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:
-
cost
- Integral de d{x}:
- cost
-
Expresiones idénticas
- cost>=-sqrt(dos)/ dos
- coseno de t más o igual a menos raíz cuadrada de (2) dividir por 2
- coseno de t más o igual a menos raíz cuadrada de (dos) dividir por dos
- cost>=-√(2)/2
- cost>=-sqrt2/2
- cost>=-sqrt(2) dividir por 2
-
Expresiones semejantes
- cos(t)<-1/2
- cost>=+sqrt(2)/2
- (sin2t)-((sin(t)+cos(t))^2)/(tg(t)+ctg(t))
- cos(t)<=-(sqrt(2)/2)
- cos(t)>=-sqrt(2)/2
-
Expresiones con funciones
- cost
- cost≤1/2
- cost>-1\7
- cost<√2
- cost<1/3
- cost≤-√2/2
- 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
cost>=-sqrt(2)/2 desigualdades
Solución
Ha introducido
[src]
___
-\/ 2
cos(t) >= -------
2
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
cos(t) >= (-sqrt(2))/2
Solución detallada
Se da la desigualdad:
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Resolvemos:
$$x_{1} = -52.621676947629$$
$$x_{2} = -33.7721210260903$$
$$x_{3} = 39349.2333843756$$
$$x_{4} = 60.4756585816035$$
$$x_{5} = 21.2057504117311$$
$$x_{6} = 90.3207887907066$$
$$x_{7} = -10.2101761241668$$
$$x_{8} = -96.6039740978861$$
$$x_{9} = 71.4712328691678$$
$$x_{10} = -41.6261026600648$$
$$x_{11} = 8.63937979737193$$
$$x_{12} = -66.7588438887831$$
$$x_{13} = 255.254403104171$$
$$x_{14} = -60.4756585816035$$
$$x_{15} = 104.457955731861$$
$$x_{16} = 27.4889357189107$$
$$x_{17} = -71.4712328691678$$
$$x_{18} = 41.6261026600648$$
$$x_{19} = -29.0597320457056$$
$$x_{20} = 40.0553063332699$$
$$x_{21} = -85.6083998103219$$
$$x_{22} = 33.7721210260903$$
$$x_{23} = -47.9092879672443$$
$$x_{24} = 84.037603483527$$
$$x_{25} = -8.63937979737193$$
$$x_{26} = -54.1924732744239$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -58.9048622548086$$
$$x_{29} = -22.776546738526$$
$$x_{30} = 3.92699081698724$$
$$x_{31} = 96.6039740978861$$
$$x_{32} = 73.0420291959627$$
$$x_{33} = -14.9225651045515$$
$$x_{34} = -77.7544181763474$$
$$x_{35} = 22.776546738526$$
$$x_{36} = 2.35619449019234$$
$$x_{37} = 79.3252145031423$$
$$x_{38} = -79.3252145031423$$
$$x_{39} = 65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 16.4933614313464$$
$$x_{42} = 10.2101761241668$$
$$x_{43} = 66.7588438887831$$
$$x_{44} = 85.6083998103219$$
$$x_{45} = -2.35619449019234$$
$$x_{46} = -21.2057504117311$$
$$x_{47} = 35.3429173528852$$
$$x_{48} = 98.174770424681$$
$$x_{49} = -335.36501577071$$
$$x_{50} = -90.3207887907066$$
$$x_{51} = -46.3384916404494$$
$$x_{52} = -16.4933614313464$$
$$x_{53} = -3.92699081698724$$
$$x_{54} = -27.4889357189107$$
$$x_{55} = -98.174770424681$$
$$x_{56} = 46.3384916404494$$
$$x_{57} = 52.621676947629$$
$$x_{58} = -84.037603483527$$
$$x_{59} = -40.0553063332699$$
$$x_{60} = -65.1880475619882$$
$$x_{61} = 47.9092879672443$$
$$x_{62} = 58.9048622548086$$
$$x_{63} = 14.9225651045515$$
$$x_{64} = -91.8915851175014$$
$$x_{65} = 54.1924732744239$$
$$x_{66} = 29.0597320457056$$
$$x_{67} = -35.3429173528852$$
$$x_{68} = 91.8915851175014$$
$$x_{69} = 77.7544181763474$$
$$x_{1} = -52.621676947629$$
$$x_{2} = -33.7721210260903$$
$$x_{3} = 39349.2333843756$$
$$x_{4} = 60.4756585816035$$
$$x_{5} = 21.2057504117311$$
$$x_{6} = 90.3207887907066$$
$$x_{7} = -10.2101761241668$$
$$x_{8} = -96.6039740978861$$
$$x_{9} = 71.4712328691678$$
$$x_{10} = -41.6261026600648$$
$$x_{11} = 8.63937979737193$$
$$x_{12} = -66.7588438887831$$
$$x_{13} = 255.254403104171$$
$$x_{14} = -60.4756585816035$$
$$x_{15} = 104.457955731861$$
$$x_{16} = 27.4889357189107$$
$$x_{17} = -71.4712328691678$$
$$x_{18} = 41.6261026600648$$
$$x_{19} = -29.0597320457056$$
$$x_{20} = 40.0553063332699$$
$$x_{21} = -85.6083998103219$$
$$x_{22} = 33.7721210260903$$
$$x_{23} = -47.9092879672443$$
$$x_{24} = 84.037603483527$$
$$x_{25} = -8.63937979737193$$
$$x_{26} = -54.1924732744239$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -58.9048622548086$$
$$x_{29} = -22.776546738526$$
$$x_{30} = 3.92699081698724$$
$$x_{31} = 96.6039740978861$$
$$x_{32} = 73.0420291959627$$
$$x_{33} = -14.9225651045515$$
$$x_{34} = -77.7544181763474$$
$$x_{35} = 22.776546738526$$
$$x_{36} = 2.35619449019234$$
$$x_{37} = 79.3252145031423$$
$$x_{38} = -79.3252145031423$$
$$x_{39} = 65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 16.4933614313464$$
$$x_{42} = 10.2101761241668$$
$$x_{43} = 66.7588438887831$$
$$x_{44} = 85.6083998103219$$
$$x_{45} = -2.35619449019234$$
$$x_{46} = -21.2057504117311$$
$$x_{47} = 35.3429173528852$$
$$x_{48} = 98.174770424681$$
$$x_{49} = -335.36501577071$$
$$x_{50} = -90.3207887907066$$
$$x_{51} = -46.3384916404494$$
$$x_{52} = -16.4933614313464$$
$$x_{53} = -3.92699081698724$$
$$x_{54} = -27.4889357189107$$
$$x_{55} = -98.174770424681$$
$$x_{56} = 46.3384916404494$$
$$x_{57} = 52.621676947629$$
$$x_{58} = -84.037603483527$$
$$x_{59} = -40.0553063332699$$
$$x_{60} = -65.1880475619882$$
$$x_{61} = 47.9092879672443$$
$$x_{62} = 58.9048622548086$$
$$x_{63} = 14.9225651045515$$
$$x_{64} = -91.8915851175014$$
$$x_{65} = 54.1924732744239$$
$$x_{66} = 29.0597320457056$$
$$x_{67} = -35.3429173528852$$
$$x_{68} = 91.8915851175014$$
$$x_{69} = 77.7544181763474$$
Las raíces dadas
$$x_{49} = -335.36501577071$$
$$x_{55} = -98.174770424681$$
$$x_{8} = -96.6039740978861$$
$$x_{64} = -91.8915851175014$$
$$x_{50} = -90.3207887907066$$
$$x_{21} = -85.6083998103219$$
$$x_{58} = -84.037603483527$$
$$x_{38} = -79.3252145031423$$
$$x_{34} = -77.7544181763474$$
$$x_{27} = -73.0420291959627$$
$$x_{17} = -71.4712328691678$$
$$x_{12} = -66.7588438887831$$
$$x_{60} = -65.1880475619882$$
$$x_{14} = -60.4756585816035$$
$$x_{28} = -58.9048622548086$$
$$x_{26} = -54.1924732744239$$
$$x_{1} = -52.621676947629$$
$$x_{23} = -47.9092879672443$$
$$x_{51} = -46.3384916404494$$
$$x_{10} = -41.6261026600648$$
$$x_{59} = -40.0553063332699$$
$$x_{67} = -35.3429173528852$$
$$x_{2} = -33.7721210260903$$
$$x_{19} = -29.0597320457056$$
$$x_{54} = -27.4889357189107$$
$$x_{29} = -22.776546738526$$
$$x_{46} = -21.2057504117311$$
$$x_{52} = -16.4933614313464$$
$$x_{33} = -14.9225651045515$$
$$x_{7} = -10.2101761241668$$
$$x_{25} = -8.63937979737193$$
$$x_{53} = -3.92699081698724$$
$$x_{45} = -2.35619449019234$$
$$x_{36} = 2.35619449019234$$
$$x_{30} = 3.92699081698724$$
$$x_{11} = 8.63937979737193$$
$$x_{42} = 10.2101761241668$$
$$x_{63} = 14.9225651045515$$
$$x_{41} = 16.4933614313464$$
$$x_{5} = 21.2057504117311$$
$$x_{35} = 22.776546738526$$
$$x_{16} = 27.4889357189107$$
$$x_{66} = 29.0597320457056$$
$$x_{22} = 33.7721210260903$$
$$x_{47} = 35.3429173528852$$
$$x_{20} = 40.0553063332699$$
$$x_{18} = 41.6261026600648$$
$$x_{56} = 46.3384916404494$$
$$x_{61} = 47.9092879672443$$
$$x_{57} = 52.621676947629$$
$$x_{65} = 54.1924732744239$$
$$x_{62} = 58.9048622548086$$
$$x_{4} = 60.4756585816035$$
$$x_{39} = 65.1880475619882$$
$$x_{43} = 66.7588438887831$$
$$x_{9} = 71.4712328691678$$
$$x_{32} = 73.0420291959627$$
$$x_{69} = 77.7544181763474$$
$$x_{37} = 79.3252145031423$$
$$x_{24} = 84.037603483527$$
$$x_{44} = 85.6083998103219$$
$$x_{6} = 90.3207887907066$$
$$x_{68} = 91.8915851175014$$
$$x_{31} = 96.6039740978861$$
$$x_{48} = 98.174770424681$$
$$x_{15} = 104.457955731861$$
$$x_{13} = 255.254403104171$$
$$x_{40} = 2584.745355741$$
$$x_{3} = 39349.2333843756$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{49}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{49} - \frac{1}{10}$$
=
$$-335.36501577071 + - \frac{1}{10}$$
=
$$-335.46501577071$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
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:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
$$x \geq -96.6039740978861 \wedge x \leq -91.8915851175014$$
$$x \geq -90.3207887907066 \wedge x \leq -85.6083998103219$$
$$x \geq -84.037603483527 \wedge x \leq -79.3252145031423$$
$$x \geq -77.7544181763474 \wedge x \leq -73.0420291959627$$
$$x \geq -71.4712328691678 \wedge x \leq -66.7588438887831$$
$$x \geq -65.1880475619882 \wedge x \leq -60.4756585816035$$
$$x \geq -58.9048622548086 \wedge x \leq -54.1924732744239$$
$$x \geq -52.621676947629 \wedge x \leq -47.9092879672443$$
$$x \geq -46.3384916404494 \wedge x \leq -41.6261026600648$$
$$x \geq -40.0553063332699 \wedge x \leq -35.3429173528852$$
$$x \geq -33.7721210260903 \wedge x \leq -29.0597320457056$$
$$x \geq -27.4889357189107 \wedge x \leq -22.776546738526$$
$$x \geq -21.2057504117311 \wedge x \leq -16.4933614313464$$
$$x \geq -14.9225651045515 \wedge x \leq -10.2101761241668$$
$$x \geq -8.63937979737193 \wedge x \leq -3.92699081698724$$
$$x \geq -2.35619449019234 \wedge x \leq 2.35619449019234$$
$$x \geq 3.92699081698724 \wedge x \leq 8.63937979737193$$
$$x \geq 10.2101761241668 \wedge x \leq 14.9225651045515$$
$$x \geq 16.4933614313464 \wedge x \leq 21.2057504117311$$
$$x \geq 22.776546738526 \wedge x \leq 27.4889357189107$$
$$x \geq 29.0597320457056 \wedge x \leq 33.7721210260903$$
$$x \geq 35.3429173528852 \wedge x \leq 40.0553063332699$$
$$x \geq 41.6261026600648 \wedge x \leq 46.3384916404494$$
$$x \geq 47.9092879672443 \wedge x \leq 52.621676947629$$
$$x \geq 54.1924732744239 \wedge x \leq 58.9048622548086$$
$$x \geq 60.4756585816035 \wedge x \leq 65.1880475619882$$
$$x \geq 66.7588438887831 \wedge x \leq 71.4712328691678$$
$$x \geq 73.0420291959627 \wedge x \leq 77.7544181763474$$
$$x \geq 79.3252145031423 \wedge x \leq 84.037603483527$$
$$x \geq 85.6083998103219 \wedge x \leq 90.3207887907066$$
$$x \geq 91.8915851175014 \wedge x \leq 96.6039740978861$$
$$x \geq 98.174770424681 \wedge x \leq 104.457955731861$$
$$x \geq 255.254403104171 \wedge x \leq 2584.745355741$$
$$x \geq 39349.2333843756$$
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Resolvemos:
$$x_{1} = -52.621676947629$$
$$x_{2} = -33.7721210260903$$
$$x_{3} = 39349.2333843756$$
$$x_{4} = 60.4756585816035$$
$$x_{5} = 21.2057504117311$$
$$x_{6} = 90.3207887907066$$
$$x_{7} = -10.2101761241668$$
$$x_{8} = -96.6039740978861$$
$$x_{9} = 71.4712328691678$$
$$x_{10} = -41.6261026600648$$
$$x_{11} = 8.63937979737193$$
$$x_{12} = -66.7588438887831$$
$$x_{13} = 255.254403104171$$
$$x_{14} = -60.4756585816035$$
$$x_{15} = 104.457955731861$$
$$x_{16} = 27.4889357189107$$
$$x_{17} = -71.4712328691678$$
$$x_{18} = 41.6261026600648$$
$$x_{19} = -29.0597320457056$$
$$x_{20} = 40.0553063332699$$
$$x_{21} = -85.6083998103219$$
$$x_{22} = 33.7721210260903$$
$$x_{23} = -47.9092879672443$$
$$x_{24} = 84.037603483527$$
$$x_{25} = -8.63937979737193$$
$$x_{26} = -54.1924732744239$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -58.9048622548086$$
$$x_{29} = -22.776546738526$$
$$x_{30} = 3.92699081698724$$
$$x_{31} = 96.6039740978861$$
$$x_{32} = 73.0420291959627$$
$$x_{33} = -14.9225651045515$$
$$x_{34} = -77.7544181763474$$
$$x_{35} = 22.776546738526$$
$$x_{36} = 2.35619449019234$$
$$x_{37} = 79.3252145031423$$
$$x_{38} = -79.3252145031423$$
$$x_{39} = 65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 16.4933614313464$$
$$x_{42} = 10.2101761241668$$
$$x_{43} = 66.7588438887831$$
$$x_{44} = 85.6083998103219$$
$$x_{45} = -2.35619449019234$$
$$x_{46} = -21.2057504117311$$
$$x_{47} = 35.3429173528852$$
$$x_{48} = 98.174770424681$$
$$x_{49} = -335.36501577071$$
$$x_{50} = -90.3207887907066$$
$$x_{51} = -46.3384916404494$$
$$x_{52} = -16.4933614313464$$
$$x_{53} = -3.92699081698724$$
$$x_{54} = -27.4889357189107$$
$$x_{55} = -98.174770424681$$
$$x_{56} = 46.3384916404494$$
$$x_{57} = 52.621676947629$$
$$x_{58} = -84.037603483527$$
$$x_{59} = -40.0553063332699$$
$$x_{60} = -65.1880475619882$$
$$x_{61} = 47.9092879672443$$
$$x_{62} = 58.9048622548086$$
$$x_{63} = 14.9225651045515$$
$$x_{64} = -91.8915851175014$$
$$x_{65} = 54.1924732744239$$
$$x_{66} = 29.0597320457056$$
$$x_{67} = -35.3429173528852$$
$$x_{68} = 91.8915851175014$$
$$x_{69} = 77.7544181763474$$
$$x_{1} = -52.621676947629$$
$$x_{2} = -33.7721210260903$$
$$x_{3} = 39349.2333843756$$
$$x_{4} = 60.4756585816035$$
$$x_{5} = 21.2057504117311$$
$$x_{6} = 90.3207887907066$$
$$x_{7} = -10.2101761241668$$
$$x_{8} = -96.6039740978861$$
$$x_{9} = 71.4712328691678$$
$$x_{10} = -41.6261026600648$$
$$x_{11} = 8.63937979737193$$
$$x_{12} = -66.7588438887831$$
$$x_{13} = 255.254403104171$$
$$x_{14} = -60.4756585816035$$
$$x_{15} = 104.457955731861$$
$$x_{16} = 27.4889357189107$$
$$x_{17} = -71.4712328691678$$
$$x_{18} = 41.6261026600648$$
$$x_{19} = -29.0597320457056$$
$$x_{20} = 40.0553063332699$$
$$x_{21} = -85.6083998103219$$
$$x_{22} = 33.7721210260903$$
$$x_{23} = -47.9092879672443$$
$$x_{24} = 84.037603483527$$
$$x_{25} = -8.63937979737193$$
$$x_{26} = -54.1924732744239$$
$$x_{27} = -73.0420291959627$$
$$x_{28} = -58.9048622548086$$
$$x_{29} = -22.776546738526$$
$$x_{30} = 3.92699081698724$$
$$x_{31} = 96.6039740978861$$
$$x_{32} = 73.0420291959627$$
$$x_{33} = -14.9225651045515$$
$$x_{34} = -77.7544181763474$$
$$x_{35} = 22.776546738526$$
$$x_{36} = 2.35619449019234$$
$$x_{37} = 79.3252145031423$$
$$x_{38} = -79.3252145031423$$
$$x_{39} = 65.1880475619882$$
$$x_{40} = 2584.745355741$$
$$x_{41} = 16.4933614313464$$
$$x_{42} = 10.2101761241668$$
$$x_{43} = 66.7588438887831$$
$$x_{44} = 85.6083998103219$$
$$x_{45} = -2.35619449019234$$
$$x_{46} = -21.2057504117311$$
$$x_{47} = 35.3429173528852$$
$$x_{48} = 98.174770424681$$
$$x_{49} = -335.36501577071$$
$$x_{50} = -90.3207887907066$$
$$x_{51} = -46.3384916404494$$
$$x_{52} = -16.4933614313464$$
$$x_{53} = -3.92699081698724$$
$$x_{54} = -27.4889357189107$$
$$x_{55} = -98.174770424681$$
$$x_{56} = 46.3384916404494$$
$$x_{57} = 52.621676947629$$
$$x_{58} = -84.037603483527$$
$$x_{59} = -40.0553063332699$$
$$x_{60} = -65.1880475619882$$
$$x_{61} = 47.9092879672443$$
$$x_{62} = 58.9048622548086$$
$$x_{63} = 14.9225651045515$$
$$x_{64} = -91.8915851175014$$
$$x_{65} = 54.1924732744239$$
$$x_{66} = 29.0597320457056$$
$$x_{67} = -35.3429173528852$$
$$x_{68} = 91.8915851175014$$
$$x_{69} = 77.7544181763474$$
Las raíces dadas
$$x_{49} = -335.36501577071$$
$$x_{55} = -98.174770424681$$
$$x_{8} = -96.6039740978861$$
$$x_{64} = -91.8915851175014$$
$$x_{50} = -90.3207887907066$$
$$x_{21} = -85.6083998103219$$
$$x_{58} = -84.037603483527$$
$$x_{38} = -79.3252145031423$$
$$x_{34} = -77.7544181763474$$
$$x_{27} = -73.0420291959627$$
$$x_{17} = -71.4712328691678$$
$$x_{12} = -66.7588438887831$$
$$x_{60} = -65.1880475619882$$
$$x_{14} = -60.4756585816035$$
$$x_{28} = -58.9048622548086$$
$$x_{26} = -54.1924732744239$$
$$x_{1} = -52.621676947629$$
$$x_{23} = -47.9092879672443$$
$$x_{51} = -46.3384916404494$$
$$x_{10} = -41.6261026600648$$
$$x_{59} = -40.0553063332699$$
$$x_{67} = -35.3429173528852$$
$$x_{2} = -33.7721210260903$$
$$x_{19} = -29.0597320457056$$
$$x_{54} = -27.4889357189107$$
$$x_{29} = -22.776546738526$$
$$x_{46} = -21.2057504117311$$
$$x_{52} = -16.4933614313464$$
$$x_{33} = -14.9225651045515$$
$$x_{7} = -10.2101761241668$$
$$x_{25} = -8.63937979737193$$
$$x_{53} = -3.92699081698724$$
$$x_{45} = -2.35619449019234$$
$$x_{36} = 2.35619449019234$$
$$x_{30} = 3.92699081698724$$
$$x_{11} = 8.63937979737193$$
$$x_{42} = 10.2101761241668$$
$$x_{63} = 14.9225651045515$$
$$x_{41} = 16.4933614313464$$
$$x_{5} = 21.2057504117311$$
$$x_{35} = 22.776546738526$$
$$x_{16} = 27.4889357189107$$
$$x_{66} = 29.0597320457056$$
$$x_{22} = 33.7721210260903$$
$$x_{47} = 35.3429173528852$$
$$x_{20} = 40.0553063332699$$
$$x_{18} = 41.6261026600648$$
$$x_{56} = 46.3384916404494$$
$$x_{61} = 47.9092879672443$$
$$x_{57} = 52.621676947629$$
$$x_{65} = 54.1924732744239$$
$$x_{62} = 58.9048622548086$$
$$x_{4} = 60.4756585816035$$
$$x_{39} = 65.1880475619882$$
$$x_{43} = 66.7588438887831$$
$$x_{9} = 71.4712328691678$$
$$x_{32} = 73.0420291959627$$
$$x_{69} = 77.7544181763474$$
$$x_{37} = 79.3252145031423$$
$$x_{24} = 84.037603483527$$
$$x_{44} = 85.6083998103219$$
$$x_{6} = 90.3207887907066$$
$$x_{68} = 91.8915851175014$$
$$x_{31} = 96.6039740978861$$
$$x_{48} = 98.174770424681$$
$$x_{15} = 104.457955731861$$
$$x_{13} = 255.254403104171$$
$$x_{40} = 2584.745355741$$
$$x_{3} = 39349.2333843756$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{49}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{49} - \frac{1}{10}$$
=
$$-335.36501577071 + - \frac{1}{10}$$
=
$$-335.46501577071$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
$$\cos{\left(t \right)} \geq \frac{\left(-1\right) \sqrt{2}}{2}$$
___
-\/ 2
cos(t) >= -------
2
Entonces
$$x \leq -335.36501577071$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -335.36501577071 \wedge x \leq -98.174770424681$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x49 x55 x8 x64 x50 x21 x58 x38 x34 x27 x17 x12 x60 x14 x28 x26 x1 x23 x51 x10 x59 x67 x2 x19 x54 x29 x46 x52 x33 x7 x25 x53 x45 x36 x30 x11 x42 x63 x41 x5 x35 x16 x66 x22 x47 x20 x18 x56 x61 x57 x65 x62 x4 x39 x43 x9 x32 x69 x37 x24 x44 x6 x68 x31 x48 x15 x13 x40 x3Recibiremos 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 2
[src]
3*pi 5*pi
[0, ----] U [----, 2*pi]
4 4
$$x\ in\ \left[0, \frac{3 \pi}{4}\right] \cup \left[\frac{5 \pi}{4}, 2 \pi\right]$$
x in Union(Interval(0, 3*pi/4), Interval(5*pi/4, 2*pi))
Respuesta rápida
[src]
/ / 3*pi\ /5*pi \\ Or|And|0 <= x, x <= ----|, And|---- <= x, x <= 2*pi|| \ \ 4 / \ 4 //
$$\left(0 \leq x \wedge x \leq \frac{3 \pi}{4}\right) \vee \left(\frac{5 \pi}{4} \leq x \wedge x \leq 2 \pi\right)$$
((0 <= x)∧(x <= 3*pi/4))∨((5*pi/4 <= x)∧(x <= 2*pi))