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+64)*(x-5)>0
- x^2-x+56>0
-
-x^2+4x+5>0
-
(x+1)*(x-19)>0
- Forma canónica:
- =0
-
Expresiones idénticas
- tres +sin(x)*cos(x)^ dos *x*x<= cero
- 3 más seno de (x) multiplicar por coseno de (x) al cuadrado multiplicar por x multiplicar por x menos o igual a 0
- tres más seno de (x) multiplicar por coseno de (x) en el grado dos multiplicar por x multiplicar por x menos o igual a cero
- 3+sin(x)*cos(x)2*x*x<=0
- 3+sinx*cosx2*x*x<=0
- 3+sin(x)*cos(x)²*x*x<=0
- 3+sin(x)*cos(x) en el grado 2*x*x<=0
- 3+sin(x)cos(x)^2xx<=0
- 3+sin(x)cos(x)2xx<=0
- 3+sinxcosx2xx<=0
- 3+sinxcosx^2xx<=0
- 3+sin(x)*cos(x)^2*x*x<=O
-
Expresiones semejantes
- 3-sin(x)*cos(x)^2*x*x<=0
- 3+sinx*cosx^2*x*x<=0
-
Expresiones con funciones
- Seno sin
- sin(x)^2>3/5
- sin(x)cos(x)>sqrt(3)/4
- sin(pi/4+x/2)>=1
- sin(3*x-pi/5)<=sqrt(3)/2
- sin(x+pi*1/4)>0
3+sin(x)*cos(x)^2*x*x<=0 desigualdades
Solución
Ha introducido
[src]
2 3 + sin(x)*cos (x)*x*x <= 0
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 \leq 0$$
x*(x*(sin(x)*cos(x)^2)) + 3 <= 0
Solución detallada
Se da la desigualdad:
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 = 0$$
Resolvemos:
$$x_{1} = -75.3987513934378$$
$$x_{2} = 86.3737416334913$$
$$x_{3} = -21.9849414550167$$
$$x_{4} = -39.3140007253354$$
$$x_{5} = 48.6590716706211$$
$$x_{6} = 65.9741349711187$$
$$x_{7} = -95.8004937019902$$
$$x_{8} = -59.6894183894572$$
$$x_{9} = -20.3349163912356$$
$$x_{10} = -72.2560564229196$$
$$x_{11} = -51.8028277406761$$
$$x_{12} = -64.3757359404798$$
$$x_{13} = -6.35788614289017$$
$$x_{14} = -87.9649820057754$$
$$x_{15} = -15.6957837414503$$
$$x_{16} = -94.248117342597$$
$$x_{17} = 28.2780855846748$$
$$x_{18} = -7.62151593866719$$
$$x_{19} = 50.264295041763$$
$$x_{20} = -95.8366513429907$$
$$x_{21} = -53.4060232912466$$
$$x_{22} = 3.42271762549536$$
$$x_{23} = -81.6818586387135$$
$$x_{24} = 100.530668073685$$
$$x_{25} = 87.9642065884176$$
$$x_{26} = 29.7868998943402$$
$$x_{27} = 56.5477295734145$$
$$x_{28} = -70.6613165562214$$
$$x_{29} = -8.07288410287559$$
$$x_{30} = 73.8508860898252$$
$$x_{31} = 40.8425029459519$$
$$x_{32} = 67.5698825491811$$
$$x_{33} = -14.0127606047508$$
$$x_{34} = 23.6353919893379$$
$$x_{35} = -89.5547343380958$$
$$x_{36} = 4.27200287186014$$
$$x_{37} = 36.1762395007365$$
$$x_{38} = 21.9973486945406$$
$$x_{39} = 34.5600309383031$$
$$x_{40} = 37.6970007376772$$
$$x_{41} = 72.2572056239334$$
$$x_{42} = -28.2705801875749$$
$$x_{43} = -45.591107341409$$
$$x_{44} = 43.9807462020811$$
$$x_{45} = 59.6911023994448$$
$$x_{46} = 47.1252406783877$$
$$x_{47} = -34.5550067102021$$
$$x_{48} = 80.1322317844239$$
$$x_{49} = 81.6809593380546$$
$$x_{50} = -58.0896361703775$$
$$x_{51} = 6.20469712816823$$
$$x_{52} = 78.5403026755375$$
$$x_{53} = 15.7201051234803$$
$$x_{54} = 29.9031335441915$$
$$x_{55} = 42.3705936995856$$
$$x_{56} = -50.2666697609198$$
$$x_{57} = -12.585319109325$$
$$x_{58} = -9.39071266046808$$
$$x_{59} = -43.9838478796983$$
$$x_{60} = 12.5473070392439$$
$$x_{61} = -65.9727564508483$$
$$x_{62} = -97.3890559599716$$
$$x_{63} = 94.2474418679494$$
$$x_{64} = -83.273008737839$$
$$x_{65} = -31.4189656161495$$
$$x_{66} = 92.6582876722496$$
$$x_{67} = -37.7012224757012$$
$$x_{68} = 11.1524865295098$$
$$x_{1} = -75.3987513934378$$
$$x_{2} = 86.3737416334913$$
$$x_{3} = -21.9849414550167$$
$$x_{4} = -39.3140007253354$$
$$x_{5} = 48.6590716706211$$
$$x_{6} = 65.9741349711187$$
$$x_{7} = -95.8004937019902$$
$$x_{8} = -59.6894183894572$$
$$x_{9} = -20.3349163912356$$
$$x_{10} = -72.2560564229196$$
$$x_{11} = -51.8028277406761$$
$$x_{12} = -64.3757359404798$$
$$x_{13} = -6.35788614289017$$
$$x_{14} = -87.9649820057754$$
$$x_{15} = -15.6957837414503$$
$$x_{16} = -94.248117342597$$
$$x_{17} = 28.2780855846748$$
$$x_{18} = -7.62151593866719$$
$$x_{19} = 50.264295041763$$
$$x_{20} = -95.8366513429907$$
$$x_{21} = -53.4060232912466$$
$$x_{22} = 3.42271762549536$$
$$x_{23} = -81.6818586387135$$
$$x_{24} = 100.530668073685$$
$$x_{25} = 87.9642065884176$$
$$x_{26} = 29.7868998943402$$
$$x_{27} = 56.5477295734145$$
$$x_{28} = -70.6613165562214$$
$$x_{29} = -8.07288410287559$$
$$x_{30} = 73.8508860898252$$
$$x_{31} = 40.8425029459519$$
$$x_{32} = 67.5698825491811$$
$$x_{33} = -14.0127606047508$$
$$x_{34} = 23.6353919893379$$
$$x_{35} = -89.5547343380958$$
$$x_{36} = 4.27200287186014$$
$$x_{37} = 36.1762395007365$$
$$x_{38} = 21.9973486945406$$
$$x_{39} = 34.5600309383031$$
$$x_{40} = 37.6970007376772$$
$$x_{41} = 72.2572056239334$$
$$x_{42} = -28.2705801875749$$
$$x_{43} = -45.591107341409$$
$$x_{44} = 43.9807462020811$$
$$x_{45} = 59.6911023994448$$
$$x_{46} = 47.1252406783877$$
$$x_{47} = -34.5550067102021$$
$$x_{48} = 80.1322317844239$$
$$x_{49} = 81.6809593380546$$
$$x_{50} = -58.0896361703775$$
$$x_{51} = 6.20469712816823$$
$$x_{52} = 78.5403026755375$$
$$x_{53} = 15.7201051234803$$
$$x_{54} = 29.9031335441915$$
$$x_{55} = 42.3705936995856$$
$$x_{56} = -50.2666697609198$$
$$x_{57} = -12.585319109325$$
$$x_{58} = -9.39071266046808$$
$$x_{59} = -43.9838478796983$$
$$x_{60} = 12.5473070392439$$
$$x_{61} = -65.9727564508483$$
$$x_{62} = -97.3890559599716$$
$$x_{63} = 94.2474418679494$$
$$x_{64} = -83.273008737839$$
$$x_{65} = -31.4189656161495$$
$$x_{66} = 92.6582876722496$$
$$x_{67} = -37.7012224757012$$
$$x_{68} = 11.1524865295098$$
Las raíces dadas
$$x_{62} = -97.3890559599716$$
$$x_{20} = -95.8366513429907$$
$$x_{7} = -95.8004937019902$$
$$x_{16} = -94.248117342597$$
$$x_{35} = -89.5547343380958$$
$$x_{14} = -87.9649820057754$$
$$x_{64} = -83.273008737839$$
$$x_{23} = -81.6818586387135$$
$$x_{1} = -75.3987513934378$$
$$x_{10} = -72.2560564229196$$
$$x_{28} = -70.6613165562214$$
$$x_{61} = -65.9727564508483$$
$$x_{12} = -64.3757359404798$$
$$x_{8} = -59.6894183894572$$
$$x_{50} = -58.0896361703775$$
$$x_{21} = -53.4060232912466$$
$$x_{11} = -51.8028277406761$$
$$x_{56} = -50.2666697609198$$
$$x_{43} = -45.591107341409$$
$$x_{59} = -43.9838478796983$$
$$x_{4} = -39.3140007253354$$
$$x_{67} = -37.7012224757012$$
$$x_{47} = -34.5550067102021$$
$$x_{65} = -31.4189656161495$$
$$x_{42} = -28.2705801875749$$
$$x_{3} = -21.9849414550167$$
$$x_{9} = -20.3349163912356$$
$$x_{15} = -15.6957837414503$$
$$x_{33} = -14.0127606047508$$
$$x_{57} = -12.585319109325$$
$$x_{58} = -9.39071266046808$$
$$x_{29} = -8.07288410287559$$
$$x_{18} = -7.62151593866719$$
$$x_{13} = -6.35788614289017$$
$$x_{22} = 3.42271762549536$$
$$x_{36} = 4.27200287186014$$
$$x_{51} = 6.20469712816823$$
$$x_{68} = 11.1524865295098$$
$$x_{60} = 12.5473070392439$$
$$x_{53} = 15.7201051234803$$
$$x_{38} = 21.9973486945406$$
$$x_{34} = 23.6353919893379$$
$$x_{17} = 28.2780855846748$$
$$x_{26} = 29.7868998943402$$
$$x_{54} = 29.9031335441915$$
$$x_{39} = 34.5600309383031$$
$$x_{37} = 36.1762395007365$$
$$x_{40} = 37.6970007376772$$
$$x_{31} = 40.8425029459519$$
$$x_{55} = 42.3705936995856$$
$$x_{44} = 43.9807462020811$$
$$x_{46} = 47.1252406783877$$
$$x_{5} = 48.6590716706211$$
$$x_{19} = 50.264295041763$$
$$x_{27} = 56.5477295734145$$
$$x_{45} = 59.6911023994448$$
$$x_{6} = 65.9741349711187$$
$$x_{32} = 67.5698825491811$$
$$x_{41} = 72.2572056239334$$
$$x_{30} = 73.8508860898252$$
$$x_{52} = 78.5403026755375$$
$$x_{48} = 80.1322317844239$$
$$x_{49} = 81.6809593380546$$
$$x_{2} = 86.3737416334913$$
$$x_{25} = 87.9642065884176$$
$$x_{66} = 92.6582876722496$$
$$x_{63} = 94.2474418679494$$
$$x_{24} = 100.530668073685$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{62}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{62} - \frac{1}{10}$$
=
$$-97.3890559599716 + - \frac{1}{10}$$
=
$$-97.4890559599716$$
lo sustituimos en la expresión
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 \leq 0$$
$$3 + \left(-97.4890559599716\right) \left(-97.4890559599716\right) \sin{\left(-97.4890559599716 \right)} \cos^{2}{\left(-97.4890559599716 \right)} \leq 0$$
pero
Entonces
$$x \leq -97.3890559599716$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -97.3890559599716 \wedge x \leq -95.8366513429907$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -97.3890559599716 \wedge x \leq -95.8366513429907$$
$$x \geq -95.8004937019902 \wedge x \leq -94.248117342597$$
$$x \geq -89.5547343380958 \wedge x \leq -87.9649820057754$$
$$x \geq -83.273008737839 \wedge x \leq -81.6818586387135$$
$$x \geq -75.3987513934378 \wedge x \leq -72.2560564229196$$
$$x \geq -70.6613165562214 \wedge x \leq -65.9727564508483$$
$$x \geq -64.3757359404798 \wedge x \leq -59.6894183894572$$
$$x \geq -58.0896361703775 \wedge x \leq -53.4060232912466$$
$$x \geq -51.8028277406761 \wedge x \leq -50.2666697609198$$
$$x \geq -45.591107341409 \wedge x \leq -43.9838478796983$$
$$x \geq -39.3140007253354 \wedge x \leq -37.7012224757012$$
$$x \geq -34.5550067102021 \wedge x \leq -31.4189656161495$$
$$x \geq -28.2705801875749 \wedge x \leq -21.9849414550167$$
$$x \geq -20.3349163912356 \wedge x \leq -15.6957837414503$$
$$x \geq -14.0127606047508 \wedge x \leq -12.585319109325$$
$$x \geq -9.39071266046808 \wedge x \leq -8.07288410287559$$
$$x \geq -7.62151593866719 \wedge x \leq -6.35788614289017$$
$$x \geq 3.42271762549536 \wedge x \leq 4.27200287186014$$
$$x \geq 6.20469712816823 \wedge x \leq 11.1524865295098$$
$$x \geq 12.5473070392439 \wedge x \leq 15.7201051234803$$
$$x \geq 21.9973486945406 \wedge x \leq 23.6353919893379$$
$$x \geq 28.2780855846748 \wedge x \leq 29.7868998943402$$
$$x \geq 29.9031335441915 \wedge x \leq 34.5600309383031$$
$$x \geq 36.1762395007365 \wedge x \leq 37.6970007376772$$
$$x \geq 40.8425029459519 \wedge x \leq 42.3705936995856$$
$$x \geq 43.9807462020811 \wedge x \leq 47.1252406783877$$
$$x \geq 48.6590716706211 \wedge x \leq 50.264295041763$$
$$x \geq 56.5477295734145 \wedge x \leq 59.6911023994448$$
$$x \geq 65.9741349711187 \wedge x \leq 67.5698825491811$$
$$x \geq 72.2572056239334 \wedge x \leq 73.8508860898252$$
$$x \geq 78.5403026755375 \wedge x \leq 80.1322317844239$$
$$x \geq 81.6809593380546 \wedge x \leq 86.3737416334913$$
$$x \geq 87.9642065884176 \wedge x \leq 92.6582876722496$$
$$x \geq 94.2474418679494 \wedge x \leq 100.530668073685$$
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 = 0$$
Resolvemos:
$$x_{1} = -75.3987513934378$$
$$x_{2} = 86.3737416334913$$
$$x_{3} = -21.9849414550167$$
$$x_{4} = -39.3140007253354$$
$$x_{5} = 48.6590716706211$$
$$x_{6} = 65.9741349711187$$
$$x_{7} = -95.8004937019902$$
$$x_{8} = -59.6894183894572$$
$$x_{9} = -20.3349163912356$$
$$x_{10} = -72.2560564229196$$
$$x_{11} = -51.8028277406761$$
$$x_{12} = -64.3757359404798$$
$$x_{13} = -6.35788614289017$$
$$x_{14} = -87.9649820057754$$
$$x_{15} = -15.6957837414503$$
$$x_{16} = -94.248117342597$$
$$x_{17} = 28.2780855846748$$
$$x_{18} = -7.62151593866719$$
$$x_{19} = 50.264295041763$$
$$x_{20} = -95.8366513429907$$
$$x_{21} = -53.4060232912466$$
$$x_{22} = 3.42271762549536$$
$$x_{23} = -81.6818586387135$$
$$x_{24} = 100.530668073685$$
$$x_{25} = 87.9642065884176$$
$$x_{26} = 29.7868998943402$$
$$x_{27} = 56.5477295734145$$
$$x_{28} = -70.6613165562214$$
$$x_{29} = -8.07288410287559$$
$$x_{30} = 73.8508860898252$$
$$x_{31} = 40.8425029459519$$
$$x_{32} = 67.5698825491811$$
$$x_{33} = -14.0127606047508$$
$$x_{34} = 23.6353919893379$$
$$x_{35} = -89.5547343380958$$
$$x_{36} = 4.27200287186014$$
$$x_{37} = 36.1762395007365$$
$$x_{38} = 21.9973486945406$$
$$x_{39} = 34.5600309383031$$
$$x_{40} = 37.6970007376772$$
$$x_{41} = 72.2572056239334$$
$$x_{42} = -28.2705801875749$$
$$x_{43} = -45.591107341409$$
$$x_{44} = 43.9807462020811$$
$$x_{45} = 59.6911023994448$$
$$x_{46} = 47.1252406783877$$
$$x_{47} = -34.5550067102021$$
$$x_{48} = 80.1322317844239$$
$$x_{49} = 81.6809593380546$$
$$x_{50} = -58.0896361703775$$
$$x_{51} = 6.20469712816823$$
$$x_{52} = 78.5403026755375$$
$$x_{53} = 15.7201051234803$$
$$x_{54} = 29.9031335441915$$
$$x_{55} = 42.3705936995856$$
$$x_{56} = -50.2666697609198$$
$$x_{57} = -12.585319109325$$
$$x_{58} = -9.39071266046808$$
$$x_{59} = -43.9838478796983$$
$$x_{60} = 12.5473070392439$$
$$x_{61} = -65.9727564508483$$
$$x_{62} = -97.3890559599716$$
$$x_{63} = 94.2474418679494$$
$$x_{64} = -83.273008737839$$
$$x_{65} = -31.4189656161495$$
$$x_{66} = 92.6582876722496$$
$$x_{67} = -37.7012224757012$$
$$x_{68} = 11.1524865295098$$
$$x_{1} = -75.3987513934378$$
$$x_{2} = 86.3737416334913$$
$$x_{3} = -21.9849414550167$$
$$x_{4} = -39.3140007253354$$
$$x_{5} = 48.6590716706211$$
$$x_{6} = 65.9741349711187$$
$$x_{7} = -95.8004937019902$$
$$x_{8} = -59.6894183894572$$
$$x_{9} = -20.3349163912356$$
$$x_{10} = -72.2560564229196$$
$$x_{11} = -51.8028277406761$$
$$x_{12} = -64.3757359404798$$
$$x_{13} = -6.35788614289017$$
$$x_{14} = -87.9649820057754$$
$$x_{15} = -15.6957837414503$$
$$x_{16} = -94.248117342597$$
$$x_{17} = 28.2780855846748$$
$$x_{18} = -7.62151593866719$$
$$x_{19} = 50.264295041763$$
$$x_{20} = -95.8366513429907$$
$$x_{21} = -53.4060232912466$$
$$x_{22} = 3.42271762549536$$
$$x_{23} = -81.6818586387135$$
$$x_{24} = 100.530668073685$$
$$x_{25} = 87.9642065884176$$
$$x_{26} = 29.7868998943402$$
$$x_{27} = 56.5477295734145$$
$$x_{28} = -70.6613165562214$$
$$x_{29} = -8.07288410287559$$
$$x_{30} = 73.8508860898252$$
$$x_{31} = 40.8425029459519$$
$$x_{32} = 67.5698825491811$$
$$x_{33} = -14.0127606047508$$
$$x_{34} = 23.6353919893379$$
$$x_{35} = -89.5547343380958$$
$$x_{36} = 4.27200287186014$$
$$x_{37} = 36.1762395007365$$
$$x_{38} = 21.9973486945406$$
$$x_{39} = 34.5600309383031$$
$$x_{40} = 37.6970007376772$$
$$x_{41} = 72.2572056239334$$
$$x_{42} = -28.2705801875749$$
$$x_{43} = -45.591107341409$$
$$x_{44} = 43.9807462020811$$
$$x_{45} = 59.6911023994448$$
$$x_{46} = 47.1252406783877$$
$$x_{47} = -34.5550067102021$$
$$x_{48} = 80.1322317844239$$
$$x_{49} = 81.6809593380546$$
$$x_{50} = -58.0896361703775$$
$$x_{51} = 6.20469712816823$$
$$x_{52} = 78.5403026755375$$
$$x_{53} = 15.7201051234803$$
$$x_{54} = 29.9031335441915$$
$$x_{55} = 42.3705936995856$$
$$x_{56} = -50.2666697609198$$
$$x_{57} = -12.585319109325$$
$$x_{58} = -9.39071266046808$$
$$x_{59} = -43.9838478796983$$
$$x_{60} = 12.5473070392439$$
$$x_{61} = -65.9727564508483$$
$$x_{62} = -97.3890559599716$$
$$x_{63} = 94.2474418679494$$
$$x_{64} = -83.273008737839$$
$$x_{65} = -31.4189656161495$$
$$x_{66} = 92.6582876722496$$
$$x_{67} = -37.7012224757012$$
$$x_{68} = 11.1524865295098$$
Las raíces dadas
$$x_{62} = -97.3890559599716$$
$$x_{20} = -95.8366513429907$$
$$x_{7} = -95.8004937019902$$
$$x_{16} = -94.248117342597$$
$$x_{35} = -89.5547343380958$$
$$x_{14} = -87.9649820057754$$
$$x_{64} = -83.273008737839$$
$$x_{23} = -81.6818586387135$$
$$x_{1} = -75.3987513934378$$
$$x_{10} = -72.2560564229196$$
$$x_{28} = -70.6613165562214$$
$$x_{61} = -65.9727564508483$$
$$x_{12} = -64.3757359404798$$
$$x_{8} = -59.6894183894572$$
$$x_{50} = -58.0896361703775$$
$$x_{21} = -53.4060232912466$$
$$x_{11} = -51.8028277406761$$
$$x_{56} = -50.2666697609198$$
$$x_{43} = -45.591107341409$$
$$x_{59} = -43.9838478796983$$
$$x_{4} = -39.3140007253354$$
$$x_{67} = -37.7012224757012$$
$$x_{47} = -34.5550067102021$$
$$x_{65} = -31.4189656161495$$
$$x_{42} = -28.2705801875749$$
$$x_{3} = -21.9849414550167$$
$$x_{9} = -20.3349163912356$$
$$x_{15} = -15.6957837414503$$
$$x_{33} = -14.0127606047508$$
$$x_{57} = -12.585319109325$$
$$x_{58} = -9.39071266046808$$
$$x_{29} = -8.07288410287559$$
$$x_{18} = -7.62151593866719$$
$$x_{13} = -6.35788614289017$$
$$x_{22} = 3.42271762549536$$
$$x_{36} = 4.27200287186014$$
$$x_{51} = 6.20469712816823$$
$$x_{68} = 11.1524865295098$$
$$x_{60} = 12.5473070392439$$
$$x_{53} = 15.7201051234803$$
$$x_{38} = 21.9973486945406$$
$$x_{34} = 23.6353919893379$$
$$x_{17} = 28.2780855846748$$
$$x_{26} = 29.7868998943402$$
$$x_{54} = 29.9031335441915$$
$$x_{39} = 34.5600309383031$$
$$x_{37} = 36.1762395007365$$
$$x_{40} = 37.6970007376772$$
$$x_{31} = 40.8425029459519$$
$$x_{55} = 42.3705936995856$$
$$x_{44} = 43.9807462020811$$
$$x_{46} = 47.1252406783877$$
$$x_{5} = 48.6590716706211$$
$$x_{19} = 50.264295041763$$
$$x_{27} = 56.5477295734145$$
$$x_{45} = 59.6911023994448$$
$$x_{6} = 65.9741349711187$$
$$x_{32} = 67.5698825491811$$
$$x_{41} = 72.2572056239334$$
$$x_{30} = 73.8508860898252$$
$$x_{52} = 78.5403026755375$$
$$x_{48} = 80.1322317844239$$
$$x_{49} = 81.6809593380546$$
$$x_{2} = 86.3737416334913$$
$$x_{25} = 87.9642065884176$$
$$x_{66} = 92.6582876722496$$
$$x_{63} = 94.2474418679494$$
$$x_{24} = 100.530668073685$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{62}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{62} - \frac{1}{10}$$
=
$$-97.3890559599716 + - \frac{1}{10}$$
=
$$-97.4890559599716$$
lo sustituimos en la expresión
$$x x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + 3 \leq 0$$
$$3 + \left(-97.4890559599716\right) \left(-97.4890559599716\right) \sin{\left(-97.4890559599716 \right)} \cos^{2}{\left(-97.4890559599716 \right)} \leq 0$$
939.469639339565 <= 0
pero
939.469639339565 >= 0
Entonces
$$x \leq -97.3890559599716$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -97.3890559599716 \wedge x \leq -95.8366513429907$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x62 x20 x7 x16 x35 x14 x64 x23 x1 x10 x28 x61 x12 x8 x50 x21 x11 x56 x43 x59 x4 x67 x47 x65 x42 x3 x9 x15 x33 x57 x58 x29 x18 x13 x22 x36 x51 x68 x60 x53 x38 x34 x17 x26 x54 x39 x37 x40 x31 x55 x44 x46 x5 x19 x27 x45 x6 x32 x41 x30 x52 x48 x49 x2 x25 x66 x63 x24Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -97.3890559599716 \wedge x \leq -95.8366513429907$$
$$x \geq -95.8004937019902 \wedge x \leq -94.248117342597$$
$$x \geq -89.5547343380958 \wedge x \leq -87.9649820057754$$
$$x \geq -83.273008737839 \wedge x \leq -81.6818586387135$$
$$x \geq -75.3987513934378 \wedge x \leq -72.2560564229196$$
$$x \geq -70.6613165562214 \wedge x \leq -65.9727564508483$$
$$x \geq -64.3757359404798 \wedge x \leq -59.6894183894572$$
$$x \geq -58.0896361703775 \wedge x \leq -53.4060232912466$$
$$x \geq -51.8028277406761 \wedge x \leq -50.2666697609198$$
$$x \geq -45.591107341409 \wedge x \leq -43.9838478796983$$
$$x \geq -39.3140007253354 \wedge x \leq -37.7012224757012$$
$$x \geq -34.5550067102021 \wedge x \leq -31.4189656161495$$
$$x \geq -28.2705801875749 \wedge x \leq -21.9849414550167$$
$$x \geq -20.3349163912356 \wedge x \leq -15.6957837414503$$
$$x \geq -14.0127606047508 \wedge x \leq -12.585319109325$$
$$x \geq -9.39071266046808 \wedge x \leq -8.07288410287559$$
$$x \geq -7.62151593866719 \wedge x \leq -6.35788614289017$$
$$x \geq 3.42271762549536 \wedge x \leq 4.27200287186014$$
$$x \geq 6.20469712816823 \wedge x \leq 11.1524865295098$$
$$x \geq 12.5473070392439 \wedge x \leq 15.7201051234803$$
$$x \geq 21.9973486945406 \wedge x \leq 23.6353919893379$$
$$x \geq 28.2780855846748 \wedge x \leq 29.7868998943402$$
$$x \geq 29.9031335441915 \wedge x \leq 34.5600309383031$$
$$x \geq 36.1762395007365 \wedge x \leq 37.6970007376772$$
$$x \geq 40.8425029459519 \wedge x \leq 42.3705936995856$$
$$x \geq 43.9807462020811 \wedge x \leq 47.1252406783877$$
$$x \geq 48.6590716706211 \wedge x \leq 50.264295041763$$
$$x \geq 56.5477295734145 \wedge x \leq 59.6911023994448$$
$$x \geq 65.9741349711187 \wedge x \leq 67.5698825491811$$
$$x \geq 72.2572056239334 \wedge x \leq 73.8508860898252$$
$$x \geq 78.5403026755375 \wedge x \leq 80.1322317844239$$
$$x \geq 81.6809593380546 \wedge x \leq 86.3737416334913$$
$$x \geq 87.9642065884176 \wedge x \leq 92.6582876722496$$
$$x \geq 94.2474418679494 \wedge x \leq 100.530668073685$$
Solución de la desigualdad en el gráfico