Sr Examen
Otras calculadoras
- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
-
(x+2)(x^2+x-12)>0
-
(x+7)*(x-5)<0
-
(x+5)(x-9)>0
-
x^2>7
-
Expresiones idénticas
- | uno +sin(x)|>= uno / dos
- módulo de 1 más seno de (x)| más o igual a 1 dividir por 2
- módulo de uno más seno de (x)| más o igual a uno dividir por dos
- |1+sinx|>=1/2
- |1+sin(x)|>=1 dividir por 2
-
Expresiones semejantes
- |1+sinx|<=1/2
- |1-sin(x)|>=1/2
- |1+sinx|>=1/2
-
Expresiones con funciones
- Seno sin
- sin(x)<=0
- sin(3x)>0
- sin((-4)*x+3*pi/2)>=0
- sin(2*x)>1/2
- sin(3*x)<-1/2
- Módulo |
- |3x+4|>2
- |2-x|<3
- |4+3x|>=2
- |2-x|<=5
- |2x-5|^(x+1)+|2x-5|^(-x-1)<=2
|1+sin(x)|>=1/2 desigualdades
Solución
Ha introducido
[src]
|1 + sin(x)| >= 1/2
$$\left|{\sin{\left(x \right)} + 1}\right| \geq \frac{1}{2}$$
Abs(sin(x) + 1) >= 1/2
Solución detallada
Se da la desigualdad:
$$\left|{\sin{\left(x \right)} + 1}\right| \geq \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(x \right)} + 1}\right| = \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\left|{\sin{\left(x \right)} + 1}\right| = \frac{1}{2}$$
cambiamos
$$\left|{\sin{\left(x \right)} + 1}\right| - \frac{1}{2} = 0$$
$$\left|{\sin{\left(x \right)} + 1}\right| - \frac{1}{2} = 0$$
Sustituimos
$$w = \left|{\sin{\left(x \right)} + 1}\right|$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\left|{\sin{\left(x \right)} + 1}\right| = w$$
sustituimos w:
$$x_{1} = -52.8834763354282$$
$$x_{2} = 47.6474885794452$$
$$x_{3} = 62.3082542961976$$
$$x_{4} = 68.5914396033772$$
$$x_{5} = -84.2994028713261$$
$$x_{6} = -195.302343298165$$
$$x_{7} = -69.6386371545737$$
$$x_{8} = 97.9129710368819$$
$$x_{9} = 93.7241808320955$$
$$x_{10} = -96.8657734856853$$
$$x_{11} = 22.5147473507269$$
$$x_{12} = 24.60914245312$$
$$x_{13} = 28.7979326579064$$
$$x_{14} = -31.9395253114962$$
$$x_{15} = 81.1578102177363$$
$$x_{16} = -8.90117918517108$$
$$x_{17} = 60.2138591938044$$
$$x_{18} = -59.1666616426078$$
$$x_{19} = 100.007366139275$$
$$x_{20} = -46.6002910282486$$
$$x_{21} = -151.320046147908$$
$$x_{22} = -44.5058959258554$$
$$x_{23} = 35.081117965086$$
$$x_{24} = -78.0162175641465$$
$$x_{25} = 56.025068989018$$
$$x_{26} = 66437.8778393414$$
$$x_{27} = 9.94837673636768$$
$$x_{28} = 12.0427718387609$$
$$x_{29} = 37.1755130674792$$
$$x_{30} = 41.3643032722656$$
$$x_{31} = 91.6297857297023$$
$$x_{32} = -38.2227106186758$$
$$x_{33} = 18.3259571459405$$
$$x_{34} = 66.497044500984$$
$$x_{35} = -63.3554518473942$$
$$x_{36} = -75.9218224617533$$
$$x_{37} = 72.7802298081635$$
$$x_{38} = 79.0634151153431$$
$$x_{39} = 53.9306738866248$$
$$x_{40} = -13.0899693899575$$
$$x_{41} = 5.75958653158129$$
$$x_{42} = -40.317105721069$$
$$x_{43} = 437.20497762458$$
$$x_{44} = 192.160750644576$$
$$x_{45} = -19.3731546971371$$
$$x_{46} = 74.8746249105567$$
$$x_{47} = 87.4409955249159$$
$$x_{48} = -65.4498469497874$$
$$x_{49} = 43.4586983746588$$
$$x_{50} = -2.61799387799149$$
$$x_{51} = -0.523598775598299$$
$$x_{52} = -6.80678408277789$$
$$x_{53} = -50.789081233035$$
$$x_{54} = 16.2315620435473$$
$$x_{55} = -88.4881930761125$$
$$x_{56} = -71.733032256967$$
$$x_{57} = -94.7713783832921$$
$$x_{58} = 30.8923277602996$$
$$x_{59} = -34.0339204138894$$
$$x_{60} = -90.5825881785057$$
$$x_{61} = 872.839158922364$$
$$x_{62} = -15.1843644923507$$
$$x_{63} = 49.7418836818384$$
$$x_{64} = -57.0722665402146$$
$$x_{65} = -21.4675497995303$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -82.2050077689329$$
$$x_{68} = -25.6563400043166$$
$$x_{69} = 3.66519142918809$$
$$x_{70} = -27.7507351067098$$
$$x_{71} = 85.3466004225227$$
$$x_{1} = -52.8834763354282$$
$$x_{2} = 47.6474885794452$$
$$x_{3} = 62.3082542961976$$
$$x_{4} = 68.5914396033772$$
$$x_{5} = -84.2994028713261$$
$$x_{6} = -195.302343298165$$
$$x_{7} = -69.6386371545737$$
$$x_{8} = 97.9129710368819$$
$$x_{9} = 93.7241808320955$$
$$x_{10} = -96.8657734856853$$
$$x_{11} = 22.5147473507269$$
$$x_{12} = 24.60914245312$$
$$x_{13} = 28.7979326579064$$
$$x_{14} = -31.9395253114962$$
$$x_{15} = 81.1578102177363$$
$$x_{16} = -8.90117918517108$$
$$x_{17} = 60.2138591938044$$
$$x_{18} = -59.1666616426078$$
$$x_{19} = 100.007366139275$$
$$x_{20} = -46.6002910282486$$
$$x_{21} = -151.320046147908$$
$$x_{22} = -44.5058959258554$$
$$x_{23} = 35.081117965086$$
$$x_{24} = -78.0162175641465$$
$$x_{25} = 56.025068989018$$
$$x_{26} = 66437.8778393414$$
$$x_{27} = 9.94837673636768$$
$$x_{28} = 12.0427718387609$$
$$x_{29} = 37.1755130674792$$
$$x_{30} = 41.3643032722656$$
$$x_{31} = 91.6297857297023$$
$$x_{32} = -38.2227106186758$$
$$x_{33} = 18.3259571459405$$
$$x_{34} = 66.497044500984$$
$$x_{35} = -63.3554518473942$$
$$x_{36} = -75.9218224617533$$
$$x_{37} = 72.7802298081635$$
$$x_{38} = 79.0634151153431$$
$$x_{39} = 53.9306738866248$$
$$x_{40} = -13.0899693899575$$
$$x_{41} = 5.75958653158129$$
$$x_{42} = -40.317105721069$$
$$x_{43} = 437.20497762458$$
$$x_{44} = 192.160750644576$$
$$x_{45} = -19.3731546971371$$
$$x_{46} = 74.8746249105567$$
$$x_{47} = 87.4409955249159$$
$$x_{48} = -65.4498469497874$$
$$x_{49} = 43.4586983746588$$
$$x_{50} = -2.61799387799149$$
$$x_{51} = -0.523598775598299$$
$$x_{52} = -6.80678408277789$$
$$x_{53} = -50.789081233035$$
$$x_{54} = 16.2315620435473$$
$$x_{55} = -88.4881930761125$$
$$x_{56} = -71.733032256967$$
$$x_{57} = -94.7713783832921$$
$$x_{58} = 30.8923277602996$$
$$x_{59} = -34.0339204138894$$
$$x_{60} = -90.5825881785057$$
$$x_{61} = 872.839158922364$$
$$x_{62} = -15.1843644923507$$
$$x_{63} = 49.7418836818384$$
$$x_{64} = -57.0722665402146$$
$$x_{65} = -21.4675497995303$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -82.2050077689329$$
$$x_{68} = -25.6563400043166$$
$$x_{69} = 3.66519142918809$$
$$x_{70} = -27.7507351067098$$
$$x_{71} = 85.3466004225227$$
Las raíces dadas
$$x_{6} = -195.302343298165$$
$$x_{21} = -151.320046147908$$
$$x_{66} = -101.054563690472$$
$$x_{10} = -96.8657734856853$$
$$x_{57} = -94.7713783832921$$
$$x_{60} = -90.5825881785057$$
$$x_{55} = -88.4881930761125$$
$$x_{5} = -84.2994028713261$$
$$x_{67} = -82.2050077689329$$
$$x_{24} = -78.0162175641465$$
$$x_{36} = -75.9218224617533$$
$$x_{56} = -71.733032256967$$
$$x_{7} = -69.6386371545737$$
$$x_{48} = -65.4498469497874$$
$$x_{35} = -63.3554518473942$$
$$x_{18} = -59.1666616426078$$
$$x_{64} = -57.0722665402146$$
$$x_{1} = -52.8834763354282$$
$$x_{53} = -50.789081233035$$
$$x_{20} = -46.6002910282486$$
$$x_{22} = -44.5058959258554$$
$$x_{42} = -40.317105721069$$
$$x_{32} = -38.2227106186758$$
$$x_{59} = -34.0339204138894$$
$$x_{14} = -31.9395253114962$$
$$x_{70} = -27.7507351067098$$
$$x_{68} = -25.6563400043166$$
$$x_{65} = -21.4675497995303$$
$$x_{45} = -19.3731546971371$$
$$x_{62} = -15.1843644923507$$
$$x_{40} = -13.0899693899575$$
$$x_{16} = -8.90117918517108$$
$$x_{52} = -6.80678408277789$$
$$x_{50} = -2.61799387799149$$
$$x_{51} = -0.523598775598299$$
$$x_{69} = 3.66519142918809$$
$$x_{41} = 5.75958653158129$$
$$x_{27} = 9.94837673636768$$
$$x_{28} = 12.0427718387609$$
$$x_{54} = 16.2315620435473$$
$$x_{33} = 18.3259571459405$$
$$x_{11} = 22.5147473507269$$
$$x_{12} = 24.60914245312$$
$$x_{13} = 28.7979326579064$$
$$x_{58} = 30.8923277602996$$
$$x_{23} = 35.081117965086$$
$$x_{29} = 37.1755130674792$$
$$x_{30} = 41.3643032722656$$
$$x_{49} = 43.4586983746588$$
$$x_{2} = 47.6474885794452$$
$$x_{63} = 49.7418836818384$$
$$x_{39} = 53.9306738866248$$
$$x_{25} = 56.025068989018$$
$$x_{17} = 60.2138591938044$$
$$x_{3} = 62.3082542961976$$
$$x_{34} = 66.497044500984$$
$$x_{4} = 68.5914396033772$$
$$x_{37} = 72.7802298081635$$
$$x_{46} = 74.8746249105567$$
$$x_{38} = 79.0634151153431$$
$$x_{15} = 81.1578102177363$$
$$x_{71} = 85.3466004225227$$
$$x_{47} = 87.4409955249159$$
$$x_{31} = 91.6297857297023$$
$$x_{9} = 93.7241808320955$$
$$x_{8} = 97.9129710368819$$
$$x_{19} = 100.007366139275$$
$$x_{44} = 192.160750644576$$
$$x_{43} = 437.20497762458$$
$$x_{61} = 872.839158922364$$
$$x_{26} = 66437.8778393414$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{6}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{6} - \frac{1}{10}$$
=
$$-195.302343298165 + - \frac{1}{10}$$
=
$$-195.402343298165$$
lo sustituimos en la expresión
$$\left|{\sin{\left(x \right)} + 1}\right| \geq \frac{1}{2}$$
$$\left|{\sin{\left(-195.402343298165 \right)} + 1}\right| \geq \frac{1}{2}$$
pero
Entonces
$$x \leq -195.302343298165$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
$$x \geq -101.054563690472 \wedge x \leq -96.8657734856853$$
$$x \geq -94.7713783832921 \wedge x \leq -90.5825881785057$$
$$x \geq -88.4881930761125 \wedge x \leq -84.2994028713261$$
$$x \geq -82.2050077689329 \wedge x \leq -78.0162175641465$$
$$x \geq -75.9218224617533 \wedge x \leq -71.733032256967$$
$$x \geq -69.6386371545737 \wedge x \leq -65.4498469497874$$
$$x \geq -63.3554518473942 \wedge x \leq -59.1666616426078$$
$$x \geq -57.0722665402146 \wedge x \leq -52.8834763354282$$
$$x \geq -50.789081233035 \wedge x \leq -46.6002910282486$$
$$x \geq -44.5058959258554 \wedge x \leq -40.317105721069$$
$$x \geq -38.2227106186758 \wedge x \leq -34.0339204138894$$
$$x \geq -31.9395253114962 \wedge x \leq -27.7507351067098$$
$$x \geq -25.6563400043166 \wedge x \leq -21.4675497995303$$
$$x \geq -19.3731546971371 \wedge x \leq -15.1843644923507$$
$$x \geq -13.0899693899575 \wedge x \leq -8.90117918517108$$
$$x \geq -6.80678408277789 \wedge x \leq -2.61799387799149$$
$$x \geq -0.523598775598299 \wedge x \leq 3.66519142918809$$
$$x \geq 5.75958653158129 \wedge x \leq 9.94837673636768$$
$$x \geq 12.0427718387609 \wedge x \leq 16.2315620435473$$
$$x \geq 18.3259571459405 \wedge x \leq 22.5147473507269$$
$$x \geq 24.60914245312 \wedge x \leq 28.7979326579064$$
$$x \geq 30.8923277602996 \wedge x \leq 35.081117965086$$
$$x \geq 37.1755130674792 \wedge x \leq 41.3643032722656$$
$$x \geq 43.4586983746588 \wedge x \leq 47.6474885794452$$
$$x \geq 49.7418836818384 \wedge x \leq 53.9306738866248$$
$$x \geq 56.025068989018 \wedge x \leq 60.2138591938044$$
$$x \geq 62.3082542961976 \wedge x \leq 66.497044500984$$
$$x \geq 68.5914396033772 \wedge x \leq 72.7802298081635$$
$$x \geq 74.8746249105567 \wedge x \leq 79.0634151153431$$
$$x \geq 81.1578102177363 \wedge x \leq 85.3466004225227$$
$$x \geq 87.4409955249159 \wedge x \leq 91.6297857297023$$
$$x \geq 93.7241808320955 \wedge x \leq 97.9129710368819$$
$$x \geq 100.007366139275 \wedge x \leq 192.160750644576$$
$$x \geq 437.20497762458 \wedge x \leq 872.839158922364$$
$$x \geq 66437.8778393414$$
$$\left|{\sin{\left(x \right)} + 1}\right| \geq \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(x \right)} + 1}\right| = \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\left|{\sin{\left(x \right)} + 1}\right| = \frac{1}{2}$$
cambiamos
$$\left|{\sin{\left(x \right)} + 1}\right| - \frac{1}{2} = 0$$
$$\left|{\sin{\left(x \right)} + 1}\right| - \frac{1}{2} = 0$$
Sustituimos
$$w = \left|{\sin{\left(x \right)} + 1}\right|$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\left|{\sin{\left(x \right)} + 1}\right| = w$$
sustituimos w:
$$x_{1} = -52.8834763354282$$
$$x_{2} = 47.6474885794452$$
$$x_{3} = 62.3082542961976$$
$$x_{4} = 68.5914396033772$$
$$x_{5} = -84.2994028713261$$
$$x_{6} = -195.302343298165$$
$$x_{7} = -69.6386371545737$$
$$x_{8} = 97.9129710368819$$
$$x_{9} = 93.7241808320955$$
$$x_{10} = -96.8657734856853$$
$$x_{11} = 22.5147473507269$$
$$x_{12} = 24.60914245312$$
$$x_{13} = 28.7979326579064$$
$$x_{14} = -31.9395253114962$$
$$x_{15} = 81.1578102177363$$
$$x_{16} = -8.90117918517108$$
$$x_{17} = 60.2138591938044$$
$$x_{18} = -59.1666616426078$$
$$x_{19} = 100.007366139275$$
$$x_{20} = -46.6002910282486$$
$$x_{21} = -151.320046147908$$
$$x_{22} = -44.5058959258554$$
$$x_{23} = 35.081117965086$$
$$x_{24} = -78.0162175641465$$
$$x_{25} = 56.025068989018$$
$$x_{26} = 66437.8778393414$$
$$x_{27} = 9.94837673636768$$
$$x_{28} = 12.0427718387609$$
$$x_{29} = 37.1755130674792$$
$$x_{30} = 41.3643032722656$$
$$x_{31} = 91.6297857297023$$
$$x_{32} = -38.2227106186758$$
$$x_{33} = 18.3259571459405$$
$$x_{34} = 66.497044500984$$
$$x_{35} = -63.3554518473942$$
$$x_{36} = -75.9218224617533$$
$$x_{37} = 72.7802298081635$$
$$x_{38} = 79.0634151153431$$
$$x_{39} = 53.9306738866248$$
$$x_{40} = -13.0899693899575$$
$$x_{41} = 5.75958653158129$$
$$x_{42} = -40.317105721069$$
$$x_{43} = 437.20497762458$$
$$x_{44} = 192.160750644576$$
$$x_{45} = -19.3731546971371$$
$$x_{46} = 74.8746249105567$$
$$x_{47} = 87.4409955249159$$
$$x_{48} = -65.4498469497874$$
$$x_{49} = 43.4586983746588$$
$$x_{50} = -2.61799387799149$$
$$x_{51} = -0.523598775598299$$
$$x_{52} = -6.80678408277789$$
$$x_{53} = -50.789081233035$$
$$x_{54} = 16.2315620435473$$
$$x_{55} = -88.4881930761125$$
$$x_{56} = -71.733032256967$$
$$x_{57} = -94.7713783832921$$
$$x_{58} = 30.8923277602996$$
$$x_{59} = -34.0339204138894$$
$$x_{60} = -90.5825881785057$$
$$x_{61} = 872.839158922364$$
$$x_{62} = -15.1843644923507$$
$$x_{63} = 49.7418836818384$$
$$x_{64} = -57.0722665402146$$
$$x_{65} = -21.4675497995303$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -82.2050077689329$$
$$x_{68} = -25.6563400043166$$
$$x_{69} = 3.66519142918809$$
$$x_{70} = -27.7507351067098$$
$$x_{71} = 85.3466004225227$$
$$x_{1} = -52.8834763354282$$
$$x_{2} = 47.6474885794452$$
$$x_{3} = 62.3082542961976$$
$$x_{4} = 68.5914396033772$$
$$x_{5} = -84.2994028713261$$
$$x_{6} = -195.302343298165$$
$$x_{7} = -69.6386371545737$$
$$x_{8} = 97.9129710368819$$
$$x_{9} = 93.7241808320955$$
$$x_{10} = -96.8657734856853$$
$$x_{11} = 22.5147473507269$$
$$x_{12} = 24.60914245312$$
$$x_{13} = 28.7979326579064$$
$$x_{14} = -31.9395253114962$$
$$x_{15} = 81.1578102177363$$
$$x_{16} = -8.90117918517108$$
$$x_{17} = 60.2138591938044$$
$$x_{18} = -59.1666616426078$$
$$x_{19} = 100.007366139275$$
$$x_{20} = -46.6002910282486$$
$$x_{21} = -151.320046147908$$
$$x_{22} = -44.5058959258554$$
$$x_{23} = 35.081117965086$$
$$x_{24} = -78.0162175641465$$
$$x_{25} = 56.025068989018$$
$$x_{26} = 66437.8778393414$$
$$x_{27} = 9.94837673636768$$
$$x_{28} = 12.0427718387609$$
$$x_{29} = 37.1755130674792$$
$$x_{30} = 41.3643032722656$$
$$x_{31} = 91.6297857297023$$
$$x_{32} = -38.2227106186758$$
$$x_{33} = 18.3259571459405$$
$$x_{34} = 66.497044500984$$
$$x_{35} = -63.3554518473942$$
$$x_{36} = -75.9218224617533$$
$$x_{37} = 72.7802298081635$$
$$x_{38} = 79.0634151153431$$
$$x_{39} = 53.9306738866248$$
$$x_{40} = -13.0899693899575$$
$$x_{41} = 5.75958653158129$$
$$x_{42} = -40.317105721069$$
$$x_{43} = 437.20497762458$$
$$x_{44} = 192.160750644576$$
$$x_{45} = -19.3731546971371$$
$$x_{46} = 74.8746249105567$$
$$x_{47} = 87.4409955249159$$
$$x_{48} = -65.4498469497874$$
$$x_{49} = 43.4586983746588$$
$$x_{50} = -2.61799387799149$$
$$x_{51} = -0.523598775598299$$
$$x_{52} = -6.80678408277789$$
$$x_{53} = -50.789081233035$$
$$x_{54} = 16.2315620435473$$
$$x_{55} = -88.4881930761125$$
$$x_{56} = -71.733032256967$$
$$x_{57} = -94.7713783832921$$
$$x_{58} = 30.8923277602996$$
$$x_{59} = -34.0339204138894$$
$$x_{60} = -90.5825881785057$$
$$x_{61} = 872.839158922364$$
$$x_{62} = -15.1843644923507$$
$$x_{63} = 49.7418836818384$$
$$x_{64} = -57.0722665402146$$
$$x_{65} = -21.4675497995303$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -82.2050077689329$$
$$x_{68} = -25.6563400043166$$
$$x_{69} = 3.66519142918809$$
$$x_{70} = -27.7507351067098$$
$$x_{71} = 85.3466004225227$$
Las raíces dadas
$$x_{6} = -195.302343298165$$
$$x_{21} = -151.320046147908$$
$$x_{66} = -101.054563690472$$
$$x_{10} = -96.8657734856853$$
$$x_{57} = -94.7713783832921$$
$$x_{60} = -90.5825881785057$$
$$x_{55} = -88.4881930761125$$
$$x_{5} = -84.2994028713261$$
$$x_{67} = -82.2050077689329$$
$$x_{24} = -78.0162175641465$$
$$x_{36} = -75.9218224617533$$
$$x_{56} = -71.733032256967$$
$$x_{7} = -69.6386371545737$$
$$x_{48} = -65.4498469497874$$
$$x_{35} = -63.3554518473942$$
$$x_{18} = -59.1666616426078$$
$$x_{64} = -57.0722665402146$$
$$x_{1} = -52.8834763354282$$
$$x_{53} = -50.789081233035$$
$$x_{20} = -46.6002910282486$$
$$x_{22} = -44.5058959258554$$
$$x_{42} = -40.317105721069$$
$$x_{32} = -38.2227106186758$$
$$x_{59} = -34.0339204138894$$
$$x_{14} = -31.9395253114962$$
$$x_{70} = -27.7507351067098$$
$$x_{68} = -25.6563400043166$$
$$x_{65} = -21.4675497995303$$
$$x_{45} = -19.3731546971371$$
$$x_{62} = -15.1843644923507$$
$$x_{40} = -13.0899693899575$$
$$x_{16} = -8.90117918517108$$
$$x_{52} = -6.80678408277789$$
$$x_{50} = -2.61799387799149$$
$$x_{51} = -0.523598775598299$$
$$x_{69} = 3.66519142918809$$
$$x_{41} = 5.75958653158129$$
$$x_{27} = 9.94837673636768$$
$$x_{28} = 12.0427718387609$$
$$x_{54} = 16.2315620435473$$
$$x_{33} = 18.3259571459405$$
$$x_{11} = 22.5147473507269$$
$$x_{12} = 24.60914245312$$
$$x_{13} = 28.7979326579064$$
$$x_{58} = 30.8923277602996$$
$$x_{23} = 35.081117965086$$
$$x_{29} = 37.1755130674792$$
$$x_{30} = 41.3643032722656$$
$$x_{49} = 43.4586983746588$$
$$x_{2} = 47.6474885794452$$
$$x_{63} = 49.7418836818384$$
$$x_{39} = 53.9306738866248$$
$$x_{25} = 56.025068989018$$
$$x_{17} = 60.2138591938044$$
$$x_{3} = 62.3082542961976$$
$$x_{34} = 66.497044500984$$
$$x_{4} = 68.5914396033772$$
$$x_{37} = 72.7802298081635$$
$$x_{46} = 74.8746249105567$$
$$x_{38} = 79.0634151153431$$
$$x_{15} = 81.1578102177363$$
$$x_{71} = 85.3466004225227$$
$$x_{47} = 87.4409955249159$$
$$x_{31} = 91.6297857297023$$
$$x_{9} = 93.7241808320955$$
$$x_{8} = 97.9129710368819$$
$$x_{19} = 100.007366139275$$
$$x_{44} = 192.160750644576$$
$$x_{43} = 437.20497762458$$
$$x_{61} = 872.839158922364$$
$$x_{26} = 66437.8778393414$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{6}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{6} - \frac{1}{10}$$
=
$$-195.302343298165 + - \frac{1}{10}$$
=
$$-195.402343298165$$
lo sustituimos en la expresión
$$\left|{\sin{\left(x \right)} + 1}\right| \geq \frac{1}{2}$$
$$\left|{\sin{\left(-195.402343298165 \right)} + 1}\right| \geq \frac{1}{2}$$
0.416039642398240 >= 1/2
pero
0.416039642398240 < 1/2
Entonces
$$x \leq -195.302343298165$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
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x6 x21 x66 x10 x57 x60 x55 x5 x67 x24 x36 x56 x7 x48 x35 x18 x64 x1 x53 x20 x22 x42 x32 x59 x14 x70 x68 x65 x45 x62 x40 x16 x52 x50 x51 x69 x41 x27 x28 x54 x33 x11 x12 x13 x58 x23 x29 x30 x49 x2 x63 x39 x25 x17 x3 x34 x4 x37 x46 x38 x15 x71 x47 x31 x9 x8 x19 x44 x43 x61 x26Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
$$x \geq -101.054563690472 \wedge x \leq -96.8657734856853$$
$$x \geq -94.7713783832921 \wedge x \leq -90.5825881785057$$
$$x \geq -88.4881930761125 \wedge x \leq -84.2994028713261$$
$$x \geq -82.2050077689329 \wedge x \leq -78.0162175641465$$
$$x \geq -75.9218224617533 \wedge x \leq -71.733032256967$$
$$x \geq -69.6386371545737 \wedge x \leq -65.4498469497874$$
$$x \geq -63.3554518473942 \wedge x \leq -59.1666616426078$$
$$x \geq -57.0722665402146 \wedge x \leq -52.8834763354282$$
$$x \geq -50.789081233035 \wedge x \leq -46.6002910282486$$
$$x \geq -44.5058959258554 \wedge x \leq -40.317105721069$$
$$x \geq -38.2227106186758 \wedge x \leq -34.0339204138894$$
$$x \geq -31.9395253114962 \wedge x \leq -27.7507351067098$$
$$x \geq -25.6563400043166 \wedge x \leq -21.4675497995303$$
$$x \geq -19.3731546971371 \wedge x \leq -15.1843644923507$$
$$x \geq -13.0899693899575 \wedge x \leq -8.90117918517108$$
$$x \geq -6.80678408277789 \wedge x \leq -2.61799387799149$$
$$x \geq -0.523598775598299 \wedge x \leq 3.66519142918809$$
$$x \geq 5.75958653158129 \wedge x \leq 9.94837673636768$$
$$x \geq 12.0427718387609 \wedge x \leq 16.2315620435473$$
$$x \geq 18.3259571459405 \wedge x \leq 22.5147473507269$$
$$x \geq 24.60914245312 \wedge x \leq 28.7979326579064$$
$$x \geq 30.8923277602996 \wedge x \leq 35.081117965086$$
$$x \geq 37.1755130674792 \wedge x \leq 41.3643032722656$$
$$x \geq 43.4586983746588 \wedge x \leq 47.6474885794452$$
$$x \geq 49.7418836818384 \wedge x \leq 53.9306738866248$$
$$x \geq 56.025068989018 \wedge x \leq 60.2138591938044$$
$$x \geq 62.3082542961976 \wedge x \leq 66.497044500984$$
$$x \geq 68.5914396033772 \wedge x \leq 72.7802298081635$$
$$x \geq 74.8746249105567 \wedge x \leq 79.0634151153431$$
$$x \geq 81.1578102177363 \wedge x \leq 85.3466004225227$$
$$x \geq 87.4409955249159 \wedge x \leq 91.6297857297023$$
$$x \geq 93.7241808320955 \wedge x \leq 97.9129710368819$$
$$x \geq 100.007366139275 \wedge x \leq 192.160750644576$$
$$x \geq 437.20497762458 \wedge x \leq 872.839158922364$$
$$x \geq 66437.8778393414$$
Solución de la desigualdad en el gráfico