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
- Integral de d{x}:
- cos(t)
- Límite de la función:
- cos(t)
- Derivada de:
-
cos(t)
-
Expresiones idénticas
- cos(t)<=-(sqrt(dos)/ dos)
- coseno de (t) menos o igual a menos ( raíz cuadrada de (2) dividir por 2)
- coseno de (t) menos o igual a menos ( raíz cuadrada de (dos) dividir por dos)
- cos(t)<=-(√(2)/2)
- cost<=-sqrt2/2
- cos(t)<=-(sqrt(2) dividir por 2)
-
Expresiones semejantes
- cost≤1/2
- cos(t)<=+(sqrt(2)/2)
-
Expresiones con funciones
- Coseno cos
- cosx<√2/2
- cosx<1/2
- cosx/2>-1/2
- cosx>√3/2
- cosx>=x^2+1
- Raíz cuadrada sqrt
- sqrt(x+8)<x+2
- sqrt(x^2-1)>1
- sqrt(x+6)>x
- sqrt(2x-1)>x-2
- sqrt(x-2)<1
cos(t)<=-(sqrt(2)/2) desigualdades
Solución
Ha introducido
[src]
___
-\/ 2
cos(t) <= -------
2
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
cos(t) <= -sqrt(2)/2
Solución detallada
Se da la desigualdad:
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = - \frac{\sqrt{2}}{2}$$
Resolvemos:
$$x_{1} = -27.4889357189107$$
$$x_{2} = 3.92699081698724$$
$$x_{3} = -40.0553063332699$$
$$x_{4} = -22.776546738526$$
$$x_{5} = -90.3207887907066$$
$$x_{6} = 47.9092879672443$$
$$x_{7} = 65.1880475619882$$
$$x_{8} = -21.2057504117311$$
$$x_{9} = -79.3252145031423$$
$$x_{10} = 40.0553063332699$$
$$x_{11} = -29.0597320457056$$
$$x_{12} = -77.7544181763474$$
$$x_{13} = -52.621676947629$$
$$x_{14} = 84.037603483527$$
$$x_{15} = -71.4712328691678$$
$$x_{16} = 85.6083998103219$$
$$x_{17} = 54.1924732744239$$
$$x_{18} = -10.2101761241668$$
$$x_{19} = -8.63937979737193$$
$$x_{20} = -33.7721210260903$$
$$x_{21} = 21.2057504117311$$
$$x_{22} = 35.3429173528852$$
$$x_{23} = -58.9048622548086$$
$$x_{24} = 104.457955731861$$
$$x_{25} = -41.6261026600648$$
$$x_{26} = 2.35619449019234$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -14.9225651045515$$
$$x_{29} = -66.7588438887831$$
$$x_{30} = 58.9048622548086$$
$$x_{31} = 79.3252145031423$$
$$x_{32} = -16.4933614313464$$
$$x_{33} = 14.9225651045515$$
$$x_{34} = -65.1880475619882$$
$$x_{35} = 10.2101761241668$$
$$x_{36} = -54.1924732744239$$
$$x_{37} = 71.4712328691678$$
$$x_{38} = 96.6039740978861$$
$$x_{39} = 60.4756585816035$$
$$x_{40} = -47.9092879672443$$
$$x_{41} = 98.174770424681$$
$$x_{42} = 8.63937979737193$$
$$x_{43} = 77.7544181763474$$
$$x_{44} = -335.36501577071$$
$$x_{45} = -60.4756585816035$$
$$x_{46} = 39349.2333843756$$
$$x_{47} = 73.0420291959627$$
$$x_{48} = -85.6083998103219$$
$$x_{49} = -35.3429173528852$$
$$x_{50} = 255.254403104171$$
$$x_{51} = -91.8915851175014$$
$$x_{52} = -2.35619449019234$$
$$x_{53} = 90.3207887907066$$
$$x_{54} = 27.4889357189107$$
$$x_{55} = -96.6039740978861$$
$$x_{56} = -98.174770424681$$
$$x_{57} = 33.7721210260903$$
$$x_{58} = -46.3384916404494$$
$$x_{59} = 22.776546738526$$
$$x_{60} = 66.7588438887831$$
$$x_{61} = 2584.745355741$$
$$x_{62} = 46.3384916404494$$
$$x_{63} = 41.6261026600648$$
$$x_{64} = 16.4933614313464$$
$$x_{65} = -3.92699081698724$$
$$x_{66} = -84.037603483527$$
$$x_{67} = 29.0597320457056$$
$$x_{68} = 52.621676947629$$
$$x_{69} = 91.8915851175014$$
$$x_{1} = -27.4889357189107$$
$$x_{2} = 3.92699081698724$$
$$x_{3} = -40.0553063332699$$
$$x_{4} = -22.776546738526$$
$$x_{5} = -90.3207887907066$$
$$x_{6} = 47.9092879672443$$
$$x_{7} = 65.1880475619882$$
$$x_{8} = -21.2057504117311$$
$$x_{9} = -79.3252145031423$$
$$x_{10} = 40.0553063332699$$
$$x_{11} = -29.0597320457056$$
$$x_{12} = -77.7544181763474$$
$$x_{13} = -52.621676947629$$
$$x_{14} = 84.037603483527$$
$$x_{15} = -71.4712328691678$$
$$x_{16} = 85.6083998103219$$
$$x_{17} = 54.1924732744239$$
$$x_{18} = -10.2101761241668$$
$$x_{19} = -8.63937979737193$$
$$x_{20} = -33.7721210260903$$
$$x_{21} = 21.2057504117311$$
$$x_{22} = 35.3429173528852$$
$$x_{23} = -58.9048622548086$$
$$x_{24} = 104.457955731861$$
$$x_{25} = -41.6261026600648$$
$$x_{26} = 2.35619449019234$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -14.9225651045515$$
$$x_{29} = -66.7588438887831$$
$$x_{30} = 58.9048622548086$$
$$x_{31} = 79.3252145031423$$
$$x_{32} = -16.4933614313464$$
$$x_{33} = 14.9225651045515$$
$$x_{34} = -65.1880475619882$$
$$x_{35} = 10.2101761241668$$
$$x_{36} = -54.1924732744239$$
$$x_{37} = 71.4712328691678$$
$$x_{38} = 96.6039740978861$$
$$x_{39} = 60.4756585816035$$
$$x_{40} = -47.9092879672443$$
$$x_{41} = 98.174770424681$$
$$x_{42} = 8.63937979737193$$
$$x_{43} = 77.7544181763474$$
$$x_{44} = -335.36501577071$$
$$x_{45} = -60.4756585816035$$
$$x_{46} = 39349.2333843756$$
$$x_{47} = 73.0420291959627$$
$$x_{48} = -85.6083998103219$$
$$x_{49} = -35.3429173528852$$
$$x_{50} = 255.254403104171$$
$$x_{51} = -91.8915851175014$$
$$x_{52} = -2.35619449019234$$
$$x_{53} = 90.3207887907066$$
$$x_{54} = 27.4889357189107$$
$$x_{55} = -96.6039740978861$$
$$x_{56} = -98.174770424681$$
$$x_{57} = 33.7721210260903$$
$$x_{58} = -46.3384916404494$$
$$x_{59} = 22.776546738526$$
$$x_{60} = 66.7588438887831$$
$$x_{61} = 2584.745355741$$
$$x_{62} = 46.3384916404494$$
$$x_{63} = 41.6261026600648$$
$$x_{64} = 16.4933614313464$$
$$x_{65} = -3.92699081698724$$
$$x_{66} = -84.037603483527$$
$$x_{67} = 29.0597320457056$$
$$x_{68} = 52.621676947629$$
$$x_{69} = 91.8915851175014$$
Las raíces dadas
$$x_{44} = -335.36501577071$$
$$x_{56} = -98.174770424681$$
$$x_{55} = -96.6039740978861$$
$$x_{51} = -91.8915851175014$$
$$x_{5} = -90.3207887907066$$
$$x_{48} = -85.6083998103219$$
$$x_{66} = -84.037603483527$$
$$x_{9} = -79.3252145031423$$
$$x_{12} = -77.7544181763474$$
$$x_{27} = -73.0420291959627$$
$$x_{15} = -71.4712328691678$$
$$x_{29} = -66.7588438887831$$
$$x_{34} = -65.1880475619882$$
$$x_{45} = -60.4756585816035$$
$$x_{23} = -58.9048622548086$$
$$x_{36} = -54.1924732744239$$
$$x_{13} = -52.621676947629$$
$$x_{40} = -47.9092879672443$$
$$x_{58} = -46.3384916404494$$
$$x_{25} = -41.6261026600648$$
$$x_{3} = -40.0553063332699$$
$$x_{49} = -35.3429173528852$$
$$x_{20} = -33.7721210260903$$
$$x_{11} = -29.0597320457056$$
$$x_{1} = -27.4889357189107$$
$$x_{4} = -22.776546738526$$
$$x_{8} = -21.2057504117311$$
$$x_{32} = -16.4933614313464$$
$$x_{28} = -14.9225651045515$$
$$x_{18} = -10.2101761241668$$
$$x_{19} = -8.63937979737193$$
$$x_{65} = -3.92699081698724$$
$$x_{52} = -2.35619449019234$$
$$x_{26} = 2.35619449019234$$
$$x_{2} = 3.92699081698724$$
$$x_{42} = 8.63937979737193$$
$$x_{35} = 10.2101761241668$$
$$x_{33} = 14.9225651045515$$
$$x_{64} = 16.4933614313464$$
$$x_{21} = 21.2057504117311$$
$$x_{59} = 22.776546738526$$
$$x_{54} = 27.4889357189107$$
$$x_{67} = 29.0597320457056$$
$$x_{57} = 33.7721210260903$$
$$x_{22} = 35.3429173528852$$
$$x_{10} = 40.0553063332699$$
$$x_{63} = 41.6261026600648$$
$$x_{62} = 46.3384916404494$$
$$x_{6} = 47.9092879672443$$
$$x_{68} = 52.621676947629$$
$$x_{17} = 54.1924732744239$$
$$x_{30} = 58.9048622548086$$
$$x_{39} = 60.4756585816035$$
$$x_{7} = 65.1880475619882$$
$$x_{60} = 66.7588438887831$$
$$x_{37} = 71.4712328691678$$
$$x_{47} = 73.0420291959627$$
$$x_{43} = 77.7544181763474$$
$$x_{31} = 79.3252145031423$$
$$x_{14} = 84.037603483527$$
$$x_{16} = 85.6083998103219$$
$$x_{53} = 90.3207887907066$$
$$x_{69} = 91.8915851175014$$
$$x_{38} = 96.6039740978861$$
$$x_{41} = 98.174770424681$$
$$x_{24} = 104.457955731861$$
$$x_{50} = 255.254403104171$$
$$x_{61} = 2584.745355741$$
$$x_{46} = 39349.2333843756$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{44}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{44} - \frac{1}{10}$$
=
$$-335.36501577071 + - \frac{1}{10}$$
=
$$-335.46501577071$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
Entonces
$$x \leq -335.36501577071$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
$$x \geq -96.6039740978861 \wedge x \leq -91.8915851175014$$
$$x \geq -90.3207887907066 \wedge x \leq -85.6083998103219$$
$$x \geq -84.037603483527 \wedge x \leq -79.3252145031423$$
$$x \geq -77.7544181763474 \wedge x \leq -73.0420291959627$$
$$x \geq -71.4712328691678 \wedge x \leq -66.7588438887831$$
$$x \geq -65.1880475619882 \wedge x \leq -60.4756585816035$$
$$x \geq -58.9048622548086 \wedge x \leq -54.1924732744239$$
$$x \geq -52.621676947629 \wedge x \leq -47.9092879672443$$
$$x \geq -46.3384916404494 \wedge x \leq -41.6261026600648$$
$$x \geq -40.0553063332699 \wedge x \leq -35.3429173528852$$
$$x \geq -33.7721210260903 \wedge x \leq -29.0597320457056$$
$$x \geq -27.4889357189107 \wedge x \leq -22.776546738526$$
$$x \geq -21.2057504117311 \wedge x \leq -16.4933614313464$$
$$x \geq -14.9225651045515 \wedge x \leq -10.2101761241668$$
$$x \geq -8.63937979737193 \wedge x \leq -3.92699081698724$$
$$x \geq -2.35619449019234 \wedge x \leq 2.35619449019234$$
$$x \geq 3.92699081698724 \wedge x \leq 8.63937979737193$$
$$x \geq 10.2101761241668 \wedge x \leq 14.9225651045515$$
$$x \geq 16.4933614313464 \wedge x \leq 21.2057504117311$$
$$x \geq 22.776546738526 \wedge x \leq 27.4889357189107$$
$$x \geq 29.0597320457056 \wedge x \leq 33.7721210260903$$
$$x \geq 35.3429173528852 \wedge x \leq 40.0553063332699$$
$$x \geq 41.6261026600648 \wedge x \leq 46.3384916404494$$
$$x \geq 47.9092879672443 \wedge x \leq 52.621676947629$$
$$x \geq 54.1924732744239 \wedge x \leq 58.9048622548086$$
$$x \geq 60.4756585816035 \wedge x \leq 65.1880475619882$$
$$x \geq 66.7588438887831 \wedge x \leq 71.4712328691678$$
$$x \geq 73.0420291959627 \wedge x \leq 77.7544181763474$$
$$x \geq 79.3252145031423 \wedge x \leq 84.037603483527$$
$$x \geq 85.6083998103219 \wedge x \leq 90.3207887907066$$
$$x \geq 91.8915851175014 \wedge x \leq 96.6039740978861$$
$$x \geq 98.174770424681 \wedge x \leq 104.457955731861$$
$$x \geq 255.254403104171 \wedge x \leq 2584.745355741$$
$$x \geq 39349.2333843756$$
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = - \frac{\sqrt{2}}{2}$$
Resolvemos:
$$x_{1} = -27.4889357189107$$
$$x_{2} = 3.92699081698724$$
$$x_{3} = -40.0553063332699$$
$$x_{4} = -22.776546738526$$
$$x_{5} = -90.3207887907066$$
$$x_{6} = 47.9092879672443$$
$$x_{7} = 65.1880475619882$$
$$x_{8} = -21.2057504117311$$
$$x_{9} = -79.3252145031423$$
$$x_{10} = 40.0553063332699$$
$$x_{11} = -29.0597320457056$$
$$x_{12} = -77.7544181763474$$
$$x_{13} = -52.621676947629$$
$$x_{14} = 84.037603483527$$
$$x_{15} = -71.4712328691678$$
$$x_{16} = 85.6083998103219$$
$$x_{17} = 54.1924732744239$$
$$x_{18} = -10.2101761241668$$
$$x_{19} = -8.63937979737193$$
$$x_{20} = -33.7721210260903$$
$$x_{21} = 21.2057504117311$$
$$x_{22} = 35.3429173528852$$
$$x_{23} = -58.9048622548086$$
$$x_{24} = 104.457955731861$$
$$x_{25} = -41.6261026600648$$
$$x_{26} = 2.35619449019234$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -14.9225651045515$$
$$x_{29} = -66.7588438887831$$
$$x_{30} = 58.9048622548086$$
$$x_{31} = 79.3252145031423$$
$$x_{32} = -16.4933614313464$$
$$x_{33} = 14.9225651045515$$
$$x_{34} = -65.1880475619882$$
$$x_{35} = 10.2101761241668$$
$$x_{36} = -54.1924732744239$$
$$x_{37} = 71.4712328691678$$
$$x_{38} = 96.6039740978861$$
$$x_{39} = 60.4756585816035$$
$$x_{40} = -47.9092879672443$$
$$x_{41} = 98.174770424681$$
$$x_{42} = 8.63937979737193$$
$$x_{43} = 77.7544181763474$$
$$x_{44} = -335.36501577071$$
$$x_{45} = -60.4756585816035$$
$$x_{46} = 39349.2333843756$$
$$x_{47} = 73.0420291959627$$
$$x_{48} = -85.6083998103219$$
$$x_{49} = -35.3429173528852$$
$$x_{50} = 255.254403104171$$
$$x_{51} = -91.8915851175014$$
$$x_{52} = -2.35619449019234$$
$$x_{53} = 90.3207887907066$$
$$x_{54} = 27.4889357189107$$
$$x_{55} = -96.6039740978861$$
$$x_{56} = -98.174770424681$$
$$x_{57} = 33.7721210260903$$
$$x_{58} = -46.3384916404494$$
$$x_{59} = 22.776546738526$$
$$x_{60} = 66.7588438887831$$
$$x_{61} = 2584.745355741$$
$$x_{62} = 46.3384916404494$$
$$x_{63} = 41.6261026600648$$
$$x_{64} = 16.4933614313464$$
$$x_{65} = -3.92699081698724$$
$$x_{66} = -84.037603483527$$
$$x_{67} = 29.0597320457056$$
$$x_{68} = 52.621676947629$$
$$x_{69} = 91.8915851175014$$
$$x_{1} = -27.4889357189107$$
$$x_{2} = 3.92699081698724$$
$$x_{3} = -40.0553063332699$$
$$x_{4} = -22.776546738526$$
$$x_{5} = -90.3207887907066$$
$$x_{6} = 47.9092879672443$$
$$x_{7} = 65.1880475619882$$
$$x_{8} = -21.2057504117311$$
$$x_{9} = -79.3252145031423$$
$$x_{10} = 40.0553063332699$$
$$x_{11} = -29.0597320457056$$
$$x_{12} = -77.7544181763474$$
$$x_{13} = -52.621676947629$$
$$x_{14} = 84.037603483527$$
$$x_{15} = -71.4712328691678$$
$$x_{16} = 85.6083998103219$$
$$x_{17} = 54.1924732744239$$
$$x_{18} = -10.2101761241668$$
$$x_{19} = -8.63937979737193$$
$$x_{20} = -33.7721210260903$$
$$x_{21} = 21.2057504117311$$
$$x_{22} = 35.3429173528852$$
$$x_{23} = -58.9048622548086$$
$$x_{24} = 104.457955731861$$
$$x_{25} = -41.6261026600648$$
$$x_{26} = 2.35619449019234$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -14.9225651045515$$
$$x_{29} = -66.7588438887831$$
$$x_{30} = 58.9048622548086$$
$$x_{31} = 79.3252145031423$$
$$x_{32} = -16.4933614313464$$
$$x_{33} = 14.9225651045515$$
$$x_{34} = -65.1880475619882$$
$$x_{35} = 10.2101761241668$$
$$x_{36} = -54.1924732744239$$
$$x_{37} = 71.4712328691678$$
$$x_{38} = 96.6039740978861$$
$$x_{39} = 60.4756585816035$$
$$x_{40} = -47.9092879672443$$
$$x_{41} = 98.174770424681$$
$$x_{42} = 8.63937979737193$$
$$x_{43} = 77.7544181763474$$
$$x_{44} = -335.36501577071$$
$$x_{45} = -60.4756585816035$$
$$x_{46} = 39349.2333843756$$
$$x_{47} = 73.0420291959627$$
$$x_{48} = -85.6083998103219$$
$$x_{49} = -35.3429173528852$$
$$x_{50} = 255.254403104171$$
$$x_{51} = -91.8915851175014$$
$$x_{52} = -2.35619449019234$$
$$x_{53} = 90.3207887907066$$
$$x_{54} = 27.4889357189107$$
$$x_{55} = -96.6039740978861$$
$$x_{56} = -98.174770424681$$
$$x_{57} = 33.7721210260903$$
$$x_{58} = -46.3384916404494$$
$$x_{59} = 22.776546738526$$
$$x_{60} = 66.7588438887831$$
$$x_{61} = 2584.745355741$$
$$x_{62} = 46.3384916404494$$
$$x_{63} = 41.6261026600648$$
$$x_{64} = 16.4933614313464$$
$$x_{65} = -3.92699081698724$$
$$x_{66} = -84.037603483527$$
$$x_{67} = 29.0597320457056$$
$$x_{68} = 52.621676947629$$
$$x_{69} = 91.8915851175014$$
Las raíces dadas
$$x_{44} = -335.36501577071$$
$$x_{56} = -98.174770424681$$
$$x_{55} = -96.6039740978861$$
$$x_{51} = -91.8915851175014$$
$$x_{5} = -90.3207887907066$$
$$x_{48} = -85.6083998103219$$
$$x_{66} = -84.037603483527$$
$$x_{9} = -79.3252145031423$$
$$x_{12} = -77.7544181763474$$
$$x_{27} = -73.0420291959627$$
$$x_{15} = -71.4712328691678$$
$$x_{29} = -66.7588438887831$$
$$x_{34} = -65.1880475619882$$
$$x_{45} = -60.4756585816035$$
$$x_{23} = -58.9048622548086$$
$$x_{36} = -54.1924732744239$$
$$x_{13} = -52.621676947629$$
$$x_{40} = -47.9092879672443$$
$$x_{58} = -46.3384916404494$$
$$x_{25} = -41.6261026600648$$
$$x_{3} = -40.0553063332699$$
$$x_{49} = -35.3429173528852$$
$$x_{20} = -33.7721210260903$$
$$x_{11} = -29.0597320457056$$
$$x_{1} = -27.4889357189107$$
$$x_{4} = -22.776546738526$$
$$x_{8} = -21.2057504117311$$
$$x_{32} = -16.4933614313464$$
$$x_{28} = -14.9225651045515$$
$$x_{18} = -10.2101761241668$$
$$x_{19} = -8.63937979737193$$
$$x_{65} = -3.92699081698724$$
$$x_{52} = -2.35619449019234$$
$$x_{26} = 2.35619449019234$$
$$x_{2} = 3.92699081698724$$
$$x_{42} = 8.63937979737193$$
$$x_{35} = 10.2101761241668$$
$$x_{33} = 14.9225651045515$$
$$x_{64} = 16.4933614313464$$
$$x_{21} = 21.2057504117311$$
$$x_{59} = 22.776546738526$$
$$x_{54} = 27.4889357189107$$
$$x_{67} = 29.0597320457056$$
$$x_{57} = 33.7721210260903$$
$$x_{22} = 35.3429173528852$$
$$x_{10} = 40.0553063332699$$
$$x_{63} = 41.6261026600648$$
$$x_{62} = 46.3384916404494$$
$$x_{6} = 47.9092879672443$$
$$x_{68} = 52.621676947629$$
$$x_{17} = 54.1924732744239$$
$$x_{30} = 58.9048622548086$$
$$x_{39} = 60.4756585816035$$
$$x_{7} = 65.1880475619882$$
$$x_{60} = 66.7588438887831$$
$$x_{37} = 71.4712328691678$$
$$x_{47} = 73.0420291959627$$
$$x_{43} = 77.7544181763474$$
$$x_{31} = 79.3252145031423$$
$$x_{14} = 84.037603483527$$
$$x_{16} = 85.6083998103219$$
$$x_{53} = 90.3207887907066$$
$$x_{69} = 91.8915851175014$$
$$x_{38} = 96.6039740978861$$
$$x_{41} = 98.174770424681$$
$$x_{24} = 104.457955731861$$
$$x_{50} = 255.254403104171$$
$$x_{61} = 2584.745355741$$
$$x_{46} = 39349.2333843756$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{44}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{44} - \frac{1}{10}$$
=
$$-335.36501577071 + - \frac{1}{10}$$
=
$$-335.46501577071$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
$$\cos{\left(t \right)} \leq - \frac{\sqrt{2}}{2}$$
___
-\/ 2
cos(t) <= -------
2
Entonces
$$x \leq -335.36501577071$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x44 x56 x55 x51 x5 x48 x66 x9 x12 x27 x15 x29 x34 x45 x23 x36 x13 x40 x58 x25 x3 x49 x20 x11 x1 x4 x8 x32 x28 x18 x19 x65 x52 x26 x2 x42 x35 x33 x64 x21 x59 x54 x67 x57 x22 x10 x63 x62 x6 x68 x17 x30 x39 x7 x60 x37 x47 x43 x31 x14 x16 x53 x69 x38 x41 x24 x50 x61 x46Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
$$x \geq -96.6039740978861 \wedge x \leq -91.8915851175014$$
$$x \geq -90.3207887907066 \wedge x \leq -85.6083998103219$$
$$x \geq -84.037603483527 \wedge x \leq -79.3252145031423$$
$$x \geq -77.7544181763474 \wedge x \leq -73.0420291959627$$
$$x \geq -71.4712328691678 \wedge x \leq -66.7588438887831$$
$$x \geq -65.1880475619882 \wedge x \leq -60.4756585816035$$
$$x \geq -58.9048622548086 \wedge x \leq -54.1924732744239$$
$$x \geq -52.621676947629 \wedge x \leq -47.9092879672443$$
$$x \geq -46.3384916404494 \wedge x \leq -41.6261026600648$$
$$x \geq -40.0553063332699 \wedge x \leq -35.3429173528852$$
$$x \geq -33.7721210260903 \wedge x \leq -29.0597320457056$$
$$x \geq -27.4889357189107 \wedge x \leq -22.776546738526$$
$$x \geq -21.2057504117311 \wedge x \leq -16.4933614313464$$
$$x \geq -14.9225651045515 \wedge x \leq -10.2101761241668$$
$$x \geq -8.63937979737193 \wedge x \leq -3.92699081698724$$
$$x \geq -2.35619449019234 \wedge x \leq 2.35619449019234$$
$$x \geq 3.92699081698724 \wedge x \leq 8.63937979737193$$
$$x \geq 10.2101761241668 \wedge x \leq 14.9225651045515$$
$$x \geq 16.4933614313464 \wedge x \leq 21.2057504117311$$
$$x \geq 22.776546738526 \wedge x \leq 27.4889357189107$$
$$x \geq 29.0597320457056 \wedge x \leq 33.7721210260903$$
$$x \geq 35.3429173528852 \wedge x \leq 40.0553063332699$$
$$x \geq 41.6261026600648 \wedge x \leq 46.3384916404494$$
$$x \geq 47.9092879672443 \wedge x \leq 52.621676947629$$
$$x \geq 54.1924732744239 \wedge x \leq 58.9048622548086$$
$$x \geq 60.4756585816035 \wedge x \leq 65.1880475619882$$
$$x \geq 66.7588438887831 \wedge x \leq 71.4712328691678$$
$$x \geq 73.0420291959627 \wedge x \leq 77.7544181763474$$
$$x \geq 79.3252145031423 \wedge x \leq 84.037603483527$$
$$x \geq 85.6083998103219 \wedge x \leq 90.3207887907066$$
$$x \geq 91.8915851175014 \wedge x \leq 96.6039740978861$$
$$x \geq 98.174770424681 \wedge x \leq 104.457955731861$$
$$x \geq 255.254403104171 \wedge x \leq 2584.745355741$$
$$x \geq 39349.2333843756$$
Respuesta rápida
[src]
/3*pi 5*pi\ And|---- <= x, x <= ----| \ 4 4 /
$$\frac{3 \pi}{4} \leq x \wedge x \leq \frac{5 \pi}{4}$$
(3*pi/4 <= x)∧(x <= 5*pi/4)
Respuesta rápida 2
[src]
3*pi 5*pi [----, ----] 4 4
$$x\ in\ \left[\frac{3 \pi}{4}, \frac{5 \pi}{4}\right]$$
x in Interval(3*pi/4, 5*pi/4)