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Popular Trigonometry Problems

(-sqrt(3))/2 <cos(x)<= 1/2	\frac{-\sqrt{3}}{2}<\cos(x)\le\:\frac{1}{2}
(-1)/2 <sin^2(x)< 1/2	\frac{-1}{2}<\sin^{2}(x)<\frac{1}{2}
cot(θ)=-1\land csc(θ)<0	\cot(θ)=-1\land\:\csc(θ)<0
cos(θ)<0\land csc(θ)>0	\cos(θ)<0\land\:\csc(θ)>0
cot(θ)=-3\land cos(θ)<0	\cot(θ)=-3\land\:\cos(θ)<0
0<cos(x)<1	0<\cos(x)<1
cos(θ)<0\land sin(θ)<0	\cos(θ)<0\land\:\sin(θ)<0
-1<= sin(x)<= 0	-1\le\:\sin(x)\le\:0
0<2sin(x)+1<1+sqrt(3)	0<2\sin(x)+1<1+\sqrt{3}
sin(x)=-4/5 \land cos(x)<0,cos(2/x)	\sin(x)=-\frac{4}{5}\land\:\cos(x)<0,\cos(\frac{2}{x})
sin(x)=-45\land cos(x)<0,cos((5pi)/6-x)	\sin(x)=-45\land\:\cos(x)<0,\cos(\frac{5π}{6}-x)
-2<= 2/(cos(x))<= 2	-2\le\:\frac{2}{\cos(x)}\le\:2
-2<= 2/(cos(x))<= 1	-2\le\:\frac{2}{\cos(x)}\le\:1
2-4sin(3x)0<= x<= 2pi	2-4\sin(3x)0\le\:x\le\:2π
(2cos(t))(t-cos(t))0<t<2pi	(2\cos(t))(t-\cos(t))0<t<2π
0<2sin(x)cos(x)<2sqrt(2)	0<2\sin(x)\cos(x)<2\sqrt{2}
cot(θ)>0\land csc(θ)<0	\cot(θ)>0\land\:\csc(θ)<0
sin(A)=(-4)/5 \land cos(A)>0,cos(A)	\sin(A)=\frac{-4}{5}\land\:\cos(A)>0,\cos(A)
sin(θ)= 2/5 \land sec(θ)>0	\sin(θ)=\frac{2}{5}\land\:\sec(θ)>0
csc(θ)<0\land cos(θ)>0	\csc(θ)<0\land\:\cos(θ)>0
sin(2x)0<= pi/2 \land 0-pi/2 <0	\sin(2x)0\le\:\frac{π}{2}\land\:0-\frac{π}{2}<0
[sin(pi)t]2<= t<= 4	[\sin(π)t]2\le\:t\le\:4
3-3(0)^2<= g(0)<= 3cos(0)	3-3(0)^{2}\le\:g(0)\le\:3\cos(0)
0<sin(x)cos(x)<sqrt(2)	0<\sin(x)\cos(x)<\sqrt{2}
csc(θ)<0\land (csc(θ))(cot(θ))>0	\csc(θ)<0\land\:(\csc(θ))(\cot(θ))>0
1>arctan(x)>0	1>\arctan(x)>0
cosh(θ)= 8/3 \land θ<0,sinh(θ)	\cosh(θ)=\frac{8}{3}\land\:θ<0,\sinh(θ)
cos(θ)=(sqrt(3))/2 \land csc(θ)<0	\cos(θ)=\frac{\sqrt{3}}{2}\land\:\csc(θ)<0
0<= y<= sin(3.1416)	0\le\:y\le\:\sin(3.1416)
-1<= 2/(cos(x))<= 1	-1\le\:\frac{2}{\cos(x)}\le\:1
0<= sin(x)<1	0\le\:\sin(x)<1
-1<sec(x)<1	-1<\sec(x)<1
-1<tan(x/2)<-1/5	-1<\tan(\frac{x}{2})<-\frac{1}{5}
1<= sin(θ)<3	1\le\:\sin(θ)<3
cos(θ)>0\land sin(θ)<0	\cos(θ)>0\land\:\sin(θ)<0
tan(θ)=1\land cos(θ)>0,csc(θ)	\tan(θ)=1\land\:\cos(θ)>0,\csc(θ)
-1<sin(x)<= 0	-1<\sin(x)\le\:0
tan(θ)= 1/3 \land sin(θ)<0	\tan(θ)=\frac{1}{3}\land\:\sin(θ)<0
cot(θ)=2\land sec(θ)>= 0	\cot(θ)=2\land\:\sec(θ)\ge\:0
sin(θ)=-(sqrt(3))/2 \land cos(θ)>= 0	\sin(θ)=-\frac{\sqrt{3}}{2}\land\:\cos(θ)\ge\:0
-1<= (pi(cos(x)-sin(x)))/(4sqrt(2))<= 1	-1\le\:\frac{π(\cos(x)-\sin(x))}{4\sqrt{2}}\le\:1
0<= cos(θ)<= 1	0\le\:\cos(θ)\le\:1
-2sin^2(x)0<x<360	-2\sin^{2}(x)0<x<360
-1<= tan(x/2-pi/3)<= sqrt(3)	-1\le\:\tan(\frac{x}{2}-\frac{π}{3})\le\:\sqrt{3}
-1>=-cos(2x)>= 1	-1\ge\:-\cos(2x)\ge\:1
0<82.5-67.5cos(pi/6 t)<20	0<82.5-67.5\cos(\frac{π}{6}t)<20
csc(x)=4\land cot(x)<0	\csc(x)=4\land\:\cot(x)<0
cos(x^2)0<x<sqrt(x)	\cos(x^{2})0<x<\sqrt{x}
sin(x)=-4/5 \land cos(x)<0,sin(2x)	\sin(x)=-\frac{4}{5}\land\:\cos(x)<0,\sin(2x)
cos(θ)= 3/7 \land sin(θ)>0	\cos(θ)=\frac{3}{7}\land\:\sin(θ)>0
cosh(θ)= 26/7 \land θ<0,sinh(θ)	\cosh(θ)=\frac{26}{7}\land\:θ<0,\sinh(θ)
-pi/2 <arcsin(x)< pi/2	-\frac{π}{2}<\arcsin(x)<\frac{π}{2}
-sqrt(2)<= cos(2x)<= sqrt(2)	-\sqrt{2}\le\:\cos(2x)\le\:\sqrt{2}
(11pi)/9 <= arctan(θ)<= (13pi)/9	\frac{11π}{9}\le\:\arctan(θ)\le\:\frac{13π}{9}
sin(x)=-(sqrt(3))/5 \land cos(x)>0	\sin(x)=-\frac{\sqrt{3}}{5}\land\:\cos(x)>0
cos(θ)=0.222\land tan(θ)<0,sin(θ)	\cos(θ)=0.222\land\:\tan(θ)<0,\sin(θ)
sin(x)0<= x<= pi	\sin(x)0\le\:x\le\:π
x=-4\land csc(x)>0	x=-4\land\:\csc(x)>0
cos(θ)<0\land (cos(θ))(sin(θ))<0	\cos(θ)<0\land\:(\cos(θ))(\sin(θ))<0
cosh(θ)= 15/4 \land θ<0,sinh(θ)	\cosh(θ)=\frac{15}{4}\land\:θ<0,\sinh(θ)
2pi>sqrt(3)tan(θ)+1>= 0	2π>\sqrt{3}\tan(θ)+1\ge\:0
sin(3x)0<= x<= 2pi	\sin(3x)0\le\:x\le\:2π
sin(θ)=-0.616\land tan(θ)>0	\sin(θ)=-0.616\land\:\tan(θ)>0
tan(θ)=-32\land csc(θ)>0	\tan(θ)=-32\land\:\csc(θ)>0
0<= arctan(x)<= pi/4	0\le\:\arctan(x)\le\:\frac{π}{4}
sin(θ)<0\land tan(θ)>0	\sin(θ)<0\land\:\tan(θ)>0
-1<sin^2(x)<1	-1<\sin^{2}(x)<1
cot(θ)= 21/20 \land cos(θ)>0	\cot(θ)=\frac{21}{20}\land\:\cos(θ)>0
sin(θ)=(sqrt(3))/2 \land tan(θ)>0	\sin(θ)=\frac{\sqrt{3}}{2}\land\:\tan(θ)>0
sin(θ)=-6/9 \land tan(θ)>0	\sin(θ)=-\frac{6}{9}\land\:\tan(θ)>0
cos(θ)= 5/7 \land cot(θ)<0,sin(θ)	\cos(θ)=\frac{5}{7}\land\:\cot(θ)<0,\sin(θ)
sec(θ)<0\land (cos(θ))(sin(θ))<0	\sec(θ)<0\land\:(\cos(θ))(\sin(θ))<0
0<= a+barctan(x)<= 1	0\le\:a+b\arctan(x)\le\:1
cos(x)<sin(x)<1	\cos(x)<\sin(x)<1
cos(θ)=45\land 0<θ<90,sin(θ)	\cos(θ)=45\land\:0^{\circ\:}<θ<90^{\circ\:},\sin(θ)
sin(a-pi/2)*csc(2pi+a)90<= a<= 180	\sin(a-\frac{π}{2})\cdot\:\csc(2π+a)90^{\circ\:}\le\:a\le\:180^{\circ\:}
arcsec(-sqrt(2))0<= x<= 2pi	\arcsec(-\sqrt{2})0\le\:x\le\:2π
-1<sin(pix)<1	-1<\sin(πx)<1
cos(θ)=25\land tan(θ)<0	\cos(θ)=25\land\:\tan(θ)<0
cos(x)>0\land tan(x)>0	\cos(x)>0\land\:\tan(x)>0
-1<cot(x)<1	-1<\cot(x)<1
tan(θ)<0\land sec(θ)>0	\tan(θ)<0\land\:\sec(θ)>0
sin(θ)= 9/41 \land cos(θ)>0	\sin(θ)=\frac{9}{41}\land\:\cos(θ)>0
sin(x)0<x<2pi	\sin(x)0<x<2π
cos(-1)-pi<t<= pi	\cos(-1)-π<t\le\:π
derivative of arcsech(cos(5x)0)<x< pi/5	\frac{d}{dx}(\arcsech(\cos(5x))0)<x<\frac{π}{5}
tan(θ)>0\land cos(θ)<0	\tan(θ)>0\land\:\cos(θ)<0
(11pi)/2 <= arctan(θ)<= (13pi)/9	\frac{11π}{2}\le\:\arctan(θ)\le\:\frac{13π}{9}
cos(1/4 x)0<x<2pi	\cos(\frac{1}{4}x)0<x<2π
0<= tan^2(x)<= 3	0\le\:\tan^{2}(x)\le\:3
tan(θ)= 7/11 \land cos(θ)>0	\tan(θ)=\frac{7}{11}\land\:\cos(θ)>0
cosh(θ)= 7/5 \land θ<0,sinh(θ)	\cosh(θ)=\frac{7}{5}\land\:θ<0,\sinh(θ)
cos(x) 1/3 e0<x<90	\cos(x)\frac{1}{3}e0<x<90^{\circ\:}
tan(θ)=2\land cos(θ)<0	\tan(θ)=2\land\:\cos(θ)<0
tan(θ)=-4/3 \land sin(θ)<0,sec(θ)	\tan(θ)=-\frac{4}{3}\land\:\sin(θ)<0,\sec(θ)
tan(x)0<= x<= pi/6	\tan(x)0\le\:x\le\:\frac{π}{6}
cot(t)<0\land sec(t)>0	\cot(t)<0\land\:\sec(t)>0
4cos(θ)4sin(θ)0<= θ<= pi/2	4\cos(θ)4\sin(θ)0\le\:θ\le\:\frac{π}{2}
-1>= cos(2x)>= 1	-1\ge\:\cos(2x)\ge\:1
-1/2 <= sin(x)<= (sqrt(3))/2	-\frac{1}{2}\le\:\sin(x)\le\:\frac{\sqrt{3}}{2}

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