Mister Exam
Other calculators
- Square Inequality Step-by-Step
- Inequality with the module Step by Step
- Logarithmic inequality online
-
How to use it?
- Inequation:
- x^2+9p^2+2x+6y+2>=0
- 3x+1/5-1-2x/2>x
- (x-2)/(x-7)>0
- (x+40)/((x^3-16*x)*((x-4)/(3*x^2+11*x-4)-16/(16-x^2)))≤0
- Integral of d{x}:
-
sint
- Derivative of:
-
sint
-
Identical expressions
- sint>=- one / two
- sinus of t greater than or equal to minus 1 divide by 2
- sinus of t greater than or equal to minus one divide by two
- sint>=-1 divide by 2
-
Similar expressions
- sin(t)<-sqrt(2)/2
- sin(t)<-0,6
- sin(t)<1
- sint>=+1/2
sint>=-1/2 inequation
The solution
Detail solution
Given the inequality:
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = - \frac{1}{2}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = - \frac{1}{2}$$
transform
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = - \frac{1}{2}$$
We get the answer: w = -1/2
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 9.94837673636768$$
$$x_{2} = -75.9218224617533$$
$$x_{3} = 37.1755130674792$$
$$x_{4} = 74.8746249105567$$
$$x_{5} = 24.60914245312$$
$$x_{6} = 60.2138591938044$$
$$x_{7} = -15.1843644923507$$
$$x_{8} = -101.054563690472$$
$$x_{9} = -31.9395253114962$$
$$x_{10} = -25.6563400043166$$
$$x_{11} = 93.7241808320955$$
$$x_{12} = -195.302343298165$$
$$x_{13} = -52.8834763354282$$
$$x_{14} = 85.3466004225227$$
$$x_{15} = -0.523598775598299$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -57.0722665402146$$
$$x_{18} = -84.2994028713261$$
$$x_{19} = -90.5825881785057$$
$$x_{20} = 62.3082542961976$$
$$x_{21} = 66.497044500984$$
$$x_{22} = 16.2315620435473$$
$$x_{23} = 22.5147473507269$$
$$x_{24} = 28.7979326579064$$
$$x_{25} = 12.0427718387609$$
$$x_{26} = -46.6002910282486$$
$$x_{27} = -78.0162175641465$$
$$x_{28} = -82.2050077689329$$
$$x_{29} = 100.007366139275$$
$$x_{30} = 5.75958653158129$$
$$x_{31} = -8.90117918517108$$
$$x_{32} = -13.0899693899575$$
$$x_{33} = -88.4881930761125$$
$$x_{34} = 437.20497762458$$
$$x_{35} = -94.7713783832921$$
$$x_{36} = -65.4498469497874$$
$$x_{37} = 79.0634151153431$$
$$x_{38} = -19.3731546971371$$
$$x_{39} = 56.025068989018$$
$$x_{40} = -34.0339204138894$$
$$x_{41} = -63.3554518473942$$
$$x_{42} = 91.6297857297023$$
$$x_{43} = -44.5058959258554$$
$$x_{44} = -6.80678408277789$$
$$x_{45} = -2.61799387799149$$
$$x_{46} = 72.7802298081635$$
$$x_{47} = 192.160750644576$$
$$x_{48} = 35.081117965086$$
$$x_{49} = -40.317105721069$$
$$x_{50} = 97.9129710368819$$
$$x_{51} = -96.8657734856853$$
$$x_{52} = -151.320046147908$$
$$x_{53} = 87.4409955249159$$
$$x_{54} = 81.1578102177363$$
$$x_{55} = 66400.1787274983$$
$$x_{56} = 53.9306738866248$$
$$x_{57} = 68.5914396033772$$
$$x_{58} = 3.66519142918809$$
$$x_{59} = -71.733032256967$$
$$x_{60} = -50.789081233035$$
$$x_{61} = -59.1666616426078$$
$$x_{62} = 30.8923277602996$$
$$x_{63} = 47.6474885794452$$
$$x_{64} = -27.7507351067098$$
$$x_{65} = 18.3259571459405$$
$$x_{66} = 43.4586983746588$$
$$x_{67} = 41.3643032722656$$
$$x_{68} = -21.4675497995303$$
$$x_{69} = 49.7418836818384$$
$$x_{70} = -69.6386371545737$$
$$x_{1} = 9.94837673636768$$
$$x_{2} = -75.9218224617533$$
$$x_{3} = 37.1755130674792$$
$$x_{4} = 74.8746249105567$$
$$x_{5} = 24.60914245312$$
$$x_{6} = 60.2138591938044$$
$$x_{7} = -15.1843644923507$$
$$x_{8} = -101.054563690472$$
$$x_{9} = -31.9395253114962$$
$$x_{10} = -25.6563400043166$$
$$x_{11} = 93.7241808320955$$
$$x_{12} = -195.302343298165$$
$$x_{13} = -52.8834763354282$$
$$x_{14} = 85.3466004225227$$
$$x_{15} = -0.523598775598299$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -57.0722665402146$$
$$x_{18} = -84.2994028713261$$
$$x_{19} = -90.5825881785057$$
$$x_{20} = 62.3082542961976$$
$$x_{21} = 66.497044500984$$
$$x_{22} = 16.2315620435473$$
$$x_{23} = 22.5147473507269$$
$$x_{24} = 28.7979326579064$$
$$x_{25} = 12.0427718387609$$
$$x_{26} = -46.6002910282486$$
$$x_{27} = -78.0162175641465$$
$$x_{28} = -82.2050077689329$$
$$x_{29} = 100.007366139275$$
$$x_{30} = 5.75958653158129$$
$$x_{31} = -8.90117918517108$$
$$x_{32} = -13.0899693899575$$
$$x_{33} = -88.4881930761125$$
$$x_{34} = 437.20497762458$$
$$x_{35} = -94.7713783832921$$
$$x_{36} = -65.4498469497874$$
$$x_{37} = 79.0634151153431$$
$$x_{38} = -19.3731546971371$$
$$x_{39} = 56.025068989018$$
$$x_{40} = -34.0339204138894$$
$$x_{41} = -63.3554518473942$$
$$x_{42} = 91.6297857297023$$
$$x_{43} = -44.5058959258554$$
$$x_{44} = -6.80678408277789$$
$$x_{45} = -2.61799387799149$$
$$x_{46} = 72.7802298081635$$
$$x_{47} = 192.160750644576$$
$$x_{48} = 35.081117965086$$
$$x_{49} = -40.317105721069$$
$$x_{50} = 97.9129710368819$$
$$x_{51} = -96.8657734856853$$
$$x_{52} = -151.320046147908$$
$$x_{53} = 87.4409955249159$$
$$x_{54} = 81.1578102177363$$
$$x_{55} = 66400.1787274983$$
$$x_{56} = 53.9306738866248$$
$$x_{57} = 68.5914396033772$$
$$x_{58} = 3.66519142918809$$
$$x_{59} = -71.733032256967$$
$$x_{60} = -50.789081233035$$
$$x_{61} = -59.1666616426078$$
$$x_{62} = 30.8923277602996$$
$$x_{63} = 47.6474885794452$$
$$x_{64} = -27.7507351067098$$
$$x_{65} = 18.3259571459405$$
$$x_{66} = 43.4586983746588$$
$$x_{67} = 41.3643032722656$$
$$x_{68} = -21.4675497995303$$
$$x_{69} = 49.7418836818384$$
$$x_{70} = -69.6386371545737$$
This roots
$$x_{12} = -195.302343298165$$
$$x_{52} = -151.320046147908$$
$$x_{8} = -101.054563690472$$
$$x_{51} = -96.8657734856853$$
$$x_{35} = -94.7713783832921$$
$$x_{19} = -90.5825881785057$$
$$x_{33} = -88.4881930761125$$
$$x_{18} = -84.2994028713261$$
$$x_{28} = -82.2050077689329$$
$$x_{27} = -78.0162175641465$$
$$x_{2} = -75.9218224617533$$
$$x_{59} = -71.733032256967$$
$$x_{70} = -69.6386371545737$$
$$x_{36} = -65.4498469497874$$
$$x_{41} = -63.3554518473942$$
$$x_{61} = -59.1666616426078$$
$$x_{17} = -57.0722665402146$$
$$x_{13} = -52.8834763354282$$
$$x_{60} = -50.789081233035$$
$$x_{26} = -46.6002910282486$$
$$x_{43} = -44.5058959258554$$
$$x_{49} = -40.317105721069$$
$$x_{16} = -38.2227106186758$$
$$x_{40} = -34.0339204138894$$
$$x_{9} = -31.9395253114962$$
$$x_{64} = -27.7507351067098$$
$$x_{10} = -25.6563400043166$$
$$x_{68} = -21.4675497995303$$
$$x_{38} = -19.3731546971371$$
$$x_{7} = -15.1843644923507$$
$$x_{32} = -13.0899693899575$$
$$x_{31} = -8.90117918517108$$
$$x_{44} = -6.80678408277789$$
$$x_{45} = -2.61799387799149$$
$$x_{15} = -0.523598775598299$$
$$x_{58} = 3.66519142918809$$
$$x_{30} = 5.75958653158129$$
$$x_{1} = 9.94837673636768$$
$$x_{25} = 12.0427718387609$$
$$x_{22} = 16.2315620435473$$
$$x_{65} = 18.3259571459405$$
$$x_{23} = 22.5147473507269$$
$$x_{5} = 24.60914245312$$
$$x_{24} = 28.7979326579064$$
$$x_{62} = 30.8923277602996$$
$$x_{48} = 35.081117965086$$
$$x_{3} = 37.1755130674792$$
$$x_{67} = 41.3643032722656$$
$$x_{66} = 43.4586983746588$$
$$x_{63} = 47.6474885794452$$
$$x_{69} = 49.7418836818384$$
$$x_{56} = 53.9306738866248$$
$$x_{39} = 56.025068989018$$
$$x_{6} = 60.2138591938044$$
$$x_{20} = 62.3082542961976$$
$$x_{21} = 66.497044500984$$
$$x_{57} = 68.5914396033772$$
$$x_{46} = 72.7802298081635$$
$$x_{4} = 74.8746249105567$$
$$x_{37} = 79.0634151153431$$
$$x_{54} = 81.1578102177363$$
$$x_{14} = 85.3466004225227$$
$$x_{53} = 87.4409955249159$$
$$x_{42} = 91.6297857297023$$
$$x_{11} = 93.7241808320955$$
$$x_{50} = 97.9129710368819$$
$$x_{29} = 100.007366139275$$
$$x_{47} = 192.160750644576$$
$$x_{34} = 437.20497762458$$
$$x_{55} = 66400.1787274983$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{12}$$
For example, let's take the point
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-195.302343298165 + - \frac{1}{10}$$
=
$$-195.402343298165$$
substitute to the expression
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
Then
$$x \leq -195.302343298165$$
no execute
one of the solutions of our inequality is:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
$$x \geq -101.054563690472 \wedge x \leq -96.8657734856853$$
$$x \geq -94.7713783832921 \wedge x \leq -90.5825881785057$$
$$x \geq -88.4881930761125 \wedge x \leq -84.2994028713261$$
$$x \geq -82.2050077689329 \wedge x \leq -78.0162175641465$$
$$x \geq -75.9218224617533 \wedge x \leq -71.733032256967$$
$$x \geq -69.6386371545737 \wedge x \leq -65.4498469497874$$
$$x \geq -63.3554518473942 \wedge x \leq -59.1666616426078$$
$$x \geq -57.0722665402146 \wedge x \leq -52.8834763354282$$
$$x \geq -50.789081233035 \wedge x \leq -46.6002910282486$$
$$x \geq -44.5058959258554 \wedge x \leq -40.317105721069$$
$$x \geq -38.2227106186758 \wedge x \leq -34.0339204138894$$
$$x \geq -31.9395253114962 \wedge x \leq -27.7507351067098$$
$$x \geq -25.6563400043166 \wedge x \leq -21.4675497995303$$
$$x \geq -19.3731546971371 \wedge x \leq -15.1843644923507$$
$$x \geq -13.0899693899575 \wedge x \leq -8.90117918517108$$
$$x \geq -6.80678408277789 \wedge x \leq -2.61799387799149$$
$$x \geq -0.523598775598299 \wedge x \leq 3.66519142918809$$
$$x \geq 5.75958653158129 \wedge x \leq 9.94837673636768$$
$$x \geq 12.0427718387609 \wedge x \leq 16.2315620435473$$
$$x \geq 18.3259571459405 \wedge x \leq 22.5147473507269$$
$$x \geq 24.60914245312 \wedge x \leq 28.7979326579064$$
$$x \geq 30.8923277602996 \wedge x \leq 35.081117965086$$
$$x \geq 37.1755130674792 \wedge x \leq 41.3643032722656$$
$$x \geq 43.4586983746588 \wedge x \leq 47.6474885794452$$
$$x \geq 49.7418836818384 \wedge x \leq 53.9306738866248$$
$$x \geq 56.025068989018 \wedge x \leq 60.2138591938044$$
$$x \geq 62.3082542961976 \wedge x \leq 66.497044500984$$
$$x \geq 68.5914396033772 \wedge x \leq 72.7802298081635$$
$$x \geq 74.8746249105567 \wedge x \leq 79.0634151153431$$
$$x \geq 81.1578102177363 \wedge x \leq 85.3466004225227$$
$$x \geq 87.4409955249159 \wedge x \leq 91.6297857297023$$
$$x \geq 93.7241808320955 \wedge x \leq 97.9129710368819$$
$$x \geq 100.007366139275 \wedge x \leq 192.160750644576$$
$$x \geq 437.20497762458 \wedge x \leq 66400.1787274983$$
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = - \frac{1}{2}$$
Solve:
Given the equation
$$\sin{\left(t \right)} = - \frac{1}{2}$$
transform
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
Do replacement
$$w = \sin{\left(t \right)}$$
Move free summands (without w)
from left part to right part, we given:
$$w = - \frac{1}{2}$$
We get the answer: w = -1/2
do backward replacement
$$\sin{\left(t \right)} = w$$
substitute w:
$$x_{1} = 9.94837673636768$$
$$x_{2} = -75.9218224617533$$
$$x_{3} = 37.1755130674792$$
$$x_{4} = 74.8746249105567$$
$$x_{5} = 24.60914245312$$
$$x_{6} = 60.2138591938044$$
$$x_{7} = -15.1843644923507$$
$$x_{8} = -101.054563690472$$
$$x_{9} = -31.9395253114962$$
$$x_{10} = -25.6563400043166$$
$$x_{11} = 93.7241808320955$$
$$x_{12} = -195.302343298165$$
$$x_{13} = -52.8834763354282$$
$$x_{14} = 85.3466004225227$$
$$x_{15} = -0.523598775598299$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -57.0722665402146$$
$$x_{18} = -84.2994028713261$$
$$x_{19} = -90.5825881785057$$
$$x_{20} = 62.3082542961976$$
$$x_{21} = 66.497044500984$$
$$x_{22} = 16.2315620435473$$
$$x_{23} = 22.5147473507269$$
$$x_{24} = 28.7979326579064$$
$$x_{25} = 12.0427718387609$$
$$x_{26} = -46.6002910282486$$
$$x_{27} = -78.0162175641465$$
$$x_{28} = -82.2050077689329$$
$$x_{29} = 100.007366139275$$
$$x_{30} = 5.75958653158129$$
$$x_{31} = -8.90117918517108$$
$$x_{32} = -13.0899693899575$$
$$x_{33} = -88.4881930761125$$
$$x_{34} = 437.20497762458$$
$$x_{35} = -94.7713783832921$$
$$x_{36} = -65.4498469497874$$
$$x_{37} = 79.0634151153431$$
$$x_{38} = -19.3731546971371$$
$$x_{39} = 56.025068989018$$
$$x_{40} = -34.0339204138894$$
$$x_{41} = -63.3554518473942$$
$$x_{42} = 91.6297857297023$$
$$x_{43} = -44.5058959258554$$
$$x_{44} = -6.80678408277789$$
$$x_{45} = -2.61799387799149$$
$$x_{46} = 72.7802298081635$$
$$x_{47} = 192.160750644576$$
$$x_{48} = 35.081117965086$$
$$x_{49} = -40.317105721069$$
$$x_{50} = 97.9129710368819$$
$$x_{51} = -96.8657734856853$$
$$x_{52} = -151.320046147908$$
$$x_{53} = 87.4409955249159$$
$$x_{54} = 81.1578102177363$$
$$x_{55} = 66400.1787274983$$
$$x_{56} = 53.9306738866248$$
$$x_{57} = 68.5914396033772$$
$$x_{58} = 3.66519142918809$$
$$x_{59} = -71.733032256967$$
$$x_{60} = -50.789081233035$$
$$x_{61} = -59.1666616426078$$
$$x_{62} = 30.8923277602996$$
$$x_{63} = 47.6474885794452$$
$$x_{64} = -27.7507351067098$$
$$x_{65} = 18.3259571459405$$
$$x_{66} = 43.4586983746588$$
$$x_{67} = 41.3643032722656$$
$$x_{68} = -21.4675497995303$$
$$x_{69} = 49.7418836818384$$
$$x_{70} = -69.6386371545737$$
$$x_{1} = 9.94837673636768$$
$$x_{2} = -75.9218224617533$$
$$x_{3} = 37.1755130674792$$
$$x_{4} = 74.8746249105567$$
$$x_{5} = 24.60914245312$$
$$x_{6} = 60.2138591938044$$
$$x_{7} = -15.1843644923507$$
$$x_{8} = -101.054563690472$$
$$x_{9} = -31.9395253114962$$
$$x_{10} = -25.6563400043166$$
$$x_{11} = 93.7241808320955$$
$$x_{12} = -195.302343298165$$
$$x_{13} = -52.8834763354282$$
$$x_{14} = 85.3466004225227$$
$$x_{15} = -0.523598775598299$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -57.0722665402146$$
$$x_{18} = -84.2994028713261$$
$$x_{19} = -90.5825881785057$$
$$x_{20} = 62.3082542961976$$
$$x_{21} = 66.497044500984$$
$$x_{22} = 16.2315620435473$$
$$x_{23} = 22.5147473507269$$
$$x_{24} = 28.7979326579064$$
$$x_{25} = 12.0427718387609$$
$$x_{26} = -46.6002910282486$$
$$x_{27} = -78.0162175641465$$
$$x_{28} = -82.2050077689329$$
$$x_{29} = 100.007366139275$$
$$x_{30} = 5.75958653158129$$
$$x_{31} = -8.90117918517108$$
$$x_{32} = -13.0899693899575$$
$$x_{33} = -88.4881930761125$$
$$x_{34} = 437.20497762458$$
$$x_{35} = -94.7713783832921$$
$$x_{36} = -65.4498469497874$$
$$x_{37} = 79.0634151153431$$
$$x_{38} = -19.3731546971371$$
$$x_{39} = 56.025068989018$$
$$x_{40} = -34.0339204138894$$
$$x_{41} = -63.3554518473942$$
$$x_{42} = 91.6297857297023$$
$$x_{43} = -44.5058959258554$$
$$x_{44} = -6.80678408277789$$
$$x_{45} = -2.61799387799149$$
$$x_{46} = 72.7802298081635$$
$$x_{47} = 192.160750644576$$
$$x_{48} = 35.081117965086$$
$$x_{49} = -40.317105721069$$
$$x_{50} = 97.9129710368819$$
$$x_{51} = -96.8657734856853$$
$$x_{52} = -151.320046147908$$
$$x_{53} = 87.4409955249159$$
$$x_{54} = 81.1578102177363$$
$$x_{55} = 66400.1787274983$$
$$x_{56} = 53.9306738866248$$
$$x_{57} = 68.5914396033772$$
$$x_{58} = 3.66519142918809$$
$$x_{59} = -71.733032256967$$
$$x_{60} = -50.789081233035$$
$$x_{61} = -59.1666616426078$$
$$x_{62} = 30.8923277602996$$
$$x_{63} = 47.6474885794452$$
$$x_{64} = -27.7507351067098$$
$$x_{65} = 18.3259571459405$$
$$x_{66} = 43.4586983746588$$
$$x_{67} = 41.3643032722656$$
$$x_{68} = -21.4675497995303$$
$$x_{69} = 49.7418836818384$$
$$x_{70} = -69.6386371545737$$
This roots
$$x_{12} = -195.302343298165$$
$$x_{52} = -151.320046147908$$
$$x_{8} = -101.054563690472$$
$$x_{51} = -96.8657734856853$$
$$x_{35} = -94.7713783832921$$
$$x_{19} = -90.5825881785057$$
$$x_{33} = -88.4881930761125$$
$$x_{18} = -84.2994028713261$$
$$x_{28} = -82.2050077689329$$
$$x_{27} = -78.0162175641465$$
$$x_{2} = -75.9218224617533$$
$$x_{59} = -71.733032256967$$
$$x_{70} = -69.6386371545737$$
$$x_{36} = -65.4498469497874$$
$$x_{41} = -63.3554518473942$$
$$x_{61} = -59.1666616426078$$
$$x_{17} = -57.0722665402146$$
$$x_{13} = -52.8834763354282$$
$$x_{60} = -50.789081233035$$
$$x_{26} = -46.6002910282486$$
$$x_{43} = -44.5058959258554$$
$$x_{49} = -40.317105721069$$
$$x_{16} = -38.2227106186758$$
$$x_{40} = -34.0339204138894$$
$$x_{9} = -31.9395253114962$$
$$x_{64} = -27.7507351067098$$
$$x_{10} = -25.6563400043166$$
$$x_{68} = -21.4675497995303$$
$$x_{38} = -19.3731546971371$$
$$x_{7} = -15.1843644923507$$
$$x_{32} = -13.0899693899575$$
$$x_{31} = -8.90117918517108$$
$$x_{44} = -6.80678408277789$$
$$x_{45} = -2.61799387799149$$
$$x_{15} = -0.523598775598299$$
$$x_{58} = 3.66519142918809$$
$$x_{30} = 5.75958653158129$$
$$x_{1} = 9.94837673636768$$
$$x_{25} = 12.0427718387609$$
$$x_{22} = 16.2315620435473$$
$$x_{65} = 18.3259571459405$$
$$x_{23} = 22.5147473507269$$
$$x_{5} = 24.60914245312$$
$$x_{24} = 28.7979326579064$$
$$x_{62} = 30.8923277602996$$
$$x_{48} = 35.081117965086$$
$$x_{3} = 37.1755130674792$$
$$x_{67} = 41.3643032722656$$
$$x_{66} = 43.4586983746588$$
$$x_{63} = 47.6474885794452$$
$$x_{69} = 49.7418836818384$$
$$x_{56} = 53.9306738866248$$
$$x_{39} = 56.025068989018$$
$$x_{6} = 60.2138591938044$$
$$x_{20} = 62.3082542961976$$
$$x_{21} = 66.497044500984$$
$$x_{57} = 68.5914396033772$$
$$x_{46} = 72.7802298081635$$
$$x_{4} = 74.8746249105567$$
$$x_{37} = 79.0634151153431$$
$$x_{54} = 81.1578102177363$$
$$x_{14} = 85.3466004225227$$
$$x_{53} = 87.4409955249159$$
$$x_{42} = 91.6297857297023$$
$$x_{11} = 93.7241808320955$$
$$x_{50} = 97.9129710368819$$
$$x_{29} = 100.007366139275$$
$$x_{47} = 192.160750644576$$
$$x_{34} = 437.20497762458$$
$$x_{55} = 66400.1787274983$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{12}$$
For example, let's take the point
$$x_{0} = x_{12} - \frac{1}{10}$$
=
$$-195.302343298165 + - \frac{1}{10}$$
=
$$-195.402343298165$$
substitute to the expression
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
sin(t) >= -1/2
Then
$$x \leq -195.302343298165$$
no execute
one of the solutions of our inequality is:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
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x12 x52 x8 x51 x35 x19 x33 x18 x28 x27 x2 x59 x70 x36 x41 x61 x17 x13 x60 x26 x43 x49 x16 x40 x9 x64 x10 x68 x38 x7 x32 x31 x44 x45 x15 x58 x30 x1 x25 x22 x65 x23 x5 x24 x62 x48 x3 x67 x66 x63 x69 x56 x39 x6 x20 x21 x57 x46 x4 x37 x54 x14 x53 x42 x11 x50 x29 x47 x34 x55Other solutions will get with the changeover to the next point
etc.
The answer:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
$$x \geq -101.054563690472 \wedge x \leq -96.8657734856853$$
$$x \geq -94.7713783832921 \wedge x \leq -90.5825881785057$$
$$x \geq -88.4881930761125 \wedge x \leq -84.2994028713261$$
$$x \geq -82.2050077689329 \wedge x \leq -78.0162175641465$$
$$x \geq -75.9218224617533 \wedge x \leq -71.733032256967$$
$$x \geq -69.6386371545737 \wedge x \leq -65.4498469497874$$
$$x \geq -63.3554518473942 \wedge x \leq -59.1666616426078$$
$$x \geq -57.0722665402146 \wedge x \leq -52.8834763354282$$
$$x \geq -50.789081233035 \wedge x \leq -46.6002910282486$$
$$x \geq -44.5058959258554 \wedge x \leq -40.317105721069$$
$$x \geq -38.2227106186758 \wedge x \leq -34.0339204138894$$
$$x \geq -31.9395253114962 \wedge x \leq -27.7507351067098$$
$$x \geq -25.6563400043166 \wedge x \leq -21.4675497995303$$
$$x \geq -19.3731546971371 \wedge x \leq -15.1843644923507$$
$$x \geq -13.0899693899575 \wedge x \leq -8.90117918517108$$
$$x \geq -6.80678408277789 \wedge x \leq -2.61799387799149$$
$$x \geq -0.523598775598299 \wedge x \leq 3.66519142918809$$
$$x \geq 5.75958653158129 \wedge x \leq 9.94837673636768$$
$$x \geq 12.0427718387609 \wedge x \leq 16.2315620435473$$
$$x \geq 18.3259571459405 \wedge x \leq 22.5147473507269$$
$$x \geq 24.60914245312 \wedge x \leq 28.7979326579064$$
$$x \geq 30.8923277602996 \wedge x \leq 35.081117965086$$
$$x \geq 37.1755130674792 \wedge x \leq 41.3643032722656$$
$$x \geq 43.4586983746588 \wedge x \leq 47.6474885794452$$
$$x \geq 49.7418836818384 \wedge x \leq 53.9306738866248$$
$$x \geq 56.025068989018 \wedge x \leq 60.2138591938044$$
$$x \geq 62.3082542961976 \wedge x \leq 66.497044500984$$
$$x \geq 68.5914396033772 \wedge x \leq 72.7802298081635$$
$$x \geq 74.8746249105567 \wedge x \leq 79.0634151153431$$
$$x \geq 81.1578102177363 \wedge x \leq 85.3466004225227$$
$$x \geq 87.4409955249159 \wedge x \leq 91.6297857297023$$
$$x \geq 93.7241808320955 \wedge x \leq 97.9129710368819$$
$$x \geq 100.007366139275 \wedge x \leq 192.160750644576$$
$$x \geq 437.20497762458 \wedge x \leq 66400.1787274983$$
Rapid solution
[src]
/ / 7*pi\ /11*pi \\ Or|And|0 <= t, t <= ----|, And|----- <= t, t <= 2*pi|| \ \ 6 / \ 6 //
$$\left(0 \leq t \wedge t \leq \frac{7 \pi}{6}\right) \vee \left(\frac{11 \pi}{6} \leq t \wedge t \leq 2 \pi\right)$$
((0 <= t)∧(t <= 7*pi/6))∨((11*pi/6 <= t)∧(t <= 2*pi))
Rapid solution 2
[src]
7*pi 11*pi
[0, ----] U [-----, 2*pi]
6 6
$$x\ in\ \left[0, \frac{7 \pi}{6}\right] \cup \left[\frac{11 \pi}{6}, 2 \pi\right]$$
x in Union(Interval(0, 7*pi/6), Interval(11*pi/6, 2*pi))