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+1)*(x-9)>0
-
x^2+x-6>0
-
(x-1)/(x-4)>0
-
-16/(x+2)^2-5>=0
- Derivada de:
-
sin(t)
- Integral de d{x}:
- sin(t)
-
Expresiones idénticas
- sin(t)>=- uno / dos
- seno de (t) más o igual a menos 1 dividir por 2
- seno de (t) más o igual a menos uno dividir por dos
- sint>=-1/2
- sin(t)>=-1 dividir por 2
-
Expresiones semejantes
- sint<√3/2
- sint>0
- sin(t)>=+1/2
- sint>=-2
-
Expresiones con funciones
- Seno sin
- sin(x)>0
- sin(x)<sqrt(3)/2
- sin(x)<√3/2
- sinx>-1
- sin(x)>1/2
sin(t)>=-1/2 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(t \right)} = - \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\sin{\left(t \right)} = - \frac{1}{2}$$
cambiamos
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
Sustituimos
$$w = \sin{\left(t \right)}$$
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
$$\sin{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 47.6474885794452$$
$$x_{2} = 74.8746249105567$$
$$x_{3} = 81.1578102177363$$
$$x_{4} = -27.7507351067098$$
$$x_{5} = 60.2138591938044$$
$$x_{6} = -19.3731546971371$$
$$x_{7} = -50.789081233035$$
$$x_{8} = 437.20497762458$$
$$x_{9} = -21.4675497995303$$
$$x_{10} = -44.5058959258554$$
$$x_{11} = -57.0722665402146$$
$$x_{12} = 43.4586983746588$$
$$x_{13} = 18.3259571459405$$
$$x_{14} = -34.0339204138894$$
$$x_{15} = -151.320046147908$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -59.1666616426078$$
$$x_{18} = 72.7802298081635$$
$$x_{19} = -13.0899693899575$$
$$x_{20} = 3.66519142918809$$
$$x_{21} = -6.80678408277789$$
$$x_{22} = -52.8834763354282$$
$$x_{23} = -65.4498469497874$$
$$x_{24} = -46.6002910282486$$
$$x_{25} = 87.4409955249159$$
$$x_{26} = -88.4881930761125$$
$$x_{27} = 24.60914245312$$
$$x_{28} = 100.007366139275$$
$$x_{29} = -31.9395253114962$$
$$x_{30} = 79.0634151153431$$
$$x_{31} = -63.3554518473942$$
$$x_{32} = 56.025068989018$$
$$x_{33} = 41.3643032722656$$
$$x_{34} = 91.6297857297023$$
$$x_{35} = 28.7979326579064$$
$$x_{36} = 93.7241808320955$$
$$x_{37} = -69.6386371545737$$
$$x_{38} = 37.1755130674792$$
$$x_{39} = 66400.1787274983$$
$$x_{40} = 53.9306738866248$$
$$x_{41} = 16.2315620435473$$
$$x_{42} = -75.9218224617533$$
$$x_{43} = -94.7713783832921$$
$$x_{44} = -78.0162175641465$$
$$x_{45} = 68.5914396033772$$
$$x_{46} = -82.2050077689329$$
$$x_{47} = -96.8657734856853$$
$$x_{48} = -84.2994028713261$$
$$x_{49} = 9.94837673636768$$
$$x_{50} = -0.523598775598299$$
$$x_{51} = 12.0427718387609$$
$$x_{52} = -2.61799387799149$$
$$x_{53} = -195.302343298165$$
$$x_{54} = 49.7418836818384$$
$$x_{55} = -71.733032256967$$
$$x_{56} = -40.317105721069$$
$$x_{57} = -8.90117918517108$$
$$x_{58} = 66.497044500984$$
$$x_{59} = 35.081117965086$$
$$x_{60} = 85.3466004225227$$
$$x_{61} = 192.160750644576$$
$$x_{62} = 5.75958653158129$$
$$x_{63} = -90.5825881785057$$
$$x_{64} = -25.6563400043166$$
$$x_{65} = 22.5147473507269$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -15.1843644923507$$
$$x_{68} = 62.3082542961976$$
$$x_{69} = 30.8923277602996$$
$$x_{70} = 97.9129710368819$$
$$x_{1} = 47.6474885794452$$
$$x_{2} = 74.8746249105567$$
$$x_{3} = 81.1578102177363$$
$$x_{4} = -27.7507351067098$$
$$x_{5} = 60.2138591938044$$
$$x_{6} = -19.3731546971371$$
$$x_{7} = -50.789081233035$$
$$x_{8} = 437.20497762458$$
$$x_{9} = -21.4675497995303$$
$$x_{10} = -44.5058959258554$$
$$x_{11} = -57.0722665402146$$
$$x_{12} = 43.4586983746588$$
$$x_{13} = 18.3259571459405$$
$$x_{14} = -34.0339204138894$$
$$x_{15} = -151.320046147908$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -59.1666616426078$$
$$x_{18} = 72.7802298081635$$
$$x_{19} = -13.0899693899575$$
$$x_{20} = 3.66519142918809$$
$$x_{21} = -6.80678408277789$$
$$x_{22} = -52.8834763354282$$
$$x_{23} = -65.4498469497874$$
$$x_{24} = -46.6002910282486$$
$$x_{25} = 87.4409955249159$$
$$x_{26} = -88.4881930761125$$
$$x_{27} = 24.60914245312$$
$$x_{28} = 100.007366139275$$
$$x_{29} = -31.9395253114962$$
$$x_{30} = 79.0634151153431$$
$$x_{31} = -63.3554518473942$$
$$x_{32} = 56.025068989018$$
$$x_{33} = 41.3643032722656$$
$$x_{34} = 91.6297857297023$$
$$x_{35} = 28.7979326579064$$
$$x_{36} = 93.7241808320955$$
$$x_{37} = -69.6386371545737$$
$$x_{38} = 37.1755130674792$$
$$x_{39} = 66400.1787274983$$
$$x_{40} = 53.9306738866248$$
$$x_{41} = 16.2315620435473$$
$$x_{42} = -75.9218224617533$$
$$x_{43} = -94.7713783832921$$
$$x_{44} = -78.0162175641465$$
$$x_{45} = 68.5914396033772$$
$$x_{46} = -82.2050077689329$$
$$x_{47} = -96.8657734856853$$
$$x_{48} = -84.2994028713261$$
$$x_{49} = 9.94837673636768$$
$$x_{50} = -0.523598775598299$$
$$x_{51} = 12.0427718387609$$
$$x_{52} = -2.61799387799149$$
$$x_{53} = -195.302343298165$$
$$x_{54} = 49.7418836818384$$
$$x_{55} = -71.733032256967$$
$$x_{56} = -40.317105721069$$
$$x_{57} = -8.90117918517108$$
$$x_{58} = 66.497044500984$$
$$x_{59} = 35.081117965086$$
$$x_{60} = 85.3466004225227$$
$$x_{61} = 192.160750644576$$
$$x_{62} = 5.75958653158129$$
$$x_{63} = -90.5825881785057$$
$$x_{64} = -25.6563400043166$$
$$x_{65} = 22.5147473507269$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -15.1843644923507$$
$$x_{68} = 62.3082542961976$$
$$x_{69} = 30.8923277602996$$
$$x_{70} = 97.9129710368819$$
Las raíces dadas
$$x_{53} = -195.302343298165$$
$$x_{15} = -151.320046147908$$
$$x_{66} = -101.054563690472$$
$$x_{47} = -96.8657734856853$$
$$x_{43} = -94.7713783832921$$
$$x_{63} = -90.5825881785057$$
$$x_{26} = -88.4881930761125$$
$$x_{48} = -84.2994028713261$$
$$x_{46} = -82.2050077689329$$
$$x_{44} = -78.0162175641465$$
$$x_{42} = -75.9218224617533$$
$$x_{55} = -71.733032256967$$
$$x_{37} = -69.6386371545737$$
$$x_{23} = -65.4498469497874$$
$$x_{31} = -63.3554518473942$$
$$x_{17} = -59.1666616426078$$
$$x_{11} = -57.0722665402146$$
$$x_{22} = -52.8834763354282$$
$$x_{7} = -50.789081233035$$
$$x_{24} = -46.6002910282486$$
$$x_{10} = -44.5058959258554$$
$$x_{56} = -40.317105721069$$
$$x_{16} = -38.2227106186758$$
$$x_{14} = -34.0339204138894$$
$$x_{29} = -31.9395253114962$$
$$x_{4} = -27.7507351067098$$
$$x_{64} = -25.6563400043166$$
$$x_{9} = -21.4675497995303$$
$$x_{6} = -19.3731546971371$$
$$x_{67} = -15.1843644923507$$
$$x_{19} = -13.0899693899575$$
$$x_{57} = -8.90117918517108$$
$$x_{21} = -6.80678408277789$$
$$x_{52} = -2.61799387799149$$
$$x_{50} = -0.523598775598299$$
$$x_{20} = 3.66519142918809$$
$$x_{62} = 5.75958653158129$$
$$x_{49} = 9.94837673636768$$
$$x_{51} = 12.0427718387609$$
$$x_{41} = 16.2315620435473$$
$$x_{13} = 18.3259571459405$$
$$x_{65} = 22.5147473507269$$
$$x_{27} = 24.60914245312$$
$$x_{35} = 28.7979326579064$$
$$x_{69} = 30.8923277602996$$
$$x_{59} = 35.081117965086$$
$$x_{38} = 37.1755130674792$$
$$x_{33} = 41.3643032722656$$
$$x_{12} = 43.4586983746588$$
$$x_{1} = 47.6474885794452$$
$$x_{54} = 49.7418836818384$$
$$x_{40} = 53.9306738866248$$
$$x_{32} = 56.025068989018$$
$$x_{5} = 60.2138591938044$$
$$x_{68} = 62.3082542961976$$
$$x_{58} = 66.497044500984$$
$$x_{45} = 68.5914396033772$$
$$x_{18} = 72.7802298081635$$
$$x_{2} = 74.8746249105567$$
$$x_{30} = 79.0634151153431$$
$$x_{3} = 81.1578102177363$$
$$x_{60} = 85.3466004225227$$
$$x_{25} = 87.4409955249159$$
$$x_{34} = 91.6297857297023$$
$$x_{36} = 93.7241808320955$$
$$x_{70} = 97.9129710368819$$
$$x_{28} = 100.007366139275$$
$$x_{61} = 192.160750644576$$
$$x_{8} = 437.20497762458$$
$$x_{39} = 66400.1787274983$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{53}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{53} - \frac{1}{10}$$
=
$$-195.302343298165 + - \frac{1}{10}$$
=
$$-195.402343298165$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
Entonces
$$x \leq -195.302343298165$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
$$x \geq -101.054563690472 \wedge x \leq -96.8657734856853$$
$$x \geq -94.7713783832921 \wedge x \leq -90.5825881785057$$
$$x \geq -88.4881930761125 \wedge x \leq -84.2994028713261$$
$$x \geq -82.2050077689329 \wedge x \leq -78.0162175641465$$
$$x \geq -75.9218224617533 \wedge x \leq -71.733032256967$$
$$x \geq -69.6386371545737 \wedge x \leq -65.4498469497874$$
$$x \geq -63.3554518473942 \wedge x \leq -59.1666616426078$$
$$x \geq -57.0722665402146 \wedge x \leq -52.8834763354282$$
$$x \geq -50.789081233035 \wedge x \leq -46.6002910282486$$
$$x \geq -44.5058959258554 \wedge x \leq -40.317105721069$$
$$x \geq -38.2227106186758 \wedge x \leq -34.0339204138894$$
$$x \geq -31.9395253114962 \wedge x \leq -27.7507351067098$$
$$x \geq -25.6563400043166 \wedge x \leq -21.4675497995303$$
$$x \geq -19.3731546971371 \wedge x \leq -15.1843644923507$$
$$x \geq -13.0899693899575 \wedge x \leq -8.90117918517108$$
$$x \geq -6.80678408277789 \wedge x \leq -2.61799387799149$$
$$x \geq -0.523598775598299 \wedge x \leq 3.66519142918809$$
$$x \geq 5.75958653158129 \wedge x \leq 9.94837673636768$$
$$x \geq 12.0427718387609 \wedge x \leq 16.2315620435473$$
$$x \geq 18.3259571459405 \wedge x \leq 22.5147473507269$$
$$x \geq 24.60914245312 \wedge x \leq 28.7979326579064$$
$$x \geq 30.8923277602996 \wedge x \leq 35.081117965086$$
$$x \geq 37.1755130674792 \wedge x \leq 41.3643032722656$$
$$x \geq 43.4586983746588 \wedge x \leq 47.6474885794452$$
$$x \geq 49.7418836818384 \wedge x \leq 53.9306738866248$$
$$x \geq 56.025068989018 \wedge x \leq 60.2138591938044$$
$$x \geq 62.3082542961976 \wedge x \leq 66.497044500984$$
$$x \geq 68.5914396033772 \wedge x \leq 72.7802298081635$$
$$x \geq 74.8746249105567 \wedge x \leq 79.0634151153431$$
$$x \geq 81.1578102177363 \wedge x \leq 85.3466004225227$$
$$x \geq 87.4409955249159 \wedge x \leq 91.6297857297023$$
$$x \geq 93.7241808320955 \wedge x \leq 97.9129710368819$$
$$x \geq 100.007366139275 \wedge x \leq 192.160750644576$$
$$x \geq 437.20497762458 \wedge x \leq 66400.1787274983$$
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(t \right)} = - \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\sin{\left(t \right)} = - \frac{1}{2}$$
cambiamos
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
$$\sin{\left(t \right)} + \frac{1}{2} = 0$$
Sustituimos
$$w = \sin{\left(t \right)}$$
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
$$\sin{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 47.6474885794452$$
$$x_{2} = 74.8746249105567$$
$$x_{3} = 81.1578102177363$$
$$x_{4} = -27.7507351067098$$
$$x_{5} = 60.2138591938044$$
$$x_{6} = -19.3731546971371$$
$$x_{7} = -50.789081233035$$
$$x_{8} = 437.20497762458$$
$$x_{9} = -21.4675497995303$$
$$x_{10} = -44.5058959258554$$
$$x_{11} = -57.0722665402146$$
$$x_{12} = 43.4586983746588$$
$$x_{13} = 18.3259571459405$$
$$x_{14} = -34.0339204138894$$
$$x_{15} = -151.320046147908$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -59.1666616426078$$
$$x_{18} = 72.7802298081635$$
$$x_{19} = -13.0899693899575$$
$$x_{20} = 3.66519142918809$$
$$x_{21} = -6.80678408277789$$
$$x_{22} = -52.8834763354282$$
$$x_{23} = -65.4498469497874$$
$$x_{24} = -46.6002910282486$$
$$x_{25} = 87.4409955249159$$
$$x_{26} = -88.4881930761125$$
$$x_{27} = 24.60914245312$$
$$x_{28} = 100.007366139275$$
$$x_{29} = -31.9395253114962$$
$$x_{30} = 79.0634151153431$$
$$x_{31} = -63.3554518473942$$
$$x_{32} = 56.025068989018$$
$$x_{33} = 41.3643032722656$$
$$x_{34} = 91.6297857297023$$
$$x_{35} = 28.7979326579064$$
$$x_{36} = 93.7241808320955$$
$$x_{37} = -69.6386371545737$$
$$x_{38} = 37.1755130674792$$
$$x_{39} = 66400.1787274983$$
$$x_{40} = 53.9306738866248$$
$$x_{41} = 16.2315620435473$$
$$x_{42} = -75.9218224617533$$
$$x_{43} = -94.7713783832921$$
$$x_{44} = -78.0162175641465$$
$$x_{45} = 68.5914396033772$$
$$x_{46} = -82.2050077689329$$
$$x_{47} = -96.8657734856853$$
$$x_{48} = -84.2994028713261$$
$$x_{49} = 9.94837673636768$$
$$x_{50} = -0.523598775598299$$
$$x_{51} = 12.0427718387609$$
$$x_{52} = -2.61799387799149$$
$$x_{53} = -195.302343298165$$
$$x_{54} = 49.7418836818384$$
$$x_{55} = -71.733032256967$$
$$x_{56} = -40.317105721069$$
$$x_{57} = -8.90117918517108$$
$$x_{58} = 66.497044500984$$
$$x_{59} = 35.081117965086$$
$$x_{60} = 85.3466004225227$$
$$x_{61} = 192.160750644576$$
$$x_{62} = 5.75958653158129$$
$$x_{63} = -90.5825881785057$$
$$x_{64} = -25.6563400043166$$
$$x_{65} = 22.5147473507269$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -15.1843644923507$$
$$x_{68} = 62.3082542961976$$
$$x_{69} = 30.8923277602996$$
$$x_{70} = 97.9129710368819$$
$$x_{1} = 47.6474885794452$$
$$x_{2} = 74.8746249105567$$
$$x_{3} = 81.1578102177363$$
$$x_{4} = -27.7507351067098$$
$$x_{5} = 60.2138591938044$$
$$x_{6} = -19.3731546971371$$
$$x_{7} = -50.789081233035$$
$$x_{8} = 437.20497762458$$
$$x_{9} = -21.4675497995303$$
$$x_{10} = -44.5058959258554$$
$$x_{11} = -57.0722665402146$$
$$x_{12} = 43.4586983746588$$
$$x_{13} = 18.3259571459405$$
$$x_{14} = -34.0339204138894$$
$$x_{15} = -151.320046147908$$
$$x_{16} = -38.2227106186758$$
$$x_{17} = -59.1666616426078$$
$$x_{18} = 72.7802298081635$$
$$x_{19} = -13.0899693899575$$
$$x_{20} = 3.66519142918809$$
$$x_{21} = -6.80678408277789$$
$$x_{22} = -52.8834763354282$$
$$x_{23} = -65.4498469497874$$
$$x_{24} = -46.6002910282486$$
$$x_{25} = 87.4409955249159$$
$$x_{26} = -88.4881930761125$$
$$x_{27} = 24.60914245312$$
$$x_{28} = 100.007366139275$$
$$x_{29} = -31.9395253114962$$
$$x_{30} = 79.0634151153431$$
$$x_{31} = -63.3554518473942$$
$$x_{32} = 56.025068989018$$
$$x_{33} = 41.3643032722656$$
$$x_{34} = 91.6297857297023$$
$$x_{35} = 28.7979326579064$$
$$x_{36} = 93.7241808320955$$
$$x_{37} = -69.6386371545737$$
$$x_{38} = 37.1755130674792$$
$$x_{39} = 66400.1787274983$$
$$x_{40} = 53.9306738866248$$
$$x_{41} = 16.2315620435473$$
$$x_{42} = -75.9218224617533$$
$$x_{43} = -94.7713783832921$$
$$x_{44} = -78.0162175641465$$
$$x_{45} = 68.5914396033772$$
$$x_{46} = -82.2050077689329$$
$$x_{47} = -96.8657734856853$$
$$x_{48} = -84.2994028713261$$
$$x_{49} = 9.94837673636768$$
$$x_{50} = -0.523598775598299$$
$$x_{51} = 12.0427718387609$$
$$x_{52} = -2.61799387799149$$
$$x_{53} = -195.302343298165$$
$$x_{54} = 49.7418836818384$$
$$x_{55} = -71.733032256967$$
$$x_{56} = -40.317105721069$$
$$x_{57} = -8.90117918517108$$
$$x_{58} = 66.497044500984$$
$$x_{59} = 35.081117965086$$
$$x_{60} = 85.3466004225227$$
$$x_{61} = 192.160750644576$$
$$x_{62} = 5.75958653158129$$
$$x_{63} = -90.5825881785057$$
$$x_{64} = -25.6563400043166$$
$$x_{65} = 22.5147473507269$$
$$x_{66} = -101.054563690472$$
$$x_{67} = -15.1843644923507$$
$$x_{68} = 62.3082542961976$$
$$x_{69} = 30.8923277602996$$
$$x_{70} = 97.9129710368819$$
Las raíces dadas
$$x_{53} = -195.302343298165$$
$$x_{15} = -151.320046147908$$
$$x_{66} = -101.054563690472$$
$$x_{47} = -96.8657734856853$$
$$x_{43} = -94.7713783832921$$
$$x_{63} = -90.5825881785057$$
$$x_{26} = -88.4881930761125$$
$$x_{48} = -84.2994028713261$$
$$x_{46} = -82.2050077689329$$
$$x_{44} = -78.0162175641465$$
$$x_{42} = -75.9218224617533$$
$$x_{55} = -71.733032256967$$
$$x_{37} = -69.6386371545737$$
$$x_{23} = -65.4498469497874$$
$$x_{31} = -63.3554518473942$$
$$x_{17} = -59.1666616426078$$
$$x_{11} = -57.0722665402146$$
$$x_{22} = -52.8834763354282$$
$$x_{7} = -50.789081233035$$
$$x_{24} = -46.6002910282486$$
$$x_{10} = -44.5058959258554$$
$$x_{56} = -40.317105721069$$
$$x_{16} = -38.2227106186758$$
$$x_{14} = -34.0339204138894$$
$$x_{29} = -31.9395253114962$$
$$x_{4} = -27.7507351067098$$
$$x_{64} = -25.6563400043166$$
$$x_{9} = -21.4675497995303$$
$$x_{6} = -19.3731546971371$$
$$x_{67} = -15.1843644923507$$
$$x_{19} = -13.0899693899575$$
$$x_{57} = -8.90117918517108$$
$$x_{21} = -6.80678408277789$$
$$x_{52} = -2.61799387799149$$
$$x_{50} = -0.523598775598299$$
$$x_{20} = 3.66519142918809$$
$$x_{62} = 5.75958653158129$$
$$x_{49} = 9.94837673636768$$
$$x_{51} = 12.0427718387609$$
$$x_{41} = 16.2315620435473$$
$$x_{13} = 18.3259571459405$$
$$x_{65} = 22.5147473507269$$
$$x_{27} = 24.60914245312$$
$$x_{35} = 28.7979326579064$$
$$x_{69} = 30.8923277602996$$
$$x_{59} = 35.081117965086$$
$$x_{38} = 37.1755130674792$$
$$x_{33} = 41.3643032722656$$
$$x_{12} = 43.4586983746588$$
$$x_{1} = 47.6474885794452$$
$$x_{54} = 49.7418836818384$$
$$x_{40} = 53.9306738866248$$
$$x_{32} = 56.025068989018$$
$$x_{5} = 60.2138591938044$$
$$x_{68} = 62.3082542961976$$
$$x_{58} = 66.497044500984$$
$$x_{45} = 68.5914396033772$$
$$x_{18} = 72.7802298081635$$
$$x_{2} = 74.8746249105567$$
$$x_{30} = 79.0634151153431$$
$$x_{3} = 81.1578102177363$$
$$x_{60} = 85.3466004225227$$
$$x_{25} = 87.4409955249159$$
$$x_{34} = 91.6297857297023$$
$$x_{36} = 93.7241808320955$$
$$x_{70} = 97.9129710368819$$
$$x_{28} = 100.007366139275$$
$$x_{61} = 192.160750644576$$
$$x_{8} = 437.20497762458$$
$$x_{39} = 66400.1787274983$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{53}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{53} - \frac{1}{10}$$
=
$$-195.302343298165 + - \frac{1}{10}$$
=
$$-195.402343298165$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
$$\sin{\left(t \right)} \geq - \frac{1}{2}$$
sin(t) >= -1/2
Entonces
$$x \leq -195.302343298165$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x53 x15 x66 x47 x43 x63 x26 x48 x46 x44 x42 x55 x37 x23 x31 x17 x11 x22 x7 x24 x10 x56 x16 x14 x29 x4 x64 x9 x6 x67 x19 x57 x21 x52 x50 x20 x62 x49 x51 x41 x13 x65 x27 x35 x69 x59 x38 x33 x12 x1 x54 x40 x32 x5 x68 x58 x45 x18 x2 x30 x3 x60 x25 x34 x36 x70 x28 x61 x8 x39Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -195.302343298165 \wedge x \leq -151.320046147908$$
$$x \geq -101.054563690472 \wedge x \leq -96.8657734856853$$
$$x \geq -94.7713783832921 \wedge x \leq -90.5825881785057$$
$$x \geq -88.4881930761125 \wedge x \leq -84.2994028713261$$
$$x \geq -82.2050077689329 \wedge x \leq -78.0162175641465$$
$$x \geq -75.9218224617533 \wedge x \leq -71.733032256967$$
$$x \geq -69.6386371545737 \wedge x \leq -65.4498469497874$$
$$x \geq -63.3554518473942 \wedge x \leq -59.1666616426078$$
$$x \geq -57.0722665402146 \wedge x \leq -52.8834763354282$$
$$x \geq -50.789081233035 \wedge x \leq -46.6002910282486$$
$$x \geq -44.5058959258554 \wedge x \leq -40.317105721069$$
$$x \geq -38.2227106186758 \wedge x \leq -34.0339204138894$$
$$x \geq -31.9395253114962 \wedge x \leq -27.7507351067098$$
$$x \geq -25.6563400043166 \wedge x \leq -21.4675497995303$$
$$x \geq -19.3731546971371 \wedge x \leq -15.1843644923507$$
$$x \geq -13.0899693899575 \wedge x \leq -8.90117918517108$$
$$x \geq -6.80678408277789 \wedge x \leq -2.61799387799149$$
$$x \geq -0.523598775598299 \wedge x \leq 3.66519142918809$$
$$x \geq 5.75958653158129 \wedge x \leq 9.94837673636768$$
$$x \geq 12.0427718387609 \wedge x \leq 16.2315620435473$$
$$x \geq 18.3259571459405 \wedge x \leq 22.5147473507269$$
$$x \geq 24.60914245312 \wedge x \leq 28.7979326579064$$
$$x \geq 30.8923277602996 \wedge x \leq 35.081117965086$$
$$x \geq 37.1755130674792 \wedge x \leq 41.3643032722656$$
$$x \geq 43.4586983746588 \wedge x \leq 47.6474885794452$$
$$x \geq 49.7418836818384 \wedge x \leq 53.9306738866248$$
$$x \geq 56.025068989018 \wedge x \leq 60.2138591938044$$
$$x \geq 62.3082542961976 \wedge x \leq 66.497044500984$$
$$x \geq 68.5914396033772 \wedge x \leq 72.7802298081635$$
$$x \geq 74.8746249105567 \wedge x \leq 79.0634151153431$$
$$x \geq 81.1578102177363 \wedge x \leq 85.3466004225227$$
$$x \geq 87.4409955249159 \wedge x \leq 91.6297857297023$$
$$x \geq 93.7241808320955 \wedge x \leq 97.9129710368819$$
$$x \geq 100.007366139275 \wedge x \leq 192.160750644576$$
$$x \geq 437.20497762458 \wedge x \leq 66400.1787274983$$
Respuesta rápida 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))
Respuesta rápida
[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))