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^2-4x+3<0
-
x^2-3x+2<0
-
-x^2+x+6>0
-
-x^2-x+12>0
- Derivada de:
-
sint
-
1/2
- Integral de d{x}:
- sint
- Suma de la serie:
-
1/2
- Límite de la función:
-
1/2
-
Expresiones idénticas
- sint< uno / dos
- seno de t menos 1 dividir por 2
- seno de t menos uno dividir por dos
- sint<1 dividir por 2
-
Expresiones semejantes
- 1/(2-x)+5/(2+x)<1
-
Expresiones con funciones
- sint
- sint>1/2
- sint<0,4
- sint<1/3
- sint>1/3
- sint>-1/2
sint<1/2 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\sin{\left(t \right)} < \frac{1}{2}$$
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:
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
Las raíces dadas
$$x_{10} = -4454.25478401473$$
$$x_{67} = -2650.98060085419$$
$$x_{4} = -627.79493194236$$
$$x_{21} = -100.007366139275$$
$$x_{42} = -97.9129710368819$$
$$x_{2} = -93.7241808320955$$
$$x_{65} = -91.6297857297023$$
$$x_{40} = -87.4409955249159$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{56} = -79.0634151153431$$
$$x_{26} = -74.8746249105567$$
$$x_{68} = -72.7802298081635$$
$$x_{33} = -68.5914396033772$$
$$x_{46} = -66.497044500984$$
$$x_{12} = -62.3082542961976$$
$$x_{11} = -60.2138591938044$$
$$x_{57} = -56.025068989018$$
$$x_{41} = -53.9306738866248$$
$$x_{54} = -49.7418836818384$$
$$x_{17} = -47.6474885794452$$
$$x_{50} = -43.4586983746588$$
$$x_{14} = -41.3643032722656$$
$$x_{19} = -37.1755130674792$$
$$x_{70} = -35.081117965086$$
$$x_{66} = -30.8923277602996$$
$$x_{18} = -28.7979326579064$$
$$x_{37} = -24.60914245312$$
$$x_{7} = -22.5147473507269$$
$$x_{28} = -18.3259571459405$$
$$x_{39} = -16.2315620435473$$
$$x_{63} = -12.0427718387609$$
$$x_{15} = -9.94837673636768$$
$$x_{6} = -5.75958653158129$$
$$x_{53} = -3.66519142918809$$
$$x_{61} = 0.523598775598299$$
$$x_{24} = 2.61799387799149$$
$$x_{71} = 6.80678408277789$$
$$x_{16} = 8.90117918517108$$
$$x_{36} = 13.0899693899575$$
$$x_{48} = 15.1843644923507$$
$$x_{47} = 19.3731546971371$$
$$x_{59} = 21.4675497995303$$
$$x_{44} = 25.6563400043166$$
$$x_{69} = 27.7507351067098$$
$$x_{22} = 31.9395253114962$$
$$x_{62} = 34.0339204138894$$
$$x_{9} = 38.2227106186758$$
$$x_{30} = 40.317105721069$$
$$x_{32} = 44.5058959258554$$
$$x_{23} = 46.6002910282486$$
$$x_{25} = 50.789081233035$$
$$x_{27} = 52.8834763354282$$
$$x_{8} = 57.0722665402146$$
$$x_{45} = 59.1666616426078$$
$$x_{5} = 63.3554518473942$$
$$x_{3} = 65.4498469497874$$
$$x_{38} = 69.6386371545737$$
$$x_{58} = 71.733032256967$$
$$x_{60} = 75.9218224617533$$
$$x_{51} = 78.0162175641465$$
$$x_{43} = 82.2050077689329$$
$$x_{1} = 84.2994028713261$$
$$x_{20} = 88.4881930761125$$
$$x_{52} = 90.5825881785057$$
$$x_{29} = 94.7713783832921$$
$$x_{49} = 96.8657734856853$$
$$x_{13} = 101.054563690472$$
$$x_{64} = 134.564885328763$$
$$x_{55} = 138.753675533549$$
$$x_{31} = 17438.4572213013$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{10}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{10} - \frac{1}{10}$$
=
$$-4454.25478401473 + - \frac{1}{10}$$
=
$$-4454.35478401473$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} < \frac{1}{2}$$
$$\sin{\left(t \right)} < \frac{1}{2}$$
Entonces
$$x < -4454.25478401473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
$$x > -627.79493194236 \wedge x < -100.007366139275$$
$$x > -97.9129710368819 \wedge x < -93.7241808320955$$
$$x > -91.6297857297023 \wedge x < -87.4409955249159$$
$$x > -85.3466004225227 \wedge x < -81.1578102177363$$
$$x > -79.0634151153431 \wedge x < -74.8746249105567$$
$$x > -72.7802298081635 \wedge x < -68.5914396033772$$
$$x > -66.497044500984 \wedge x < -62.3082542961976$$
$$x > -60.2138591938044 \wedge x < -56.025068989018$$
$$x > -53.9306738866248 \wedge x < -49.7418836818384$$
$$x > -47.6474885794452 \wedge x < -43.4586983746588$$
$$x > -41.3643032722656 \wedge x < -37.1755130674792$$
$$x > -35.081117965086 \wedge x < -30.8923277602996$$
$$x > -28.7979326579064 \wedge x < -24.60914245312$$
$$x > -22.5147473507269 \wedge x < -18.3259571459405$$
$$x > -16.2315620435473 \wedge x < -12.0427718387609$$
$$x > -9.94837673636768 \wedge x < -5.75958653158129$$
$$x > -3.66519142918809 \wedge x < 0.523598775598299$$
$$x > 2.61799387799149 \wedge x < 6.80678408277789$$
$$x > 8.90117918517108 \wedge x < 13.0899693899575$$
$$x > 15.1843644923507 \wedge x < 19.3731546971371$$
$$x > 21.4675497995303 \wedge x < 25.6563400043166$$
$$x > 27.7507351067098 \wedge x < 31.9395253114962$$
$$x > 34.0339204138894 \wedge x < 38.2227106186758$$
$$x > 40.317105721069 \wedge x < 44.5058959258554$$
$$x > 46.6002910282486 \wedge x < 50.789081233035$$
$$x > 52.8834763354282 \wedge x < 57.0722665402146$$
$$x > 59.1666616426078 \wedge x < 63.3554518473942$$
$$x > 65.4498469497874 \wedge x < 69.6386371545737$$
$$x > 71.733032256967 \wedge x < 75.9218224617533$$
$$x > 78.0162175641465 \wedge x < 82.2050077689329$$
$$x > 84.2994028713261 \wedge x < 88.4881930761125$$
$$x > 90.5825881785057 \wedge x < 94.7713783832921$$
$$x > 96.8657734856853 \wedge x < 101.054563690472$$
$$x > 134.564885328763 \wedge x < 138.753675533549$$
$$x > 17438.4572213013$$
$$\sin{\left(t \right)} < \frac{1}{2}$$
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:
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
Las raíces dadas
$$x_{10} = -4454.25478401473$$
$$x_{67} = -2650.98060085419$$
$$x_{4} = -627.79493194236$$
$$x_{21} = -100.007366139275$$
$$x_{42} = -97.9129710368819$$
$$x_{2} = -93.7241808320955$$
$$x_{65} = -91.6297857297023$$
$$x_{40} = -87.4409955249159$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{56} = -79.0634151153431$$
$$x_{26} = -74.8746249105567$$
$$x_{68} = -72.7802298081635$$
$$x_{33} = -68.5914396033772$$
$$x_{46} = -66.497044500984$$
$$x_{12} = -62.3082542961976$$
$$x_{11} = -60.2138591938044$$
$$x_{57} = -56.025068989018$$
$$x_{41} = -53.9306738866248$$
$$x_{54} = -49.7418836818384$$
$$x_{17} = -47.6474885794452$$
$$x_{50} = -43.4586983746588$$
$$x_{14} = -41.3643032722656$$
$$x_{19} = -37.1755130674792$$
$$x_{70} = -35.081117965086$$
$$x_{66} = -30.8923277602996$$
$$x_{18} = -28.7979326579064$$
$$x_{37} = -24.60914245312$$
$$x_{7} = -22.5147473507269$$
$$x_{28} = -18.3259571459405$$
$$x_{39} = -16.2315620435473$$
$$x_{63} = -12.0427718387609$$
$$x_{15} = -9.94837673636768$$
$$x_{6} = -5.75958653158129$$
$$x_{53} = -3.66519142918809$$
$$x_{61} = 0.523598775598299$$
$$x_{24} = 2.61799387799149$$
$$x_{71} = 6.80678408277789$$
$$x_{16} = 8.90117918517108$$
$$x_{36} = 13.0899693899575$$
$$x_{48} = 15.1843644923507$$
$$x_{47} = 19.3731546971371$$
$$x_{59} = 21.4675497995303$$
$$x_{44} = 25.6563400043166$$
$$x_{69} = 27.7507351067098$$
$$x_{22} = 31.9395253114962$$
$$x_{62} = 34.0339204138894$$
$$x_{9} = 38.2227106186758$$
$$x_{30} = 40.317105721069$$
$$x_{32} = 44.5058959258554$$
$$x_{23} = 46.6002910282486$$
$$x_{25} = 50.789081233035$$
$$x_{27} = 52.8834763354282$$
$$x_{8} = 57.0722665402146$$
$$x_{45} = 59.1666616426078$$
$$x_{5} = 63.3554518473942$$
$$x_{3} = 65.4498469497874$$
$$x_{38} = 69.6386371545737$$
$$x_{58} = 71.733032256967$$
$$x_{60} = 75.9218224617533$$
$$x_{51} = 78.0162175641465$$
$$x_{43} = 82.2050077689329$$
$$x_{1} = 84.2994028713261$$
$$x_{20} = 88.4881930761125$$
$$x_{52} = 90.5825881785057$$
$$x_{29} = 94.7713783832921$$
$$x_{49} = 96.8657734856853$$
$$x_{13} = 101.054563690472$$
$$x_{64} = 134.564885328763$$
$$x_{55} = 138.753675533549$$
$$x_{31} = 17438.4572213013$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{10}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{10} - \frac{1}{10}$$
=
$$-4454.25478401473 + - \frac{1}{10}$$
=
$$-4454.35478401473$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} < \frac{1}{2}$$
$$\sin{\left(t \right)} < \frac{1}{2}$$
sin(t) < 1/2
Entonces
$$x < -4454.25478401473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x10 x67 x4 x21 x42 x2 x65 x40 x34 x35 x56 x26 x68 x33 x46 x12 x11 x57 x41 x54 x17 x50 x14 x19 x70 x66 x18 x37 x7 x28 x39 x63 x15 x6 x53 x61 x24 x71 x16 x36 x48 x47 x59 x44 x69 x22 x62 x9 x30 x32 x23 x25 x27 x8 x45 x5 x3 x38 x58 x60 x51 x43 x1 x20 x52 x29 x49 x13 x64 x55 x31Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -4454.25478401473 \wedge x < -2650.98060085419$$
$$x > -627.79493194236 \wedge x < -100.007366139275$$
$$x > -97.9129710368819 \wedge x < -93.7241808320955$$
$$x > -91.6297857297023 \wedge x < -87.4409955249159$$
$$x > -85.3466004225227 \wedge x < -81.1578102177363$$
$$x > -79.0634151153431 \wedge x < -74.8746249105567$$
$$x > -72.7802298081635 \wedge x < -68.5914396033772$$
$$x > -66.497044500984 \wedge x < -62.3082542961976$$
$$x > -60.2138591938044 \wedge x < -56.025068989018$$
$$x > -53.9306738866248 \wedge x < -49.7418836818384$$
$$x > -47.6474885794452 \wedge x < -43.4586983746588$$
$$x > -41.3643032722656 \wedge x < -37.1755130674792$$
$$x > -35.081117965086 \wedge x < -30.8923277602996$$
$$x > -28.7979326579064 \wedge x < -24.60914245312$$
$$x > -22.5147473507269 \wedge x < -18.3259571459405$$
$$x > -16.2315620435473 \wedge x < -12.0427718387609$$
$$x > -9.94837673636768 \wedge x < -5.75958653158129$$
$$x > -3.66519142918809 \wedge x < 0.523598775598299$$
$$x > 2.61799387799149 \wedge x < 6.80678408277789$$
$$x > 8.90117918517108 \wedge x < 13.0899693899575$$
$$x > 15.1843644923507 \wedge x < 19.3731546971371$$
$$x > 21.4675497995303 \wedge x < 25.6563400043166$$
$$x > 27.7507351067098 \wedge x < 31.9395253114962$$
$$x > 34.0339204138894 \wedge x < 38.2227106186758$$
$$x > 40.317105721069 \wedge x < 44.5058959258554$$
$$x > 46.6002910282486 \wedge x < 50.789081233035$$
$$x > 52.8834763354282 \wedge x < 57.0722665402146$$
$$x > 59.1666616426078 \wedge x < 63.3554518473942$$
$$x > 65.4498469497874 \wedge x < 69.6386371545737$$
$$x > 71.733032256967 \wedge x < 75.9218224617533$$
$$x > 78.0162175641465 \wedge x < 82.2050077689329$$
$$x > 84.2994028713261 \wedge x < 88.4881930761125$$
$$x > 90.5825881785057 \wedge x < 94.7713783832921$$
$$x > 96.8657734856853 \wedge x < 101.054563690472$$
$$x > 134.564885328763 \wedge x < 138.753675533549$$
$$x > 17438.4572213013$$
Respuesta rápida
[src]
/ / pi\ / 5*pi \\ Or|And|0 <= t, t < --|, And|t <= 2*pi, ---- < t|| \ \ 6 / \ 6 //
$$\left(0 \leq t \wedge t < \frac{\pi}{6}\right) \vee \left(t \leq 2 \pi \wedge \frac{5 \pi}{6} < t\right)$$
((0 <= t)∧(t < pi/6))∨((t <= 2*pi)∧(5*pi/6 < t))
Respuesta rápida 2
[src]
pi 5*pi
[0, --) U (----, 2*pi]
6 6
$$x\ in\ \left[0, \frac{\pi}{6}\right) \cup \left(\frac{5 \pi}{6}, 2 \pi\right]$$
x in Union(Interval.Ropen(0, pi/6), Interval.Lopen(5*pi/6, 2*pi))