi*x)/2)>0	\frac{π}{2}\cos(\frac{π\cdot\:x}{2})>0
cos(x)>(((1))/((2)))	\cos(x)>(\frac{(1)}{(2)})
-1<tan(x)<1	-1<\tan(x)<1
0<cos(θ)<= sqrt(3)sin(θ)	0<\cos(θ)\le\:\sqrt{3}\sin(θ)
sin(t)<0\land cos(t)<0	\sin(t)<0\land\:\cos(t)<0
csc(x)=-2sqrt(5)\land cos(x)<0,cot(2x)	\csc(x)=-2\sqrt{5}\land\:\cos(x)<0,\cot(2x)
-1<= sin(x)<= 1	-1\le\:\sin(x)\le\:1
sin(θ)= 7/25 \land cos(θ)>0	\sin(θ)=\frac{7}{25}\land\:\cos(θ)>0
sin(x)=-4/5 \land cos(x)<0,cos(x/2)	\sin(x)=-\frac{4}{5}\land\:\cos(x)<0,\cos(\frac{x}{2})
0<sin(x)< 1/2	0<\sin(x)<\frac{1}{2}
1/2 <sin(θ)<(sqrt(2))/2	\frac{1}{2}<\sin(θ)<\frac{\sqrt{2}}{2}
sin(θ)= 2/3 \land tan(θ)>0	\sin(θ)=\frac{2}{3}\land\:\tan(θ)>0
cos(θ)<0\land tan(θ)>0	\cos(θ)<0\land\:\tan(θ)>0
cosh(θ)= 29/8 \land θ<0,sinh(θ)	\cosh(θ)=\frac{29}{8}\land\:θ<0,\sinh(θ)
0<arcsin(y)<pi	0<\arcsin(y)<π
-1<= cos(x)<= 1	-1\le\:\cos(x)\le\:1
-pi/2 <arctan(y)<0	-\frac{π}{2}<\arctan(y)<0
sin(θ)=(sqrt(3))/2 \land tan(θ)<0	\sin(θ)=\frac{\sqrt{3}}{2}\land\:\tan(θ)<0
sin(x)0<x<pi	\sin(x)0<x<π
0<= sin(x)<= 1	0\le\:\sin(x)\le\:1
-pi/2 <arcsin(y)< pi/2	-\frac{π}{2}<\arcsin(y)<\frac{π}{2}
sin(θ)=-1/2 \land cos(θ)>0	\sin(θ)=-\frac{1}{2}\land\:\cos(θ)>0
-1/2 <sin(x)< 1/2	-\frac{1}{2}<\sin(x)<\frac{1}{2}
sin(θ)>0\land sec(θ)<0	\sin(θ)>0\land\:\sec(θ)<0
0<= arctan(x)<= 1	0\le\:\arctan(x)\le\:1
tan(θ)>0\land sin(θ)<0	\tan(θ)>0\land\:\sin(θ)<0
sin(θ)<0\land cos(θ)>0	\sin(θ)<0\land\:\cos(θ)>0
cot(θ)=-1/3 \land cos(θ)>0,sec(θ)	\cot(θ)=-\frac{1}{3}\land\:\cos(θ)>0,\sec(θ)
tan(θ)=-4/5 \land cos(θ)>0,csc(θ)	\tan(θ)=-\frac{4}{5}\land\:\cos(θ)>0,\csc(θ)
-1/2 <cos(x)< 1/2	-\frac{1}{2}<\cos(x)<\frac{1}{2}
sin(θ)>0\land cos(θ)<0	\sin(θ)>0\land\:\cos(θ)<0
sin(θ)<0\land (csc(θ))(cos(θ))>0	\sin(θ)<0\land\:(\csc(θ))(\cos(θ))>0
cosh(θ)= 12/7 \land θ<0,sinh(θ)	\cosh(θ)=\frac{12}{7}\land\:θ<0,\sinh(θ)
0<= sin^2(x)<= 1	0\le\:\sin^{2}(x)\le\:1
cos(θ)=45\land 0<θ<90,sec(θ)	\cos(θ)=45\land\:0^{\circ\:}<θ<90^{\circ\:},\sec(θ)
sin(θ)<0\land cot(θ)<0	\sin(θ)<0\land\:\cot(θ)<0
5<= 20cos(pi/(20)(x-20))+23<= 20	5\le\:20\cos(\frac{π}{20}(x-20))+23\le\:20
tan(θ)=-1\land sin(θ)>0	\tan(θ)=-1\land\:\sin(θ)>0
sin(x/2-pi/3)0<= x<= 2pi	\sin(\frac{x}{2}-\frac{π}{3})0\le\:x\le\:2π
cos(θ)= 1/4 \land 0>θ>90,tan(θ)	\cos(θ)=\frac{1}{4}\land\:0^{\circ\:}>θ>90^{\circ\:},\tan(θ)
cot(θ)=-sqrt(2)\land cos(θ)>0	\cot(θ)=-\sqrt{2}\land\:\cos(θ)>0
csc(θ)>0\land cot(θ)>0	\csc(θ)>0\land\:\cot(θ)>0
sin(pi*x)0<x<1	\sin(π\cdot\:x)0<x<1
-(sqrt(2))/2 <sin(x)<(sqrt(2))/2	-\frac{\sqrt{2}}{2}<\sin(x)<\frac{\sqrt{2}}{2}
-sqrt(2)<= sin(θ)+cos(θ)<= sqrt(2)	-\sqrt{2}\le\:\sin(θ)+\cos(θ)\le\:\sqrt{2}
cos(θ)= 13/5 \land 180<θ<270,tan(2θ)	\cos(θ)=\frac{13}{5}\land\:180<θ<270,\tan(2θ)
sin(θ)=-1/3 \land tan(θ)>0	\sin(θ)=-\frac{1}{3}\land\:\tan(θ)>0
tan(θ)= 1/3 \land sin(θ)>0	\tan(θ)=\frac{1}{3}\land\:\sin(θ)>0
cot(θ)>0\land cos(θ)>0	\cot(θ)>0\land\:\cos(θ)>0
sin(t)=-7/8 \land sec(t)<0	\sin(t)=-\frac{7}{8}\land\:\sec(t)<0
csc(θ)>0\land sec(θ)<0	\csc(θ)>0\land\:\sec(θ)<0
tan(θ)<0\land cos(θ)>0	\tan(θ)<0\land\:\cos(θ)>0
sec(θ)= 4/3 \land cot(θ)<0	\sec(θ)=\frac{4}{3}\land\:\cot(θ)<0
0<cos(x)<sin(x)	0<\cos(x)<\sin(x)
1/2 <sin(θ)<(sqrt(3))/2	\frac{1}{2}<\sin(θ)<\frac{\sqrt{3}}{2}
(x^2)/(sqrt(2))-sin^2(x)in^0<x<2pi	\frac{x^{2}}{\sqrt{2}}-\sin^{2}(x)in^{0}<x<2π
tan(θ)=-4/5 \land cos(θ)>0	\tan(θ)=-\frac{4}{5}\land\:\cos(θ)>0
csc(θ)<0\land cos(θ)<0	\csc(θ)<0\land\:\cos(θ)<0
cos(θ)= 2/5 \land tan(θ)<0	\cos(θ)=\frac{2}{5}\land\:\tan(θ)<0
0>= 1/(sin^2(x))>= 1	0\ge\:\frac{1}{\sin^{2}(x)}\ge\:1
(1-sin(x))0<x< pi/2	(1-\sin(x))0<x<\frac{π}{2}
sin(θ)=-1/8 \land sec(θ)<0	\sin(θ)=-\frac{1}{8}\land\:\sec(θ)<0
(sin(2x))/(cos(x))0<= x<= pi	\frac{\sin(2x)}{\cos(x)}0\le\:x\le\:π
cos(x)= 3/5 \land sin(x)<0,sin(2x)	\cos(x)=\frac{3}{5}\land\:\sin(x)<0,\sin(2x)
csc(θ)=-5/4 \land cos(θ)>0	\csc(θ)=-\frac{5}{4}\land\:\cos(θ)>0
sin(θ)<0\land tan(θ)<0	\sin(θ)<0\land\:\tan(θ)<0
sin(t)0<= t<pi	\sin(t)0\le\:t<π
csc(θ)=4\land cot(θ)<0	\csc(θ)=4\land\:\cot(θ)<0
-(sqrt(2))/2 <sin(x/2)<(sqrt(2))/2	-\frac{\sqrt{2}}{2}<\sin(\frac{x}{2})<\frac{\sqrt{2}}{2}
-sqrt(3)<= tan(x)<= ((sqrt(3)))/3	-\sqrt{3}\le\:\tan(x)\le\:\frac{(\sqrt{3})}{3}
0<cos(θ)<1	0<\cos(θ)<1
tan(θ)=-12/5 \land sin(θ)>0	\tan(θ)=-\frac{12}{5}\land\:\sin(θ)>0
-1<= arccos(x^2)<= 1	-1\le\:\arccos(x^{2})\le\:1
1-cos(θ)0<= θ<= 2pi	1-\cos(θ)0\le\:θ\le\:2π
4(1-sin(θ))0<= θ<= pi	4(1-\sin(θ))0\le\:θ\le\:π
-1<sin(x)<-1/2	-1<\sin(x)<-\frac{1}{2}
sin(θ)>0\land tan(θ)>0	\sin(θ)>0\land\:\tan(θ)>0
tan(x)<0<5sin(x)	\tan(x)<0<5\sin(x)
cos(θ)<0\land sin(θ)>0	\cos(θ)<0\land\:\sin(θ)>0
-720<cos(1/2 x-10)<720	-720<\cos(\frac{1}{2}x-10)<720
sin(2arcsin(t))0<t<= 1	\sin(2\arcsin(t))0<t\le\:1
-1<= cos(2x)<= 1	-1\le\:\cos(2x)\le\:1

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