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^2-10x<0
-
(x-2)^2/(x-1)<0
-
-x^2+3x-2<0
-
-x^2+4x-4<0
- Derivada de:
-
sin(y)
- Integral de d{x}:
- sin(y)
- Gráfico de la función y =:
- sin(y)
-
Expresiones idénticas
- sin(y)<(- uno)/sqrt(dos)
- seno de (y) menos ( menos 1) dividir por raíz cuadrada de (2)
- seno de (y) menos ( menos uno) dividir por raíz cuadrada de (dos)
- sin(y)<(-1)/√(2)
- siny<-1/sqrt2
- sin(y)<(-1) dividir por sqrt(2)
-
Expresiones semejantes
- 2siny<-p/4
- (sqrt(1-3x)-1)/(sqrt(2+x)-1)<1
- sinx-siny-sin(x-y)>0
- sin(y)<(1)/sqrt(2)
- cos(x)<=-1/(sqrt(2))
- sin(x/3)<=-1/(sqrt(2))
- 2*|x-2|*(asin(y+1))^2<pi*(2-x)
-
Expresiones con funciones
- Seno sin
- sin(x)<=1/sqrt(2)
- sin2x>=1/2
- sin(x)<-2
- sin((π/2)+x)≤0
- sinП/4*cosx+cosП/8*sinx<=1
- Raíz cuadrada sqrt
- sqrt(x+5)+sqrt(5-x)>4
- sqrt(x+7)-x-1>0
- sqrt((x+5)/(x-7))>2
- sqrt(x+3)-sqrt(x-1)<sqrt(x-2)
- sqrt(x)<3-2*cos(pi*x)
sin(y)<(-1)/sqrt(2) desigualdades
Solución
Ha introducido
[src]
-1
sin(y) < -----
___
\/ 2
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
sin(y) < -1/sqrt(2)
Solución detallada
Se da la desigualdad:
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(y \right)} = - \frac{1}{\sqrt{2}}$$
Resolvemos:
$$x_{1} = 68.329640215578$$
$$x_{2} = 73.0420291959627$$
$$x_{3} = -65.1880475619882$$
$$x_{4} = -46.3384916404494$$
$$x_{5} = 62.0464549083984$$
$$x_{6} = -63.6172512351933$$
$$x_{7} = 98.174770424681$$
$$x_{8} = -90.3207887907066$$
$$x_{9} = -38.484510006475$$
$$x_{10} = -128.019900633784$$
$$x_{11} = 74.6128255227576$$
$$x_{12} = 66.7588438887831$$
$$x_{13} = -51.0508806208341$$
$$x_{14} = -96.6039740978861$$
$$x_{15} = -27.4889357189107$$
$$x_{16} = 5.49778714378214$$
$$x_{17} = -52.621676947629$$
$$x_{18} = 80.8960108299372$$
$$x_{19} = -0.785398163397448$$
$$x_{20} = 18.0641577581413$$
$$x_{21} = -40.0553063332699$$
$$x_{22} = 93.4623814442964$$
$$x_{23} = -13.3517687777566$$
$$x_{24} = 41.6261026600648$$
$$x_{25} = 22.776546738526$$
$$x_{26} = 3.92699081698724$$
$$x_{27} = -215482.625507887$$
$$x_{28} = 91.8915851175014$$
$$x_{29} = 55.7632696012188$$
$$x_{30} = -2.35619449019234$$
$$x_{31} = 16.4933614313464$$
$$x_{32} = -101.316363078271$$
$$x_{33} = -8.63937979737193$$
$$x_{34} = 10.2101761241668$$
$$x_{35} = 11.7809724509617$$
$$x_{36} = -57.3340659280137$$
$$x_{37} = 49.4800842940392$$
$$x_{38} = -830.165858711103$$
$$x_{39} = -77.7544181763474$$
$$x_{40} = -44.7676953136546$$
$$x_{41} = 54.1924732744239$$
$$x_{42} = -69.9004365423729$$
$$x_{43} = -58.9048622548086$$
$$x_{44} = -76.1836218495525$$
$$x_{45} = 652.665873783279$$
$$x_{46} = -2865.91789823729$$
$$x_{47} = -25.9181393921158$$
$$x_{48} = 36.9137136796801$$
$$x_{49} = -371.493331286993$$
$$x_{50} = 30.6305283725005$$
$$x_{51} = 85.6083998103219$$
$$x_{52} = -19.6349540849362$$
$$x_{53} = -14.9225651045515$$
$$x_{54} = 99.7455667514759$$
$$x_{55} = 35.3429173528852$$
$$x_{56} = -21.2057504117311$$
$$x_{57} = -84.037603483527$$
$$x_{58} = 29.0597320457056$$
$$x_{59} = 87.1791961371168$$
$$x_{60} = -71.4712328691678$$
$$x_{61} = -82.4668071567321$$
$$x_{62} = -704.502152567511$$
$$x_{63} = 60.4756585816035$$
$$x_{64} = -88.7499924639117$$
$$x_{65} = -32.2013246992954$$
$$x_{66} = 43.1968989868597$$
$$x_{67} = -95.0331777710912$$
$$x_{68} = 79.3252145031423$$
$$x_{69} = -33.7721210260903$$
$$x_{70} = 47.9092879672443$$
$$x_{71} = -7.06858347057703$$
$$x_{72} = 24.3473430653209$$
$$x_{1} = 68.329640215578$$
$$x_{2} = 73.0420291959627$$
$$x_{3} = -65.1880475619882$$
$$x_{4} = -46.3384916404494$$
$$x_{5} = 62.0464549083984$$
$$x_{6} = -63.6172512351933$$
$$x_{7} = 98.174770424681$$
$$x_{8} = -90.3207887907066$$
$$x_{9} = -38.484510006475$$
$$x_{10} = -128.019900633784$$
$$x_{11} = 74.6128255227576$$
$$x_{12} = 66.7588438887831$$
$$x_{13} = -51.0508806208341$$
$$x_{14} = -96.6039740978861$$
$$x_{15} = -27.4889357189107$$
$$x_{16} = 5.49778714378214$$
$$x_{17} = -52.621676947629$$
$$x_{18} = 80.8960108299372$$
$$x_{19} = -0.785398163397448$$
$$x_{20} = 18.0641577581413$$
$$x_{21} = -40.0553063332699$$
$$x_{22} = 93.4623814442964$$
$$x_{23} = -13.3517687777566$$
$$x_{24} = 41.6261026600648$$
$$x_{25} = 22.776546738526$$
$$x_{26} = 3.92699081698724$$
$$x_{27} = -215482.625507887$$
$$x_{28} = 91.8915851175014$$
$$x_{29} = 55.7632696012188$$
$$x_{30} = -2.35619449019234$$
$$x_{31} = 16.4933614313464$$
$$x_{32} = -101.316363078271$$
$$x_{33} = -8.63937979737193$$
$$x_{34} = 10.2101761241668$$
$$x_{35} = 11.7809724509617$$
$$x_{36} = -57.3340659280137$$
$$x_{37} = 49.4800842940392$$
$$x_{38} = -830.165858711103$$
$$x_{39} = -77.7544181763474$$
$$x_{40} = -44.7676953136546$$
$$x_{41} = 54.1924732744239$$
$$x_{42} = -69.9004365423729$$
$$x_{43} = -58.9048622548086$$
$$x_{44} = -76.1836218495525$$
$$x_{45} = 652.665873783279$$
$$x_{46} = -2865.91789823729$$
$$x_{47} = -25.9181393921158$$
$$x_{48} = 36.9137136796801$$
$$x_{49} = -371.493331286993$$
$$x_{50} = 30.6305283725005$$
$$x_{51} = 85.6083998103219$$
$$x_{52} = -19.6349540849362$$
$$x_{53} = -14.9225651045515$$
$$x_{54} = 99.7455667514759$$
$$x_{55} = 35.3429173528852$$
$$x_{56} = -21.2057504117311$$
$$x_{57} = -84.037603483527$$
$$x_{58} = 29.0597320457056$$
$$x_{59} = 87.1791961371168$$
$$x_{60} = -71.4712328691678$$
$$x_{61} = -82.4668071567321$$
$$x_{62} = -704.502152567511$$
$$x_{63} = 60.4756585816035$$
$$x_{64} = -88.7499924639117$$
$$x_{65} = -32.2013246992954$$
$$x_{66} = 43.1968989868597$$
$$x_{67} = -95.0331777710912$$
$$x_{68} = 79.3252145031423$$
$$x_{69} = -33.7721210260903$$
$$x_{70} = 47.9092879672443$$
$$x_{71} = -7.06858347057703$$
$$x_{72} = 24.3473430653209$$
Las raíces dadas
$$x_{27} = -215482.625507887$$
$$x_{46} = -2865.91789823729$$
$$x_{38} = -830.165858711103$$
$$x_{62} = -704.502152567511$$
$$x_{49} = -371.493331286993$$
$$x_{10} = -128.019900633784$$
$$x_{32} = -101.316363078271$$
$$x_{14} = -96.6039740978861$$
$$x_{67} = -95.0331777710912$$
$$x_{8} = -90.3207887907066$$
$$x_{64} = -88.7499924639117$$
$$x_{57} = -84.037603483527$$
$$x_{61} = -82.4668071567321$$
$$x_{39} = -77.7544181763474$$
$$x_{44} = -76.1836218495525$$
$$x_{60} = -71.4712328691678$$
$$x_{42} = -69.9004365423729$$
$$x_{3} = -65.1880475619882$$
$$x_{6} = -63.6172512351933$$
$$x_{43} = -58.9048622548086$$
$$x_{36} = -57.3340659280137$$
$$x_{17} = -52.621676947629$$
$$x_{13} = -51.0508806208341$$
$$x_{4} = -46.3384916404494$$
$$x_{40} = -44.7676953136546$$
$$x_{21} = -40.0553063332699$$
$$x_{9} = -38.484510006475$$
$$x_{69} = -33.7721210260903$$
$$x_{65} = -32.2013246992954$$
$$x_{15} = -27.4889357189107$$
$$x_{47} = -25.9181393921158$$
$$x_{56} = -21.2057504117311$$
$$x_{52} = -19.6349540849362$$
$$x_{53} = -14.9225651045515$$
$$x_{23} = -13.3517687777566$$
$$x_{33} = -8.63937979737193$$
$$x_{71} = -7.06858347057703$$
$$x_{30} = -2.35619449019234$$
$$x_{19} = -0.785398163397448$$
$$x_{26} = 3.92699081698724$$
$$x_{16} = 5.49778714378214$$
$$x_{34} = 10.2101761241668$$
$$x_{35} = 11.7809724509617$$
$$x_{31} = 16.4933614313464$$
$$x_{20} = 18.0641577581413$$
$$x_{25} = 22.776546738526$$
$$x_{72} = 24.3473430653209$$
$$x_{58} = 29.0597320457056$$
$$x_{50} = 30.6305283725005$$
$$x_{55} = 35.3429173528852$$
$$x_{48} = 36.9137136796801$$
$$x_{24} = 41.6261026600648$$
$$x_{66} = 43.1968989868597$$
$$x_{70} = 47.9092879672443$$
$$x_{37} = 49.4800842940392$$
$$x_{41} = 54.1924732744239$$
$$x_{29} = 55.7632696012188$$
$$x_{63} = 60.4756585816035$$
$$x_{5} = 62.0464549083984$$
$$x_{12} = 66.7588438887831$$
$$x_{1} = 68.329640215578$$
$$x_{2} = 73.0420291959627$$
$$x_{11} = 74.6128255227576$$
$$x_{68} = 79.3252145031423$$
$$x_{18} = 80.8960108299372$$
$$x_{51} = 85.6083998103219$$
$$x_{59} = 87.1791961371168$$
$$x_{28} = 91.8915851175014$$
$$x_{22} = 93.4623814442964$$
$$x_{7} = 98.174770424681$$
$$x_{54} = 99.7455667514759$$
$$x_{45} = 652.665873783279$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{27}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{27} - \frac{1}{10}$$
=
$$-215482.625507887 + - \frac{1}{10}$$
=
$$-215482.725507887$$
lo sustituimos en la expresión
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
Entonces
$$x < -215482.625507887$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -215482.625507887 \wedge x < -2865.91789823729$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -215482.625507887 \wedge x < -2865.91789823729$$
$$x > -830.165858711103 \wedge x < -704.502152567511$$
$$x > -371.493331286993 \wedge x < -128.019900633784$$
$$x > -101.316363078271 \wedge x < -96.6039740978861$$
$$x > -95.0331777710912 \wedge x < -90.3207887907066$$
$$x > -88.7499924639117 \wedge x < -84.037603483527$$
$$x > -82.4668071567321 \wedge x < -77.7544181763474$$
$$x > -76.1836218495525 \wedge x < -71.4712328691678$$
$$x > -69.9004365423729 \wedge x < -65.1880475619882$$
$$x > -63.6172512351933 \wedge x < -58.9048622548086$$
$$x > -57.3340659280137 \wedge x < -52.621676947629$$
$$x > -51.0508806208341 \wedge x < -46.3384916404494$$
$$x > -44.7676953136546 \wedge x < -40.0553063332699$$
$$x > -38.484510006475 \wedge x < -33.7721210260903$$
$$x > -32.2013246992954 \wedge x < -27.4889357189107$$
$$x > -25.9181393921158 \wedge x < -21.2057504117311$$
$$x > -19.6349540849362 \wedge x < -14.9225651045515$$
$$x > -13.3517687777566 \wedge x < -8.63937979737193$$
$$x > -7.06858347057703 \wedge x < -2.35619449019234$$
$$x > -0.785398163397448 \wedge x < 3.92699081698724$$
$$x > 5.49778714378214 \wedge x < 10.2101761241668$$
$$x > 11.7809724509617 \wedge x < 16.4933614313464$$
$$x > 18.0641577581413 \wedge x < 22.776546738526$$
$$x > 24.3473430653209 \wedge x < 29.0597320457056$$
$$x > 30.6305283725005 \wedge x < 35.3429173528852$$
$$x > 36.9137136796801 \wedge x < 41.6261026600648$$
$$x > 43.1968989868597 \wedge x < 47.9092879672443$$
$$x > 49.4800842940392 \wedge x < 54.1924732744239$$
$$x > 55.7632696012188 \wedge x < 60.4756585816035$$
$$x > 62.0464549083984 \wedge x < 66.7588438887831$$
$$x > 68.329640215578 \wedge x < 73.0420291959627$$
$$x > 74.6128255227576 \wedge x < 79.3252145031423$$
$$x > 80.8960108299372 \wedge x < 85.6083998103219$$
$$x > 87.1791961371168 \wedge x < 91.8915851175014$$
$$x > 93.4623814442964 \wedge x < 98.174770424681$$
$$x > 99.7455667514759 \wedge x < 652.665873783279$$
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(y \right)} = - \frac{1}{\sqrt{2}}$$
Resolvemos:
$$x_{1} = 68.329640215578$$
$$x_{2} = 73.0420291959627$$
$$x_{3} = -65.1880475619882$$
$$x_{4} = -46.3384916404494$$
$$x_{5} = 62.0464549083984$$
$$x_{6} = -63.6172512351933$$
$$x_{7} = 98.174770424681$$
$$x_{8} = -90.3207887907066$$
$$x_{9} = -38.484510006475$$
$$x_{10} = -128.019900633784$$
$$x_{11} = 74.6128255227576$$
$$x_{12} = 66.7588438887831$$
$$x_{13} = -51.0508806208341$$
$$x_{14} = -96.6039740978861$$
$$x_{15} = -27.4889357189107$$
$$x_{16} = 5.49778714378214$$
$$x_{17} = -52.621676947629$$
$$x_{18} = 80.8960108299372$$
$$x_{19} = -0.785398163397448$$
$$x_{20} = 18.0641577581413$$
$$x_{21} = -40.0553063332699$$
$$x_{22} = 93.4623814442964$$
$$x_{23} = -13.3517687777566$$
$$x_{24} = 41.6261026600648$$
$$x_{25} = 22.776546738526$$
$$x_{26} = 3.92699081698724$$
$$x_{27} = -215482.625507887$$
$$x_{28} = 91.8915851175014$$
$$x_{29} = 55.7632696012188$$
$$x_{30} = -2.35619449019234$$
$$x_{31} = 16.4933614313464$$
$$x_{32} = -101.316363078271$$
$$x_{33} = -8.63937979737193$$
$$x_{34} = 10.2101761241668$$
$$x_{35} = 11.7809724509617$$
$$x_{36} = -57.3340659280137$$
$$x_{37} = 49.4800842940392$$
$$x_{38} = -830.165858711103$$
$$x_{39} = -77.7544181763474$$
$$x_{40} = -44.7676953136546$$
$$x_{41} = 54.1924732744239$$
$$x_{42} = -69.9004365423729$$
$$x_{43} = -58.9048622548086$$
$$x_{44} = -76.1836218495525$$
$$x_{45} = 652.665873783279$$
$$x_{46} = -2865.91789823729$$
$$x_{47} = -25.9181393921158$$
$$x_{48} = 36.9137136796801$$
$$x_{49} = -371.493331286993$$
$$x_{50} = 30.6305283725005$$
$$x_{51} = 85.6083998103219$$
$$x_{52} = -19.6349540849362$$
$$x_{53} = -14.9225651045515$$
$$x_{54} = 99.7455667514759$$
$$x_{55} = 35.3429173528852$$
$$x_{56} = -21.2057504117311$$
$$x_{57} = -84.037603483527$$
$$x_{58} = 29.0597320457056$$
$$x_{59} = 87.1791961371168$$
$$x_{60} = -71.4712328691678$$
$$x_{61} = -82.4668071567321$$
$$x_{62} = -704.502152567511$$
$$x_{63} = 60.4756585816035$$
$$x_{64} = -88.7499924639117$$
$$x_{65} = -32.2013246992954$$
$$x_{66} = 43.1968989868597$$
$$x_{67} = -95.0331777710912$$
$$x_{68} = 79.3252145031423$$
$$x_{69} = -33.7721210260903$$
$$x_{70} = 47.9092879672443$$
$$x_{71} = -7.06858347057703$$
$$x_{72} = 24.3473430653209$$
$$x_{1} = 68.329640215578$$
$$x_{2} = 73.0420291959627$$
$$x_{3} = -65.1880475619882$$
$$x_{4} = -46.3384916404494$$
$$x_{5} = 62.0464549083984$$
$$x_{6} = -63.6172512351933$$
$$x_{7} = 98.174770424681$$
$$x_{8} = -90.3207887907066$$
$$x_{9} = -38.484510006475$$
$$x_{10} = -128.019900633784$$
$$x_{11} = 74.6128255227576$$
$$x_{12} = 66.7588438887831$$
$$x_{13} = -51.0508806208341$$
$$x_{14} = -96.6039740978861$$
$$x_{15} = -27.4889357189107$$
$$x_{16} = 5.49778714378214$$
$$x_{17} = -52.621676947629$$
$$x_{18} = 80.8960108299372$$
$$x_{19} = -0.785398163397448$$
$$x_{20} = 18.0641577581413$$
$$x_{21} = -40.0553063332699$$
$$x_{22} = 93.4623814442964$$
$$x_{23} = -13.3517687777566$$
$$x_{24} = 41.6261026600648$$
$$x_{25} = 22.776546738526$$
$$x_{26} = 3.92699081698724$$
$$x_{27} = -215482.625507887$$
$$x_{28} = 91.8915851175014$$
$$x_{29} = 55.7632696012188$$
$$x_{30} = -2.35619449019234$$
$$x_{31} = 16.4933614313464$$
$$x_{32} = -101.316363078271$$
$$x_{33} = -8.63937979737193$$
$$x_{34} = 10.2101761241668$$
$$x_{35} = 11.7809724509617$$
$$x_{36} = -57.3340659280137$$
$$x_{37} = 49.4800842940392$$
$$x_{38} = -830.165858711103$$
$$x_{39} = -77.7544181763474$$
$$x_{40} = -44.7676953136546$$
$$x_{41} = 54.1924732744239$$
$$x_{42} = -69.9004365423729$$
$$x_{43} = -58.9048622548086$$
$$x_{44} = -76.1836218495525$$
$$x_{45} = 652.665873783279$$
$$x_{46} = -2865.91789823729$$
$$x_{47} = -25.9181393921158$$
$$x_{48} = 36.9137136796801$$
$$x_{49} = -371.493331286993$$
$$x_{50} = 30.6305283725005$$
$$x_{51} = 85.6083998103219$$
$$x_{52} = -19.6349540849362$$
$$x_{53} = -14.9225651045515$$
$$x_{54} = 99.7455667514759$$
$$x_{55} = 35.3429173528852$$
$$x_{56} = -21.2057504117311$$
$$x_{57} = -84.037603483527$$
$$x_{58} = 29.0597320457056$$
$$x_{59} = 87.1791961371168$$
$$x_{60} = -71.4712328691678$$
$$x_{61} = -82.4668071567321$$
$$x_{62} = -704.502152567511$$
$$x_{63} = 60.4756585816035$$
$$x_{64} = -88.7499924639117$$
$$x_{65} = -32.2013246992954$$
$$x_{66} = 43.1968989868597$$
$$x_{67} = -95.0331777710912$$
$$x_{68} = 79.3252145031423$$
$$x_{69} = -33.7721210260903$$
$$x_{70} = 47.9092879672443$$
$$x_{71} = -7.06858347057703$$
$$x_{72} = 24.3473430653209$$
Las raíces dadas
$$x_{27} = -215482.625507887$$
$$x_{46} = -2865.91789823729$$
$$x_{38} = -830.165858711103$$
$$x_{62} = -704.502152567511$$
$$x_{49} = -371.493331286993$$
$$x_{10} = -128.019900633784$$
$$x_{32} = -101.316363078271$$
$$x_{14} = -96.6039740978861$$
$$x_{67} = -95.0331777710912$$
$$x_{8} = -90.3207887907066$$
$$x_{64} = -88.7499924639117$$
$$x_{57} = -84.037603483527$$
$$x_{61} = -82.4668071567321$$
$$x_{39} = -77.7544181763474$$
$$x_{44} = -76.1836218495525$$
$$x_{60} = -71.4712328691678$$
$$x_{42} = -69.9004365423729$$
$$x_{3} = -65.1880475619882$$
$$x_{6} = -63.6172512351933$$
$$x_{43} = -58.9048622548086$$
$$x_{36} = -57.3340659280137$$
$$x_{17} = -52.621676947629$$
$$x_{13} = -51.0508806208341$$
$$x_{4} = -46.3384916404494$$
$$x_{40} = -44.7676953136546$$
$$x_{21} = -40.0553063332699$$
$$x_{9} = -38.484510006475$$
$$x_{69} = -33.7721210260903$$
$$x_{65} = -32.2013246992954$$
$$x_{15} = -27.4889357189107$$
$$x_{47} = -25.9181393921158$$
$$x_{56} = -21.2057504117311$$
$$x_{52} = -19.6349540849362$$
$$x_{53} = -14.9225651045515$$
$$x_{23} = -13.3517687777566$$
$$x_{33} = -8.63937979737193$$
$$x_{71} = -7.06858347057703$$
$$x_{30} = -2.35619449019234$$
$$x_{19} = -0.785398163397448$$
$$x_{26} = 3.92699081698724$$
$$x_{16} = 5.49778714378214$$
$$x_{34} = 10.2101761241668$$
$$x_{35} = 11.7809724509617$$
$$x_{31} = 16.4933614313464$$
$$x_{20} = 18.0641577581413$$
$$x_{25} = 22.776546738526$$
$$x_{72} = 24.3473430653209$$
$$x_{58} = 29.0597320457056$$
$$x_{50} = 30.6305283725005$$
$$x_{55} = 35.3429173528852$$
$$x_{48} = 36.9137136796801$$
$$x_{24} = 41.6261026600648$$
$$x_{66} = 43.1968989868597$$
$$x_{70} = 47.9092879672443$$
$$x_{37} = 49.4800842940392$$
$$x_{41} = 54.1924732744239$$
$$x_{29} = 55.7632696012188$$
$$x_{63} = 60.4756585816035$$
$$x_{5} = 62.0464549083984$$
$$x_{12} = 66.7588438887831$$
$$x_{1} = 68.329640215578$$
$$x_{2} = 73.0420291959627$$
$$x_{11} = 74.6128255227576$$
$$x_{68} = 79.3252145031423$$
$$x_{18} = 80.8960108299372$$
$$x_{51} = 85.6083998103219$$
$$x_{59} = 87.1791961371168$$
$$x_{28} = 91.8915851175014$$
$$x_{22} = 93.4623814442964$$
$$x_{7} = 98.174770424681$$
$$x_{54} = 99.7455667514759$$
$$x_{45} = 652.665873783279$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{27}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{27} - \frac{1}{10}$$
=
$$-215482.625507887 + - \frac{1}{10}$$
=
$$-215482.725507887$$
lo sustituimos en la expresión
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
$$\sin{\left(y \right)} < - \frac{1}{\sqrt{2}}$$
___
-\/ 2
sin(y) < -------
2
Entonces
$$x < -215482.625507887$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -215482.625507887 \wedge x < -2865.91789823729$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------ο-------
x27 x46 x38 x62 x49 x10 x32 x14 x67 x8 x64 x57 x61 x39 x44 x60 x42 x3 x6 x43 x36 x17 x13 x4 x40 x21 x9 x69 x65 x15 x47 x56 x52 x53 x23 x33 x71 x30 x19 x26 x16 x34 x35 x31 x20 x25 x72 x58 x50 x55 x48 x24 x66 x70 x37 x41 x29 x63 x5 x12 x1 x2 x11 x68 x18 x51 x59 x28 x22 x7 x54 x45Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -215482.625507887 \wedge x < -2865.91789823729$$
$$x > -830.165858711103 \wedge x < -704.502152567511$$
$$x > -371.493331286993 \wedge x < -128.019900633784$$
$$x > -101.316363078271 \wedge x < -96.6039740978861$$
$$x > -95.0331777710912 \wedge x < -90.3207887907066$$
$$x > -88.7499924639117 \wedge x < -84.037603483527$$
$$x > -82.4668071567321 \wedge x < -77.7544181763474$$
$$x > -76.1836218495525 \wedge x < -71.4712328691678$$
$$x > -69.9004365423729 \wedge x < -65.1880475619882$$
$$x > -63.6172512351933 \wedge x < -58.9048622548086$$
$$x > -57.3340659280137 \wedge x < -52.621676947629$$
$$x > -51.0508806208341 \wedge x < -46.3384916404494$$
$$x > -44.7676953136546 \wedge x < -40.0553063332699$$
$$x > -38.484510006475 \wedge x < -33.7721210260903$$
$$x > -32.2013246992954 \wedge x < -27.4889357189107$$
$$x > -25.9181393921158 \wedge x < -21.2057504117311$$
$$x > -19.6349540849362 \wedge x < -14.9225651045515$$
$$x > -13.3517687777566 \wedge x < -8.63937979737193$$
$$x > -7.06858347057703 \wedge x < -2.35619449019234$$
$$x > -0.785398163397448 \wedge x < 3.92699081698724$$
$$x > 5.49778714378214 \wedge x < 10.2101761241668$$
$$x > 11.7809724509617 \wedge x < 16.4933614313464$$
$$x > 18.0641577581413 \wedge x < 22.776546738526$$
$$x > 24.3473430653209 \wedge x < 29.0597320457056$$
$$x > 30.6305283725005 \wedge x < 35.3429173528852$$
$$x > 36.9137136796801 \wedge x < 41.6261026600648$$
$$x > 43.1968989868597 \wedge x < 47.9092879672443$$
$$x > 49.4800842940392 \wedge x < 54.1924732744239$$
$$x > 55.7632696012188 \wedge x < 60.4756585816035$$
$$x > 62.0464549083984 \wedge x < 66.7588438887831$$
$$x > 68.329640215578 \wedge x < 73.0420291959627$$
$$x > 74.6128255227576 \wedge x < 79.3252145031423$$
$$x > 80.8960108299372 \wedge x < 85.6083998103219$$
$$x > 87.1791961371168 \wedge x < 91.8915851175014$$
$$x > 93.4623814442964 \wedge x < 98.174770424681$$
$$x > 99.7455667514759 \wedge x < 652.665873783279$$
Respuesta rápida
[src]
/5*pi 7*pi\ And|---- < x, x < ----| \ 4 4 /
$$\frac{5 \pi}{4} < x \wedge x < \frac{7 \pi}{4}$$
(5*pi/4 < x)∧(x < 7*pi/4)
Respuesta rápida 2
[src]
5*pi 7*pi (----, ----) 4 4
$$x\ in\ \left(\frac{5 \pi}{4}, \frac{7 \pi}{4}\right)$$
x in Interval.open(5*pi/4, 7*pi/4)