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:
-
3^x-1-4*3^0,5x-1+1>0
-
(x-1)/(x-6)>0
- x^2+64>=0
-
2x-x^2<0
- Integral de d{x}:
- cos(t)
- Límite de la función:
- cos(t)
- Derivada de:
-
cos(t)
- Forma canónica:
- =0
-
Expresiones idénticas
- cos(t)<= cero
- coseno de (t) menos o igual a 0
- coseno de (t) menos o igual a cero
- cost<=0
- cos(t)<=O
-
Expresiones con funciones
- Coseno cos
- cos(x)^2≥1/2
- cos(6x)>=sqrt(2)/2
- cos2x+5sinx<=-2
- cos^2(x)<1/4
- cos(x)>=-(1/√2)
cos(t)<=0 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\cos{\left(t \right)} \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = 0$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = 0$$
cambiamos
$$\cos{\left(t \right)} - 1 = 0$$
$$\cos{\left(t \right)} - 1 = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 1$$
Obtenemos la respuesta: w = 1
hacemos cambio inverso
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
Las raíces dadas
$$x_{67} = -2266.65909956504$$
$$x_{40} = -387.986692718339$$
$$x_{15} = -168.075206967054$$
$$x_{3} = -98.9601685880785$$
$$x_{48} = -95.8185759344887$$
$$x_{62} = -92.6769832808989$$
$$x_{25} = -89.5353906273091$$
$$x_{21} = -86.3937979737193$$
$$x_{53} = -83.2522053201295$$
$$x_{65} = -80.1106126665397$$
$$x_{54} = -76.9690200129499$$
$$x_{32} = -73.8274273593601$$
$$x_{60} = -70.6858347057703$$
$$x_{18} = -67.5442420521806$$
$$x_{17} = -64.4026493985908$$
$$x_{31} = -61.261056745001$$
$$x_{30} = -58.1194640914112$$
$$x_{46} = -54.9778714378214$$
$$x_{20} = -51.8362787842316$$
$$x_{45} = -48.6946861306418$$
$$x_{24} = -45.553093477052$$
$$x_{55} = -42.4115008234622$$
$$x_{13} = -39.2699081698724$$
$$x_{11} = -36.1283155162826$$
$$x_{56} = -32.9867228626928$$
$$x_{9} = -29.845130209103$$
$$x_{41} = -26.7035375555132$$
$$x_{51} = -23.5619449019235$$
$$x_{39} = -20.4203522483337$$
$$x_{23} = -17.2787595947439$$
$$x_{16} = -14.1371669411541$$
$$x_{61} = -10.9955742875643$$
$$x_{52} = -7.85398163397448$$
$$x_{12} = -4.71238898038469$$
$$x_{26} = -1.5707963267949$$
$$x_{14} = 1.5707963267949$$
$$x_{35} = 4.71238898038469$$
$$x_{29} = 7.85398163397448$$
$$x_{64} = 10.9955742875643$$
$$x_{8} = 14.1371669411541$$
$$x_{57} = 17.2787595947439$$
$$x_{59} = 20.4203522483337$$
$$x_{28} = 23.5619449019235$$
$$x_{49} = 26.7035375555132$$
$$x_{34} = 29.845130209103$$
$$x_{58} = 32.9867228626928$$
$$x_{6} = 36.1283155162826$$
$$x_{27} = 39.2699081698724$$
$$x_{22} = 42.4115008234622$$
$$x_{63} = 45.553093477052$$
$$x_{1} = 48.6946861306418$$
$$x_{43} = 51.8362787842316$$
$$x_{2} = 54.9778714378214$$
$$x_{7} = 58.1194640914112$$
$$x_{10} = 61.261056745001$$
$$x_{37} = 64.4026493985908$$
$$x_{4} = 67.5442420521806$$
$$x_{47} = 70.6858347057703$$
$$x_{33} = 73.8274273593601$$
$$x_{5} = 76.9690200129499$$
$$x_{50} = 80.1106126665397$$
$$x_{44} = 83.2522053201295$$
$$x_{36} = 86.3937979737193$$
$$x_{38} = 89.5353906273091$$
$$x_{19} = 92.6769832808989$$
$$x_{66} = 95.8185759344887$$
$$x_{42} = 98.9601685880785$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{67}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{67} - \frac{1}{10}$$
=
$$-2266.65909956504 + - \frac{1}{10}$$
=
$$-2266.75909956504$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \leq 0$$
$$\cos{\left(t \right)} \leq 0$$
Entonces
$$x \leq -2266.65909956504$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
$$x \geq -168.075206967054 \wedge x \leq -98.9601685880785$$
$$x \geq -95.8185759344887 \wedge x \leq -92.6769832808989$$
$$x \geq -89.5353906273091 \wedge x \leq -86.3937979737193$$
$$x \geq -83.2522053201295 \wedge x \leq -80.1106126665397$$
$$x \geq -76.9690200129499 \wedge x \leq -73.8274273593601$$
$$x \geq -70.6858347057703 \wedge x \leq -67.5442420521806$$
$$x \geq -64.4026493985908 \wedge x \leq -61.261056745001$$
$$x \geq -58.1194640914112 \wedge x \leq -54.9778714378214$$
$$x \geq -51.8362787842316 \wedge x \leq -48.6946861306418$$
$$x \geq -45.553093477052 \wedge x \leq -42.4115008234622$$
$$x \geq -39.2699081698724 \wedge x \leq -36.1283155162826$$
$$x \geq -32.9867228626928 \wedge x \leq -29.845130209103$$
$$x \geq -26.7035375555132 \wedge x \leq -23.5619449019235$$
$$x \geq -20.4203522483337 \wedge x \leq -17.2787595947439$$
$$x \geq -14.1371669411541 \wedge x \leq -10.9955742875643$$
$$x \geq -7.85398163397448 \wedge x \leq -4.71238898038469$$
$$x \geq -1.5707963267949 \wedge x \leq 1.5707963267949$$
$$x \geq 4.71238898038469 \wedge x \leq 7.85398163397448$$
$$x \geq 10.9955742875643 \wedge x \leq 14.1371669411541$$
$$x \geq 17.2787595947439 \wedge x \leq 20.4203522483337$$
$$x \geq 23.5619449019235 \wedge x \leq 26.7035375555132$$
$$x \geq 29.845130209103 \wedge x \leq 32.9867228626928$$
$$x \geq 36.1283155162826 \wedge x \leq 39.2699081698724$$
$$x \geq 42.4115008234622 \wedge x \leq 45.553093477052$$
$$x \geq 48.6946861306418 \wedge x \leq 51.8362787842316$$
$$x \geq 54.9778714378214 \wedge x \leq 58.1194640914112$$
$$x \geq 61.261056745001 \wedge x \leq 64.4026493985908$$
$$x \geq 67.5442420521806 \wedge x \leq 70.6858347057703$$
$$x \geq 73.8274273593601 \wedge x \leq 76.9690200129499$$
$$x \geq 80.1106126665397 \wedge x \leq 83.2522053201295$$
$$x \geq 86.3937979737193 \wedge x \leq 89.5353906273091$$
$$x \geq 92.6769832808989 \wedge x \leq 95.8185759344887$$
$$x \geq 98.9601685880785$$
$$\cos{\left(t \right)} \leq 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = 0$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = 0$$
cambiamos
$$\cos{\left(t \right)} - 1 = 0$$
$$\cos{\left(t \right)} - 1 = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 1$$
Obtenemos la respuesta: w = 1
hacemos cambio inverso
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
$$x_{1} = 48.6946861306418$$
$$x_{2} = 54.9778714378214$$
$$x_{3} = -98.9601685880785$$
$$x_{4} = 67.5442420521806$$
$$x_{5} = 76.9690200129499$$
$$x_{6} = 36.1283155162826$$
$$x_{7} = 58.1194640914112$$
$$x_{8} = 14.1371669411541$$
$$x_{9} = -29.845130209103$$
$$x_{10} = 61.261056745001$$
$$x_{11} = -36.1283155162826$$
$$x_{12} = -4.71238898038469$$
$$x_{13} = -39.2699081698724$$
$$x_{14} = 1.5707963267949$$
$$x_{15} = -168.075206967054$$
$$x_{16} = -14.1371669411541$$
$$x_{17} = -64.4026493985908$$
$$x_{18} = -67.5442420521806$$
$$x_{19} = 92.6769832808989$$
$$x_{20} = -51.8362787842316$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = 42.4115008234622$$
$$x_{23} = -17.2787595947439$$
$$x_{24} = -45.553093477052$$
$$x_{25} = -89.5353906273091$$
$$x_{26} = -1.5707963267949$$
$$x_{27} = 39.2699081698724$$
$$x_{28} = 23.5619449019235$$
$$x_{29} = 7.85398163397448$$
$$x_{30} = -58.1194640914112$$
$$x_{31} = -61.261056745001$$
$$x_{32} = -73.8274273593601$$
$$x_{33} = 73.8274273593601$$
$$x_{34} = 29.845130209103$$
$$x_{35} = 4.71238898038469$$
$$x_{36} = 86.3937979737193$$
$$x_{37} = 64.4026493985908$$
$$x_{38} = 89.5353906273091$$
$$x_{39} = -20.4203522483337$$
$$x_{40} = -387.986692718339$$
$$x_{41} = -26.7035375555132$$
$$x_{42} = 98.9601685880785$$
$$x_{43} = 51.8362787842316$$
$$x_{44} = 83.2522053201295$$
$$x_{45} = -48.6946861306418$$
$$x_{46} = -54.9778714378214$$
$$x_{47} = 70.6858347057703$$
$$x_{48} = -95.8185759344887$$
$$x_{49} = 26.7035375555132$$
$$x_{50} = 80.1106126665397$$
$$x_{51} = -23.5619449019235$$
$$x_{52} = -7.85398163397448$$
$$x_{53} = -83.2522053201295$$
$$x_{54} = -76.9690200129499$$
$$x_{55} = -42.4115008234622$$
$$x_{56} = -32.9867228626928$$
$$x_{57} = 17.2787595947439$$
$$x_{58} = 32.9867228626928$$
$$x_{59} = 20.4203522483337$$
$$x_{60} = -70.6858347057703$$
$$x_{61} = -10.9955742875643$$
$$x_{62} = -92.6769832808989$$
$$x_{63} = 45.553093477052$$
$$x_{64} = 10.9955742875643$$
$$x_{65} = -80.1106126665397$$
$$x_{66} = 95.8185759344887$$
$$x_{67} = -2266.65909956504$$
Las raíces dadas
$$x_{67} = -2266.65909956504$$
$$x_{40} = -387.986692718339$$
$$x_{15} = -168.075206967054$$
$$x_{3} = -98.9601685880785$$
$$x_{48} = -95.8185759344887$$
$$x_{62} = -92.6769832808989$$
$$x_{25} = -89.5353906273091$$
$$x_{21} = -86.3937979737193$$
$$x_{53} = -83.2522053201295$$
$$x_{65} = -80.1106126665397$$
$$x_{54} = -76.9690200129499$$
$$x_{32} = -73.8274273593601$$
$$x_{60} = -70.6858347057703$$
$$x_{18} = -67.5442420521806$$
$$x_{17} = -64.4026493985908$$
$$x_{31} = -61.261056745001$$
$$x_{30} = -58.1194640914112$$
$$x_{46} = -54.9778714378214$$
$$x_{20} = -51.8362787842316$$
$$x_{45} = -48.6946861306418$$
$$x_{24} = -45.553093477052$$
$$x_{55} = -42.4115008234622$$
$$x_{13} = -39.2699081698724$$
$$x_{11} = -36.1283155162826$$
$$x_{56} = -32.9867228626928$$
$$x_{9} = -29.845130209103$$
$$x_{41} = -26.7035375555132$$
$$x_{51} = -23.5619449019235$$
$$x_{39} = -20.4203522483337$$
$$x_{23} = -17.2787595947439$$
$$x_{16} = -14.1371669411541$$
$$x_{61} = -10.9955742875643$$
$$x_{52} = -7.85398163397448$$
$$x_{12} = -4.71238898038469$$
$$x_{26} = -1.5707963267949$$
$$x_{14} = 1.5707963267949$$
$$x_{35} = 4.71238898038469$$
$$x_{29} = 7.85398163397448$$
$$x_{64} = 10.9955742875643$$
$$x_{8} = 14.1371669411541$$
$$x_{57} = 17.2787595947439$$
$$x_{59} = 20.4203522483337$$
$$x_{28} = 23.5619449019235$$
$$x_{49} = 26.7035375555132$$
$$x_{34} = 29.845130209103$$
$$x_{58} = 32.9867228626928$$
$$x_{6} = 36.1283155162826$$
$$x_{27} = 39.2699081698724$$
$$x_{22} = 42.4115008234622$$
$$x_{63} = 45.553093477052$$
$$x_{1} = 48.6946861306418$$
$$x_{43} = 51.8362787842316$$
$$x_{2} = 54.9778714378214$$
$$x_{7} = 58.1194640914112$$
$$x_{10} = 61.261056745001$$
$$x_{37} = 64.4026493985908$$
$$x_{4} = 67.5442420521806$$
$$x_{47} = 70.6858347057703$$
$$x_{33} = 73.8274273593601$$
$$x_{5} = 76.9690200129499$$
$$x_{50} = 80.1106126665397$$
$$x_{44} = 83.2522053201295$$
$$x_{36} = 86.3937979737193$$
$$x_{38} = 89.5353906273091$$
$$x_{19} = 92.6769832808989$$
$$x_{66} = 95.8185759344887$$
$$x_{42} = 98.9601685880785$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{67}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{67} - \frac{1}{10}$$
=
$$-2266.65909956504 + - \frac{1}{10}$$
=
$$-2266.75909956504$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \leq 0$$
$$\cos{\left(t \right)} \leq 0$$
cos(t) <= 0
Entonces
$$x \leq -2266.65909956504$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x67 x40 x15 x3 x48 x62 x25 x21 x53 x65 x54 x32 x60 x18 x17 x31 x30 x46 x20 x45 x24 x55 x13 x11 x56 x9 x41 x51 x39 x23 x16 x61 x52 x12 x26 x14 x35 x29 x64 x8 x57 x59 x28 x49 x34 x58 x6 x27 x22 x63 x1 x43 x2 x7 x10 x37 x4 x47 x33 x5 x50 x44 x36 x38 x19 x66 x42Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -2266.65909956504 \wedge x \leq -387.986692718339$$
$$x \geq -168.075206967054 \wedge x \leq -98.9601685880785$$
$$x \geq -95.8185759344887 \wedge x \leq -92.6769832808989$$
$$x \geq -89.5353906273091 \wedge x \leq -86.3937979737193$$
$$x \geq -83.2522053201295 \wedge x \leq -80.1106126665397$$
$$x \geq -76.9690200129499 \wedge x \leq -73.8274273593601$$
$$x \geq -70.6858347057703 \wedge x \leq -67.5442420521806$$
$$x \geq -64.4026493985908 \wedge x \leq -61.261056745001$$
$$x \geq -58.1194640914112 \wedge x \leq -54.9778714378214$$
$$x \geq -51.8362787842316 \wedge x \leq -48.6946861306418$$
$$x \geq -45.553093477052 \wedge x \leq -42.4115008234622$$
$$x \geq -39.2699081698724 \wedge x \leq -36.1283155162826$$
$$x \geq -32.9867228626928 \wedge x \leq -29.845130209103$$
$$x \geq -26.7035375555132 \wedge x \leq -23.5619449019235$$
$$x \geq -20.4203522483337 \wedge x \leq -17.2787595947439$$
$$x \geq -14.1371669411541 \wedge x \leq -10.9955742875643$$
$$x \geq -7.85398163397448 \wedge x \leq -4.71238898038469$$
$$x \geq -1.5707963267949 \wedge x \leq 1.5707963267949$$
$$x \geq 4.71238898038469 \wedge x \leq 7.85398163397448$$
$$x \geq 10.9955742875643 \wedge x \leq 14.1371669411541$$
$$x \geq 17.2787595947439 \wedge x \leq 20.4203522483337$$
$$x \geq 23.5619449019235 \wedge x \leq 26.7035375555132$$
$$x \geq 29.845130209103 \wedge x \leq 32.9867228626928$$
$$x \geq 36.1283155162826 \wedge x \leq 39.2699081698724$$
$$x \geq 42.4115008234622 \wedge x \leq 45.553093477052$$
$$x \geq 48.6946861306418 \wedge x \leq 51.8362787842316$$
$$x \geq 54.9778714378214 \wedge x \leq 58.1194640914112$$
$$x \geq 61.261056745001 \wedge x \leq 64.4026493985908$$
$$x \geq 67.5442420521806 \wedge x \leq 70.6858347057703$$
$$x \geq 73.8274273593601 \wedge x \leq 76.9690200129499$$
$$x \geq 80.1106126665397 \wedge x \leq 83.2522053201295$$
$$x \geq 86.3937979737193 \wedge x \leq 89.5353906273091$$
$$x \geq 92.6769832808989 \wedge x \leq 95.8185759344887$$
$$x \geq 98.9601685880785$$
Respuesta rápida
[src]
/pi 3*pi\ And|-- <= t, t <= ----| \2 2 /
$$\frac{\pi}{2} \leq t \wedge t \leq \frac{3 \pi}{2}$$
(pi/2 <= t)∧(t <= 3*pi/2)
Respuesta rápida 2
[src]
pi 3*pi [--, ----] 2 2
$$x\ in\ \left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]$$
x in Interval(pi/2, 3*pi/2)