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+4)(x-8)>0
-
(x+4)*(x-8)>0
-
(x-1)^2*(x-4)<=0
-
(x-1)(x-3)>0
- Derivada de:
-
sint
- Integral de d{x}:
- sint
-
Expresiones idénticas
- sint>= uno / dos
- seno de t más o igual a 1 dividir por 2
- seno de t más o igual a uno dividir por dos
- sint>=1 dividir por 2
-
Expresiones semejantes
- (sin2t)-((sin(t)+cos(t))^2)/(tg(t)+ctg(t))
-
Expresiones con funciones
- sint
- sint<=1/2
- sint<0
- sint>√3/2
- sint<-√2/2
- sint>-√3
sint>=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:
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
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:
$$x_{0} \leq x_{10}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{10} - \frac{1}{10}$$
=
$$-4454.25478401473 + - \frac{1}{10}$$
=
$$-4454.35478401473$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} \geq \frac{1}{2}$$
$$\sin{\left(t \right)} \geq \frac{1}{2}$$
Entonces
$$x \leq -4454.25478401473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -4454.25478401473 \wedge x \leq -2650.98060085419$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -4454.25478401473 \wedge x \leq -2650.98060085419$$
$$x \geq -627.79493194236 \wedge x \leq -100.007366139275$$
$$x \geq -97.9129710368819 \wedge x \leq -93.7241808320955$$
$$x \geq -91.6297857297023 \wedge x \leq -87.4409955249159$$
$$x \geq -85.3466004225227 \wedge x \leq -81.1578102177363$$
$$x \geq -79.0634151153431 \wedge x \leq -74.8746249105567$$
$$x \geq -72.7802298081635 \wedge x \leq -68.5914396033772$$
$$x \geq -66.497044500984 \wedge x \leq -62.3082542961976$$
$$x \geq -60.2138591938044 \wedge x \leq -56.025068989018$$
$$x \geq -53.9306738866248 \wedge x \leq -49.7418836818384$$
$$x \geq -47.6474885794452 \wedge x \leq -43.4586983746588$$
$$x \geq -41.3643032722656 \wedge x \leq -37.1755130674792$$
$$x \geq -35.081117965086 \wedge x \leq -30.8923277602996$$
$$x \geq -28.7979326579064 \wedge x \leq -24.60914245312$$
$$x \geq -22.5147473507269 \wedge x \leq -18.3259571459405$$
$$x \geq -16.2315620435473 \wedge x \leq -12.0427718387609$$
$$x \geq -9.94837673636768 \wedge x \leq -5.75958653158129$$
$$x \geq -3.66519142918809 \wedge x \leq 0.523598775598299$$
$$x \geq 2.61799387799149 \wedge x \leq 6.80678408277789$$
$$x \geq 8.90117918517108 \wedge x \leq 13.0899693899575$$
$$x \geq 15.1843644923507 \wedge x \leq 19.3731546971371$$
$$x \geq 21.4675497995303 \wedge x \leq 25.6563400043166$$
$$x \geq 27.7507351067098 \wedge x \leq 31.9395253114962$$
$$x \geq 34.0339204138894 \wedge x \leq 38.2227106186758$$
$$x \geq 40.317105721069 \wedge x \leq 44.5058959258554$$
$$x \geq 46.6002910282486 \wedge x \leq 50.789081233035$$
$$x \geq 52.8834763354282 \wedge x \leq 57.0722665402146$$
$$x \geq 59.1666616426078 \wedge x \leq 63.3554518473942$$
$$x \geq 65.4498469497874 \wedge x \leq 69.6386371545737$$
$$x \geq 71.733032256967 \wedge x \leq 75.9218224617533$$
$$x \geq 78.0162175641465 \wedge x \leq 82.2050077689329$$
$$x \geq 84.2994028713261 \wedge x \leq 88.4881930761125$$
$$x \geq 90.5825881785057 \wedge x \leq 94.7713783832921$$
$$x \geq 96.8657734856853 \wedge x \leq 101.054563690472$$
$$x \geq 134.564885328763 \wedge x \leq 138.753675533549$$
$$x \geq 17438.4572213013$$
$$\sin{\left(t \right)} \geq \frac{1}{2}$$
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:
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
$$x_{1} = 84.2994028713261$$
$$x_{2} = -93.7241808320955$$
$$x_{3} = 65.4498469497874$$
$$x_{4} = -627.79493194236$$
$$x_{5} = 63.3554518473942$$
$$x_{6} = -5.75958653158129$$
$$x_{7} = -22.5147473507269$$
$$x_{8} = 57.0722665402146$$
$$x_{9} = 38.2227106186758$$
$$x_{10} = -4454.25478401473$$
$$x_{11} = -60.2138591938044$$
$$x_{12} = -62.3082542961976$$
$$x_{13} = 101.054563690472$$
$$x_{14} = -41.3643032722656$$
$$x_{15} = -9.94837673636768$$
$$x_{16} = 8.90117918517108$$
$$x_{17} = -47.6474885794452$$
$$x_{18} = -28.7979326579064$$
$$x_{19} = -37.1755130674792$$
$$x_{20} = 88.4881930761125$$
$$x_{21} = -100.007366139275$$
$$x_{22} = 31.9395253114962$$
$$x_{23} = 46.6002910282486$$
$$x_{24} = 2.61799387799149$$
$$x_{25} = 50.789081233035$$
$$x_{26} = -74.8746249105567$$
$$x_{27} = 52.8834763354282$$
$$x_{28} = -18.3259571459405$$
$$x_{29} = 94.7713783832921$$
$$x_{30} = 40.317105721069$$
$$x_{31} = 17438.4572213013$$
$$x_{32} = 44.5058959258554$$
$$x_{33} = -68.5914396033772$$
$$x_{34} = -85.3466004225227$$
$$x_{35} = -81.1578102177363$$
$$x_{36} = 13.0899693899575$$
$$x_{37} = -24.60914245312$$
$$x_{38} = 69.6386371545737$$
$$x_{39} = -16.2315620435473$$
$$x_{40} = -87.4409955249159$$
$$x_{41} = -53.9306738866248$$
$$x_{42} = -97.9129710368819$$
$$x_{43} = 82.2050077689329$$
$$x_{44} = 25.6563400043166$$
$$x_{45} = 59.1666616426078$$
$$x_{46} = -66.497044500984$$
$$x_{47} = 19.3731546971371$$
$$x_{48} = 15.1843644923507$$
$$x_{49} = 96.8657734856853$$
$$x_{50} = -43.4586983746588$$
$$x_{51} = 78.0162175641465$$
$$x_{52} = 90.5825881785057$$
$$x_{53} = -3.66519142918809$$
$$x_{54} = -49.7418836818384$$
$$x_{55} = 138.753675533549$$
$$x_{56} = -79.0634151153431$$
$$x_{57} = -56.025068989018$$
$$x_{58} = 71.733032256967$$
$$x_{59} = 21.4675497995303$$
$$x_{60} = 75.9218224617533$$
$$x_{61} = 0.523598775598299$$
$$x_{62} = 34.0339204138894$$
$$x_{63} = -12.0427718387609$$
$$x_{64} = 134.564885328763$$
$$x_{65} = -91.6297857297023$$
$$x_{66} = -30.8923277602996$$
$$x_{67} = -2650.98060085419$$
$$x_{68} = -72.7802298081635$$
$$x_{69} = 27.7507351067098$$
$$x_{70} = -35.081117965086$$
$$x_{71} = 6.80678408277789$$
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:
$$x_{0} \leq x_{10}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{10} - \frac{1}{10}$$
=
$$-4454.25478401473 + - \frac{1}{10}$$
=
$$-4454.35478401473$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} \geq \frac{1}{2}$$
$$\sin{\left(t \right)} \geq \frac{1}{2}$$
sin(t) >= 1/2
Entonces
$$x \leq -4454.25478401473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -4454.25478401473 \wedge x \leq -2650.98060085419$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
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:
$$x \geq -4454.25478401473 \wedge x \leq -2650.98060085419$$
$$x \geq -627.79493194236 \wedge x \leq -100.007366139275$$
$$x \geq -97.9129710368819 \wedge x \leq -93.7241808320955$$
$$x \geq -91.6297857297023 \wedge x \leq -87.4409955249159$$
$$x \geq -85.3466004225227 \wedge x \leq -81.1578102177363$$
$$x \geq -79.0634151153431 \wedge x \leq -74.8746249105567$$
$$x \geq -72.7802298081635 \wedge x \leq -68.5914396033772$$
$$x \geq -66.497044500984 \wedge x \leq -62.3082542961976$$
$$x \geq -60.2138591938044 \wedge x \leq -56.025068989018$$
$$x \geq -53.9306738866248 \wedge x \leq -49.7418836818384$$
$$x \geq -47.6474885794452 \wedge x \leq -43.4586983746588$$
$$x \geq -41.3643032722656 \wedge x \leq -37.1755130674792$$
$$x \geq -35.081117965086 \wedge x \leq -30.8923277602996$$
$$x \geq -28.7979326579064 \wedge x \leq -24.60914245312$$
$$x \geq -22.5147473507269 \wedge x \leq -18.3259571459405$$
$$x \geq -16.2315620435473 \wedge x \leq -12.0427718387609$$
$$x \geq -9.94837673636768 \wedge x \leq -5.75958653158129$$
$$x \geq -3.66519142918809 \wedge x \leq 0.523598775598299$$
$$x \geq 2.61799387799149 \wedge x \leq 6.80678408277789$$
$$x \geq 8.90117918517108 \wedge x \leq 13.0899693899575$$
$$x \geq 15.1843644923507 \wedge x \leq 19.3731546971371$$
$$x \geq 21.4675497995303 \wedge x \leq 25.6563400043166$$
$$x \geq 27.7507351067098 \wedge x \leq 31.9395253114962$$
$$x \geq 34.0339204138894 \wedge x \leq 38.2227106186758$$
$$x \geq 40.317105721069 \wedge x \leq 44.5058959258554$$
$$x \geq 46.6002910282486 \wedge x \leq 50.789081233035$$
$$x \geq 52.8834763354282 \wedge x \leq 57.0722665402146$$
$$x \geq 59.1666616426078 \wedge x \leq 63.3554518473942$$
$$x \geq 65.4498469497874 \wedge x \leq 69.6386371545737$$
$$x \geq 71.733032256967 \wedge x \leq 75.9218224617533$$
$$x \geq 78.0162175641465 \wedge x \leq 82.2050077689329$$
$$x \geq 84.2994028713261 \wedge x \leq 88.4881930761125$$
$$x \geq 90.5825881785057 \wedge x \leq 94.7713783832921$$
$$x \geq 96.8657734856853 \wedge x \leq 101.054563690472$$
$$x \geq 134.564885328763 \wedge x \leq 138.753675533549$$
$$x \geq 17438.4572213013$$
Respuesta rápida 2
[src]
pi 5*pi [--, ----] 6 6
$$x\ in\ \left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]$$
x in Interval(pi/6, 5*pi/6)
Respuesta rápida
[src]
/pi 5*pi\ And|-- <= t, t <= ----| \6 6 /
$$\frac{\pi}{6} \leq t \wedge t \leq \frac{5 \pi}{6}$$
(pi/6 <= t)∧(t <= 5*pi/6)