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:
-
2^x>-1
- x^2+64<0
-
x^2<=6,5-9*(4-x)^2
-
(x+4)(x-1)>(x-7)(x+10)
- Integral de d{x}:
- cos(t)
- 1/7
- Límite de la función:
- cos(t)
- 1/7
- Derivada de:
-
cos(t)
-
Expresiones idénticas
- cos(t)< uno / siete
- coseno de (t) menos 1 dividir por 7
- coseno de (t) menos uno dividir por siete
- cost<1/7
- cos(t)<1 dividir por 7
-
Expresiones semejantes
- 3cost-1>0
- (11x-3)/14<(7x+1)/7-x/3
-
Expresiones con funciones
- Coseno cos
- cosπ/3<1/2
- cos(3*x)<=sqrt*3/2
- cos2x<=(sqrt)3x/2
- cos(sin1996x)>0
- cos6*x>=-1/2
cos(t)<1/7 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\cos{\left(t \right)} < \frac{1}{7}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = \frac{1}{7}$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = \frac{1}{7}$$
cambiamos
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{7}$$
Obtenemos la respuesta: w = 1/7
hacemos cambio inverso
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 76.8256724440446$$
$$x_{2} = 36.271663085188$$
$$x_{3} = 95.6752283655833$$
$$x_{4} = 80.2539602354451$$
$$x_{5} = -42.5548483923676$$
$$x_{6} = -73.9707749282655$$
$$x_{7} = -1.42744875788953$$
$$x_{8} = -11.1389218564696$$
$$x_{9} = -51.6929312153262$$
$$x_{10} = 57.9761165225058$$
$$x_{11} = -80.2539602354451$$
$$x_{12} = -92.8203308498043$$
$$x_{13} = -26.5601899866079$$
$$x_{14} = -57.9761165225058$$
$$x_{15} = 45.4097459081466$$
$$x_{16} = 61.4044043139063$$
$$x_{17} = 64.2593018296854$$
$$x_{18} = -83.1088577512241$$
$$x_{19} = -95.6752283655833$$
$$x_{20} = -13.9938193722487$$
$$x_{21} = -20.2770046794283$$
$$x_{22} = 17.4221071636492$$
$$x_{23} = -4.85573654929006$$
$$x_{24} = -23.7052924708288$$
$$x_{25} = -12017630.0530054$$
$$x_{26} = 73.9707749282655$$
$$x_{27} = -76.8256724440446$$
$$x_{28} = 1.42744875788953$$
$$x_{29} = -89.3920430584037$$
$$x_{30} = 23.7052924708288$$
$$x_{31} = -7.71063406506912$$
$$x_{32} = 32.8433752937875$$
$$x_{33} = 99.1035161569839$$
$$x_{34} = 11.1389218564696$$
$$x_{35} = -29.9884777780084$$
$$x_{36} = -39.1265606009671$$
$$x_{37} = -32.8433752937875$$
$$x_{38} = -13252.6652615996$$
$$x_{39} = 26.5601899866079$$
$$x_{40} = -61.4044043139063$$
$$x_{41} = 42.5548483923676$$
$$x_{42} = -48.8380336995472$$
$$x_{43} = -86.5371455426247$$
$$x_{44} = 48.8380336995472$$
$$x_{45} = 29.9884777780084$$
$$x_{46} = 39.1265606009671$$
$$x_{47} = -64.2593018296854$$
$$x_{48} = 70.542487136865$$
$$x_{49} = 51.6929312153262$$
$$x_{50} = 92.8203308498043$$
$$x_{51} = 55.1212190067267$$
$$x_{52} = -36.271663085188$$
$$x_{53} = 7.71063406506912$$
$$x_{54} = 4.85573654929006$$
$$x_{55} = 89.3920430584037$$
$$x_{56} = 86.5371455426247$$
$$x_{57} = -55.1212190067267$$
$$x_{58} = 120.807969594302$$
$$x_{59} = 13.9938193722487$$
$$x_{60} = 83.1088577512241$$
$$x_{61} = 67.6875896210859$$
$$x_{62} = -70.542487136865$$
$$x_{63} = -45.4097459081466$$
$$x_{64} = -67.6875896210859$$
$$x_{65} = -17.4221071636492$$
$$x_{66} = -99.1035161569839$$
$$x_{67} = 20.2770046794283$$
$$x_{1} = 76.8256724440446$$
$$x_{2} = 36.271663085188$$
$$x_{3} = 95.6752283655833$$
$$x_{4} = 80.2539602354451$$
$$x_{5} = -42.5548483923676$$
$$x_{6} = -73.9707749282655$$
$$x_{7} = -1.42744875788953$$
$$x_{8} = -11.1389218564696$$
$$x_{9} = -51.6929312153262$$
$$x_{10} = 57.9761165225058$$
$$x_{11} = -80.2539602354451$$
$$x_{12} = -92.8203308498043$$
$$x_{13} = -26.5601899866079$$
$$x_{14} = -57.9761165225058$$
$$x_{15} = 45.4097459081466$$
$$x_{16} = 61.4044043139063$$
$$x_{17} = 64.2593018296854$$
$$x_{18} = -83.1088577512241$$
$$x_{19} = -95.6752283655833$$
$$x_{20} = -13.9938193722487$$
$$x_{21} = -20.2770046794283$$
$$x_{22} = 17.4221071636492$$
$$x_{23} = -4.85573654929006$$
$$x_{24} = -23.7052924708288$$
$$x_{25} = -12017630.0530054$$
$$x_{26} = 73.9707749282655$$
$$x_{27} = -76.8256724440446$$
$$x_{28} = 1.42744875788953$$
$$x_{29} = -89.3920430584037$$
$$x_{30} = 23.7052924708288$$
$$x_{31} = -7.71063406506912$$
$$x_{32} = 32.8433752937875$$
$$x_{33} = 99.1035161569839$$
$$x_{34} = 11.1389218564696$$
$$x_{35} = -29.9884777780084$$
$$x_{36} = -39.1265606009671$$
$$x_{37} = -32.8433752937875$$
$$x_{38} = -13252.6652615996$$
$$x_{39} = 26.5601899866079$$
$$x_{40} = -61.4044043139063$$
$$x_{41} = 42.5548483923676$$
$$x_{42} = -48.8380336995472$$
$$x_{43} = -86.5371455426247$$
$$x_{44} = 48.8380336995472$$
$$x_{45} = 29.9884777780084$$
$$x_{46} = 39.1265606009671$$
$$x_{47} = -64.2593018296854$$
$$x_{48} = 70.542487136865$$
$$x_{49} = 51.6929312153262$$
$$x_{50} = 92.8203308498043$$
$$x_{51} = 55.1212190067267$$
$$x_{52} = -36.271663085188$$
$$x_{53} = 7.71063406506912$$
$$x_{54} = 4.85573654929006$$
$$x_{55} = 89.3920430584037$$
$$x_{56} = 86.5371455426247$$
$$x_{57} = -55.1212190067267$$
$$x_{58} = 120.807969594302$$
$$x_{59} = 13.9938193722487$$
$$x_{60} = 83.1088577512241$$
$$x_{61} = 67.6875896210859$$
$$x_{62} = -70.542487136865$$
$$x_{63} = -45.4097459081466$$
$$x_{64} = -67.6875896210859$$
$$x_{65} = -17.4221071636492$$
$$x_{66} = -99.1035161569839$$
$$x_{67} = 20.2770046794283$$
Las raíces dadas
$$x_{25} = -12017630.0530054$$
$$x_{38} = -13252.6652615996$$
$$x_{66} = -99.1035161569839$$
$$x_{19} = -95.6752283655833$$
$$x_{12} = -92.8203308498043$$
$$x_{29} = -89.3920430584037$$
$$x_{43} = -86.5371455426247$$
$$x_{18} = -83.1088577512241$$
$$x_{11} = -80.2539602354451$$
$$x_{27} = -76.8256724440446$$
$$x_{6} = -73.9707749282655$$
$$x_{62} = -70.542487136865$$
$$x_{64} = -67.6875896210859$$
$$x_{47} = -64.2593018296854$$
$$x_{40} = -61.4044043139063$$
$$x_{14} = -57.9761165225058$$
$$x_{57} = -55.1212190067267$$
$$x_{9} = -51.6929312153262$$
$$x_{42} = -48.8380336995472$$
$$x_{63} = -45.4097459081466$$
$$x_{5} = -42.5548483923676$$
$$x_{36} = -39.1265606009671$$
$$x_{52} = -36.271663085188$$
$$x_{37} = -32.8433752937875$$
$$x_{35} = -29.9884777780084$$
$$x_{13} = -26.5601899866079$$
$$x_{24} = -23.7052924708288$$
$$x_{21} = -20.2770046794283$$
$$x_{65} = -17.4221071636492$$
$$x_{20} = -13.9938193722487$$
$$x_{8} = -11.1389218564696$$
$$x_{31} = -7.71063406506912$$
$$x_{23} = -4.85573654929006$$
$$x_{7} = -1.42744875788953$$
$$x_{28} = 1.42744875788953$$
$$x_{54} = 4.85573654929006$$
$$x_{53} = 7.71063406506912$$
$$x_{34} = 11.1389218564696$$
$$x_{59} = 13.9938193722487$$
$$x_{22} = 17.4221071636492$$
$$x_{67} = 20.2770046794283$$
$$x_{30} = 23.7052924708288$$
$$x_{39} = 26.5601899866079$$
$$x_{45} = 29.9884777780084$$
$$x_{32} = 32.8433752937875$$
$$x_{2} = 36.271663085188$$
$$x_{46} = 39.1265606009671$$
$$x_{41} = 42.5548483923676$$
$$x_{15} = 45.4097459081466$$
$$x_{44} = 48.8380336995472$$
$$x_{49} = 51.6929312153262$$
$$x_{51} = 55.1212190067267$$
$$x_{10} = 57.9761165225058$$
$$x_{16} = 61.4044043139063$$
$$x_{17} = 64.2593018296854$$
$$x_{61} = 67.6875896210859$$
$$x_{48} = 70.542487136865$$
$$x_{26} = 73.9707749282655$$
$$x_{1} = 76.8256724440446$$
$$x_{4} = 80.2539602354451$$
$$x_{60} = 83.1088577512241$$
$$x_{56} = 86.5371455426247$$
$$x_{55} = 89.3920430584037$$
$$x_{50} = 92.8203308498043$$
$$x_{3} = 95.6752283655833$$
$$x_{33} = 99.1035161569839$$
$$x_{58} = 120.807969594302$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{25}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{25} - \frac{1}{10}$$
=
$$-12017630.0530054 + - \frac{1}{10}$$
=
$$-12017630.1530054$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} < \frac{1}{7}$$
$$\cos{\left(t \right)} < \frac{1}{7}$$
Entonces
$$x < -12017630.0530054$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
$$x > -99.1035161569839 \wedge x < -95.6752283655833$$
$$x > -92.8203308498043 \wedge x < -89.3920430584037$$
$$x > -86.5371455426247 \wedge x < -83.1088577512241$$
$$x > -80.2539602354451 \wedge x < -76.8256724440446$$
$$x > -73.9707749282655 \wedge x < -70.542487136865$$
$$x > -67.6875896210859 \wedge x < -64.2593018296854$$
$$x > -61.4044043139063 \wedge x < -57.9761165225058$$
$$x > -55.1212190067267 \wedge x < -51.6929312153262$$
$$x > -48.8380336995472 \wedge x < -45.4097459081466$$
$$x > -42.5548483923676 \wedge x < -39.1265606009671$$
$$x > -36.271663085188 \wedge x < -32.8433752937875$$
$$x > -29.9884777780084 \wedge x < -26.5601899866079$$
$$x > -23.7052924708288 \wedge x < -20.2770046794283$$
$$x > -17.4221071636492 \wedge x < -13.9938193722487$$
$$x > -11.1389218564696 \wedge x < -7.71063406506912$$
$$x > -4.85573654929006 \wedge x < -1.42744875788953$$
$$x > 1.42744875788953 \wedge x < 4.85573654929006$$
$$x > 7.71063406506912 \wedge x < 11.1389218564696$$
$$x > 13.9938193722487 \wedge x < 17.4221071636492$$
$$x > 20.2770046794283 \wedge x < 23.7052924708288$$
$$x > 26.5601899866079 \wedge x < 29.9884777780084$$
$$x > 32.8433752937875 \wedge x < 36.271663085188$$
$$x > 39.1265606009671 \wedge x < 42.5548483923676$$
$$x > 45.4097459081466 \wedge x < 48.8380336995472$$
$$x > 51.6929312153262 \wedge x < 55.1212190067267$$
$$x > 57.9761165225058 \wedge x < 61.4044043139063$$
$$x > 64.2593018296854 \wedge x < 67.6875896210859$$
$$x > 70.542487136865 \wedge x < 73.9707749282655$$
$$x > 76.8256724440446 \wedge x < 80.2539602354451$$
$$x > 83.1088577512241 \wedge x < 86.5371455426247$$
$$x > 89.3920430584037 \wedge x < 92.8203308498043$$
$$x > 95.6752283655833 \wedge x < 99.1035161569839$$
$$x > 120.807969594302$$
$$\cos{\left(t \right)} < \frac{1}{7}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = \frac{1}{7}$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = \frac{1}{7}$$
cambiamos
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
$$\cos{\left(t \right)} - \frac{1}{7} = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{7}$$
Obtenemos la respuesta: w = 1/7
hacemos cambio inverso
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 76.8256724440446$$
$$x_{2} = 36.271663085188$$
$$x_{3} = 95.6752283655833$$
$$x_{4} = 80.2539602354451$$
$$x_{5} = -42.5548483923676$$
$$x_{6} = -73.9707749282655$$
$$x_{7} = -1.42744875788953$$
$$x_{8} = -11.1389218564696$$
$$x_{9} = -51.6929312153262$$
$$x_{10} = 57.9761165225058$$
$$x_{11} = -80.2539602354451$$
$$x_{12} = -92.8203308498043$$
$$x_{13} = -26.5601899866079$$
$$x_{14} = -57.9761165225058$$
$$x_{15} = 45.4097459081466$$
$$x_{16} = 61.4044043139063$$
$$x_{17} = 64.2593018296854$$
$$x_{18} = -83.1088577512241$$
$$x_{19} = -95.6752283655833$$
$$x_{20} = -13.9938193722487$$
$$x_{21} = -20.2770046794283$$
$$x_{22} = 17.4221071636492$$
$$x_{23} = -4.85573654929006$$
$$x_{24} = -23.7052924708288$$
$$x_{25} = -12017630.0530054$$
$$x_{26} = 73.9707749282655$$
$$x_{27} = -76.8256724440446$$
$$x_{28} = 1.42744875788953$$
$$x_{29} = -89.3920430584037$$
$$x_{30} = 23.7052924708288$$
$$x_{31} = -7.71063406506912$$
$$x_{32} = 32.8433752937875$$
$$x_{33} = 99.1035161569839$$
$$x_{34} = 11.1389218564696$$
$$x_{35} = -29.9884777780084$$
$$x_{36} = -39.1265606009671$$
$$x_{37} = -32.8433752937875$$
$$x_{38} = -13252.6652615996$$
$$x_{39} = 26.5601899866079$$
$$x_{40} = -61.4044043139063$$
$$x_{41} = 42.5548483923676$$
$$x_{42} = -48.8380336995472$$
$$x_{43} = -86.5371455426247$$
$$x_{44} = 48.8380336995472$$
$$x_{45} = 29.9884777780084$$
$$x_{46} = 39.1265606009671$$
$$x_{47} = -64.2593018296854$$
$$x_{48} = 70.542487136865$$
$$x_{49} = 51.6929312153262$$
$$x_{50} = 92.8203308498043$$
$$x_{51} = 55.1212190067267$$
$$x_{52} = -36.271663085188$$
$$x_{53} = 7.71063406506912$$
$$x_{54} = 4.85573654929006$$
$$x_{55} = 89.3920430584037$$
$$x_{56} = 86.5371455426247$$
$$x_{57} = -55.1212190067267$$
$$x_{58} = 120.807969594302$$
$$x_{59} = 13.9938193722487$$
$$x_{60} = 83.1088577512241$$
$$x_{61} = 67.6875896210859$$
$$x_{62} = -70.542487136865$$
$$x_{63} = -45.4097459081466$$
$$x_{64} = -67.6875896210859$$
$$x_{65} = -17.4221071636492$$
$$x_{66} = -99.1035161569839$$
$$x_{67} = 20.2770046794283$$
$$x_{1} = 76.8256724440446$$
$$x_{2} = 36.271663085188$$
$$x_{3} = 95.6752283655833$$
$$x_{4} = 80.2539602354451$$
$$x_{5} = -42.5548483923676$$
$$x_{6} = -73.9707749282655$$
$$x_{7} = -1.42744875788953$$
$$x_{8} = -11.1389218564696$$
$$x_{9} = -51.6929312153262$$
$$x_{10} = 57.9761165225058$$
$$x_{11} = -80.2539602354451$$
$$x_{12} = -92.8203308498043$$
$$x_{13} = -26.5601899866079$$
$$x_{14} = -57.9761165225058$$
$$x_{15} = 45.4097459081466$$
$$x_{16} = 61.4044043139063$$
$$x_{17} = 64.2593018296854$$
$$x_{18} = -83.1088577512241$$
$$x_{19} = -95.6752283655833$$
$$x_{20} = -13.9938193722487$$
$$x_{21} = -20.2770046794283$$
$$x_{22} = 17.4221071636492$$
$$x_{23} = -4.85573654929006$$
$$x_{24} = -23.7052924708288$$
$$x_{25} = -12017630.0530054$$
$$x_{26} = 73.9707749282655$$
$$x_{27} = -76.8256724440446$$
$$x_{28} = 1.42744875788953$$
$$x_{29} = -89.3920430584037$$
$$x_{30} = 23.7052924708288$$
$$x_{31} = -7.71063406506912$$
$$x_{32} = 32.8433752937875$$
$$x_{33} = 99.1035161569839$$
$$x_{34} = 11.1389218564696$$
$$x_{35} = -29.9884777780084$$
$$x_{36} = -39.1265606009671$$
$$x_{37} = -32.8433752937875$$
$$x_{38} = -13252.6652615996$$
$$x_{39} = 26.5601899866079$$
$$x_{40} = -61.4044043139063$$
$$x_{41} = 42.5548483923676$$
$$x_{42} = -48.8380336995472$$
$$x_{43} = -86.5371455426247$$
$$x_{44} = 48.8380336995472$$
$$x_{45} = 29.9884777780084$$
$$x_{46} = 39.1265606009671$$
$$x_{47} = -64.2593018296854$$
$$x_{48} = 70.542487136865$$
$$x_{49} = 51.6929312153262$$
$$x_{50} = 92.8203308498043$$
$$x_{51} = 55.1212190067267$$
$$x_{52} = -36.271663085188$$
$$x_{53} = 7.71063406506912$$
$$x_{54} = 4.85573654929006$$
$$x_{55} = 89.3920430584037$$
$$x_{56} = 86.5371455426247$$
$$x_{57} = -55.1212190067267$$
$$x_{58} = 120.807969594302$$
$$x_{59} = 13.9938193722487$$
$$x_{60} = 83.1088577512241$$
$$x_{61} = 67.6875896210859$$
$$x_{62} = -70.542487136865$$
$$x_{63} = -45.4097459081466$$
$$x_{64} = -67.6875896210859$$
$$x_{65} = -17.4221071636492$$
$$x_{66} = -99.1035161569839$$
$$x_{67} = 20.2770046794283$$
Las raíces dadas
$$x_{25} = -12017630.0530054$$
$$x_{38} = -13252.6652615996$$
$$x_{66} = -99.1035161569839$$
$$x_{19} = -95.6752283655833$$
$$x_{12} = -92.8203308498043$$
$$x_{29} = -89.3920430584037$$
$$x_{43} = -86.5371455426247$$
$$x_{18} = -83.1088577512241$$
$$x_{11} = -80.2539602354451$$
$$x_{27} = -76.8256724440446$$
$$x_{6} = -73.9707749282655$$
$$x_{62} = -70.542487136865$$
$$x_{64} = -67.6875896210859$$
$$x_{47} = -64.2593018296854$$
$$x_{40} = -61.4044043139063$$
$$x_{14} = -57.9761165225058$$
$$x_{57} = -55.1212190067267$$
$$x_{9} = -51.6929312153262$$
$$x_{42} = -48.8380336995472$$
$$x_{63} = -45.4097459081466$$
$$x_{5} = -42.5548483923676$$
$$x_{36} = -39.1265606009671$$
$$x_{52} = -36.271663085188$$
$$x_{37} = -32.8433752937875$$
$$x_{35} = -29.9884777780084$$
$$x_{13} = -26.5601899866079$$
$$x_{24} = -23.7052924708288$$
$$x_{21} = -20.2770046794283$$
$$x_{65} = -17.4221071636492$$
$$x_{20} = -13.9938193722487$$
$$x_{8} = -11.1389218564696$$
$$x_{31} = -7.71063406506912$$
$$x_{23} = -4.85573654929006$$
$$x_{7} = -1.42744875788953$$
$$x_{28} = 1.42744875788953$$
$$x_{54} = 4.85573654929006$$
$$x_{53} = 7.71063406506912$$
$$x_{34} = 11.1389218564696$$
$$x_{59} = 13.9938193722487$$
$$x_{22} = 17.4221071636492$$
$$x_{67} = 20.2770046794283$$
$$x_{30} = 23.7052924708288$$
$$x_{39} = 26.5601899866079$$
$$x_{45} = 29.9884777780084$$
$$x_{32} = 32.8433752937875$$
$$x_{2} = 36.271663085188$$
$$x_{46} = 39.1265606009671$$
$$x_{41} = 42.5548483923676$$
$$x_{15} = 45.4097459081466$$
$$x_{44} = 48.8380336995472$$
$$x_{49} = 51.6929312153262$$
$$x_{51} = 55.1212190067267$$
$$x_{10} = 57.9761165225058$$
$$x_{16} = 61.4044043139063$$
$$x_{17} = 64.2593018296854$$
$$x_{61} = 67.6875896210859$$
$$x_{48} = 70.542487136865$$
$$x_{26} = 73.9707749282655$$
$$x_{1} = 76.8256724440446$$
$$x_{4} = 80.2539602354451$$
$$x_{60} = 83.1088577512241$$
$$x_{56} = 86.5371455426247$$
$$x_{55} = 89.3920430584037$$
$$x_{50} = 92.8203308498043$$
$$x_{3} = 95.6752283655833$$
$$x_{33} = 99.1035161569839$$
$$x_{58} = 120.807969594302$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{25}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{25} - \frac{1}{10}$$
=
$$-12017630.0530054 + - \frac{1}{10}$$
=
$$-12017630.1530054$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} < \frac{1}{7}$$
$$\cos{\left(t \right)} < \frac{1}{7}$$
cos(t) < 1/7
Entonces
$$x < -12017630.0530054$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x25 x38 x66 x19 x12 x29 x43 x18 x11 x27 x6 x62 x64 x47 x40 x14 x57 x9 x42 x63 x5 x36 x52 x37 x35 x13 x24 x21 x65 x20 x8 x31 x23 x7 x28 x54 x53 x34 x59 x22 x67 x30 x39 x45 x32 x2 x46 x41 x15 x44 x49 x51 x10 x16 x17 x61 x48 x26 x1 x4 x60 x56 x55 x50 x3 x33 x58Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -12017630.0530054 \wedge x < -13252.6652615996$$
$$x > -99.1035161569839 \wedge x < -95.6752283655833$$
$$x > -92.8203308498043 \wedge x < -89.3920430584037$$
$$x > -86.5371455426247 \wedge x < -83.1088577512241$$
$$x > -80.2539602354451 \wedge x < -76.8256724440446$$
$$x > -73.9707749282655 \wedge x < -70.542487136865$$
$$x > -67.6875896210859 \wedge x < -64.2593018296854$$
$$x > -61.4044043139063 \wedge x < -57.9761165225058$$
$$x > -55.1212190067267 \wedge x < -51.6929312153262$$
$$x > -48.8380336995472 \wedge x < -45.4097459081466$$
$$x > -42.5548483923676 \wedge x < -39.1265606009671$$
$$x > -36.271663085188 \wedge x < -32.8433752937875$$
$$x > -29.9884777780084 \wedge x < -26.5601899866079$$
$$x > -23.7052924708288 \wedge x < -20.2770046794283$$
$$x > -17.4221071636492 \wedge x < -13.9938193722487$$
$$x > -11.1389218564696 \wedge x < -7.71063406506912$$
$$x > -4.85573654929006 \wedge x < -1.42744875788953$$
$$x > 1.42744875788953 \wedge x < 4.85573654929006$$
$$x > 7.71063406506912 \wedge x < 11.1389218564696$$
$$x > 13.9938193722487 \wedge x < 17.4221071636492$$
$$x > 20.2770046794283 \wedge x < 23.7052924708288$$
$$x > 26.5601899866079 \wedge x < 29.9884777780084$$
$$x > 32.8433752937875 \wedge x < 36.271663085188$$
$$x > 39.1265606009671 \wedge x < 42.5548483923676$$
$$x > 45.4097459081466 \wedge x < 48.8380336995472$$
$$x > 51.6929312153262 \wedge x < 55.1212190067267$$
$$x > 57.9761165225058 \wedge x < 61.4044043139063$$
$$x > 64.2593018296854 \wedge x < 67.6875896210859$$
$$x > 70.542487136865 \wedge x < 73.9707749282655$$
$$x > 76.8256724440446 \wedge x < 80.2539602354451$$
$$x > 83.1088577512241 \wedge x < 86.5371455426247$$
$$x > 89.3920430584037 \wedge x < 92.8203308498043$$
$$x > 95.6752283655833 \wedge x < 99.1035161569839$$
$$x > 120.807969594302$$
Respuesta rápida 2
[src]
/ ___\ / ___\ (atan\4*\/ 3 /, - atan\4*\/ 3 / + 2*pi)
$$x\ in\ \left(\operatorname{atan}{\left(4 \sqrt{3} \right)}, - \operatorname{atan}{\left(4 \sqrt{3} \right)} + 2 \pi\right)$$
x in Interval.open(atan(4*sqrt(3)), -atan(4*sqrt(3)) + 2*pi)
Respuesta rápida
[src]
/ / ___\ / ___\ \ And\t < - atan\4*\/ 3 / + 2*pi, atan\4*\/ 3 / < t/
$$t < - \operatorname{atan}{\left(4 \sqrt{3} \right)} + 2 \pi \wedge \operatorname{atan}{\left(4 \sqrt{3} \right)} < t$$
(atan(4*sqrt(3)) < t)∧(t < -atan(4*sqrt(3)) + 2*pi)