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:
-
-16/((x+2)^2-5)>=0
-
(x-2)/(x^2+2x-8)>0
-
x^2-10x<0
- 5(y-1,4)-6<4y-1,5
-
Expresiones idénticas
- sinπ/4cosx+cosπ/4sinxx<-√ dos / dos
- seno de π dividir por 4 coseno de x más coseno de π dividir por 4 seno de xx menos menos √2 dividir por 2
- seno de π dividir por 4 coseno de x más coseno de π dividir por 4 seno de xx menos menos √ dos dividir por dos
- sinπ dividir por 4cosx+cosπ dividir por 4sinxx<-√2 dividir por 2
-
Expresiones semejantes
- sinπ/4cosx+cosπ/4sinxx<+√2/2
- sinπ/4cosx-cosπ/4sinxx<-√2/2
sinπ/4cosx+cosπ/4sinxx<-√2/2 desigualdades
Solución
Ha introducido
[src]
___ sin(pi) cos(pi) -\/ 2 -------*cos(x) + -------*sin(x)*x < ------- 4 4 2
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
x*((cos(pi)/4)*sin(x)) + (sin(pi)/4)*cos(x) < (-sqrt(2))/2
Solución detallada
Se da la desigualdad:
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Resolvemos:
$$x_{1} = -87.9967422448965$$
$$x_{2} = 28.1737722723591$$
$$x_{3} = -47.0637557911179$$
$$x_{4} = -100.559095639214$$
$$x_{5} = 15.524751792341$$
$$x_{6} = -81.7160287887195$$
$$x_{7} = 94.2777851024745$$
$$x_{8} = -12.789368792168$$
$$x_{9} = 91.0751259816486$$
$$x_{10} = -6.71777296700565$$
$$x_{11} = -62.8768518560757$$
$$x_{12} = -9.1090512714554$$
$$x_{13} = 62.8768518560757$$
$$x_{14} = -25.2450159931248$$
$$x_{15} = -21.8614049429289$$
$$x_{16} = 31.5058223091142$$
$$x_{17} = -37.7740594883425$$
$$x_{18} = -97.3603170444132$$
$$x_{19} = -40.7712756967684$$
$$x_{20} = 25.2450159931248$$
$$x_{21} = -15.524751792341$$
$$x_{22} = 47.0637557911179$$
$$x_{23} = 97.3603170444132$$
$$x_{24} = 12.789368792168$$
$$x_{25} = -31.5058223091142$$
$$x_{26} = -50.3217189805734$$
$$x_{27} = -65.9305324449798$$
$$x_{28} = -34.4753849437034$$
$$x_{29} = 18.9989839374818$$
$$x_{30} = 59.6428198653341$$
$$x_{31} = 65.9305324449798$$
$$x_{32} = 6.71777296700561$$
$$x_{33} = -94.2777851024745$$
$$x_{34} = 69.1559490497049$$
$$x_{35} = -113.122341393481$$
$$x_{36} = 84.7896372872959$$
$$x_{37} = 56.5986619801693$$
$$x_{38} = 75.4357270068736$$
$$x_{39} = -18.9989839374818$$
$$x_{40} = -44.0465558538625$$
$$x_{41} = 78.5037793560876$$
$$x_{42} = 116.214587809701$$
$$x_{43} = -69.1559490497049$$
$$x_{44} = 53.354037820599$$
$$x_{45} = 100.559095639214$$
$$x_{46} = 44.0465558538625$$
$$x_{47} = 21.8614049429289$$
$$x_{48} = -56.5986619801693$$
$$x_{49} = -6.71777296700561$$
$$x_{50} = 72.217455590799$$
$$x_{51} = -28.1737722723591$$
$$x_{52} = 37.7740594883425$$
$$x_{53} = -91.0751259816486$$
$$x_{54} = -53.354037820599$$
$$x_{55} = 40.7712756967684$$
$$x_{56} = -78.5037793560876$$
$$x_{57} = -75.4357270068736$$
$$x_{58} = 81.7160287887195$$
$$x_{59} = 87.9967422448965$$
$$x_{60} = 9.1090512714554$$
$$x_{61} = 50.3217189805734$$
$$x_{62} = -59.6428198653341$$
$$x_{63} = -72.217455590799$$
$$x_{64} = 34.4753849437034$$
$$x_{65} = -84.7896372872959$$
$$x_{1} = -87.9967422448965$$
$$x_{2} = 28.1737722723591$$
$$x_{3} = -47.0637557911179$$
$$x_{4} = -100.559095639214$$
$$x_{5} = 15.524751792341$$
$$x_{6} = -81.7160287887195$$
$$x_{7} = 94.2777851024745$$
$$x_{8} = -12.789368792168$$
$$x_{9} = 91.0751259816486$$
$$x_{10} = -6.71777296700565$$
$$x_{11} = -62.8768518560757$$
$$x_{12} = -9.1090512714554$$
$$x_{13} = 62.8768518560757$$
$$x_{14} = -25.2450159931248$$
$$x_{15} = -21.8614049429289$$
$$x_{16} = 31.5058223091142$$
$$x_{17} = -37.7740594883425$$
$$x_{18} = -97.3603170444132$$
$$x_{19} = -40.7712756967684$$
$$x_{20} = 25.2450159931248$$
$$x_{21} = -15.524751792341$$
$$x_{22} = 47.0637557911179$$
$$x_{23} = 97.3603170444132$$
$$x_{24} = 12.789368792168$$
$$x_{25} = -31.5058223091142$$
$$x_{26} = -50.3217189805734$$
$$x_{27} = -65.9305324449798$$
$$x_{28} = -34.4753849437034$$
$$x_{29} = 18.9989839374818$$
$$x_{30} = 59.6428198653341$$
$$x_{31} = 65.9305324449798$$
$$x_{32} = 6.71777296700561$$
$$x_{33} = -94.2777851024745$$
$$x_{34} = 69.1559490497049$$
$$x_{35} = -113.122341393481$$
$$x_{36} = 84.7896372872959$$
$$x_{37} = 56.5986619801693$$
$$x_{38} = 75.4357270068736$$
$$x_{39} = -18.9989839374818$$
$$x_{40} = -44.0465558538625$$
$$x_{41} = 78.5037793560876$$
$$x_{42} = 116.214587809701$$
$$x_{43} = -69.1559490497049$$
$$x_{44} = 53.354037820599$$
$$x_{45} = 100.559095639214$$
$$x_{46} = 44.0465558538625$$
$$x_{47} = 21.8614049429289$$
$$x_{48} = -56.5986619801693$$
$$x_{49} = -6.71777296700561$$
$$x_{50} = 72.217455590799$$
$$x_{51} = -28.1737722723591$$
$$x_{52} = 37.7740594883425$$
$$x_{53} = -91.0751259816486$$
$$x_{54} = -53.354037820599$$
$$x_{55} = 40.7712756967684$$
$$x_{56} = -78.5037793560876$$
$$x_{57} = -75.4357270068736$$
$$x_{58} = 81.7160287887195$$
$$x_{59} = 87.9967422448965$$
$$x_{60} = 9.1090512714554$$
$$x_{61} = 50.3217189805734$$
$$x_{62} = -59.6428198653341$$
$$x_{63} = -72.217455590799$$
$$x_{64} = 34.4753849437034$$
$$x_{65} = -84.7896372872959$$
Las raíces dadas
$$x_{35} = -113.122341393481$$
$$x_{4} = -100.559095639214$$
$$x_{18} = -97.3603170444132$$
$$x_{33} = -94.2777851024745$$
$$x_{53} = -91.0751259816486$$
$$x_{1} = -87.9967422448965$$
$$x_{65} = -84.7896372872959$$
$$x_{6} = -81.7160287887195$$
$$x_{56} = -78.5037793560876$$
$$x_{57} = -75.4357270068736$$
$$x_{63} = -72.217455590799$$
$$x_{43} = -69.1559490497049$$
$$x_{27} = -65.9305324449798$$
$$x_{11} = -62.8768518560757$$
$$x_{62} = -59.6428198653341$$
$$x_{48} = -56.5986619801693$$
$$x_{54} = -53.354037820599$$
$$x_{26} = -50.3217189805734$$
$$x_{3} = -47.0637557911179$$
$$x_{40} = -44.0465558538625$$
$$x_{19} = -40.7712756967684$$
$$x_{17} = -37.7740594883425$$
$$x_{28} = -34.4753849437034$$
$$x_{25} = -31.5058223091142$$
$$x_{51} = -28.1737722723591$$
$$x_{14} = -25.2450159931248$$
$$x_{15} = -21.8614049429289$$
$$x_{39} = -18.9989839374818$$
$$x_{21} = -15.524751792341$$
$$x_{8} = -12.789368792168$$
$$x_{12} = -9.1090512714554$$
$$x_{10} = -6.71777296700565$$
$$x_{49} = -6.71777296700561$$
$$x_{32} = 6.71777296700561$$
$$x_{60} = 9.1090512714554$$
$$x_{24} = 12.789368792168$$
$$x_{5} = 15.524751792341$$
$$x_{29} = 18.9989839374818$$
$$x_{47} = 21.8614049429289$$
$$x_{20} = 25.2450159931248$$
$$x_{2} = 28.1737722723591$$
$$x_{16} = 31.5058223091142$$
$$x_{64} = 34.4753849437034$$
$$x_{52} = 37.7740594883425$$
$$x_{55} = 40.7712756967684$$
$$x_{46} = 44.0465558538625$$
$$x_{22} = 47.0637557911179$$
$$x_{61} = 50.3217189805734$$
$$x_{44} = 53.354037820599$$
$$x_{37} = 56.5986619801693$$
$$x_{30} = 59.6428198653341$$
$$x_{13} = 62.8768518560757$$
$$x_{31} = 65.9305324449798$$
$$x_{34} = 69.1559490497049$$
$$x_{50} = 72.217455590799$$
$$x_{38} = 75.4357270068736$$
$$x_{41} = 78.5037793560876$$
$$x_{58} = 81.7160287887195$$
$$x_{36} = 84.7896372872959$$
$$x_{59} = 87.9967422448965$$
$$x_{9} = 91.0751259816486$$
$$x_{7} = 94.2777851024745$$
$$x_{23} = 97.3603170444132$$
$$x_{45} = 100.559095639214$$
$$x_{42} = 116.214587809701$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{35}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{35} - \frac{1}{10}$$
=
$$-113.122341393481 + - \frac{1}{10}$$
=
$$-113.222341393481$$
lo sustituimos en la expresión
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
$$\left(-113.222341393481\right) \frac{\cos{\left(\pi \right)}}{4} \sin{\left(-113.222341393481 \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(-113.222341393481 \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -113.122341393481$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -113.122341393481$$
$$x > -100.559095639214 \wedge x < -97.3603170444132$$
$$x > -94.2777851024745 \wedge x < -91.0751259816486$$
$$x > -87.9967422448965 \wedge x < -84.7896372872959$$
$$x > -81.7160287887195 \wedge x < -78.5037793560876$$
$$x > -75.4357270068736 \wedge x < -72.217455590799$$
$$x > -69.1559490497049 \wedge x < -65.9305324449798$$
$$x > -62.8768518560757 \wedge x < -59.6428198653341$$
$$x > -56.5986619801693 \wedge x < -53.354037820599$$
$$x > -50.3217189805734 \wedge x < -47.0637557911179$$
$$x > -44.0465558538625 \wedge x < -40.7712756967684$$
$$x > -37.7740594883425 \wedge x < -34.4753849437034$$
$$x > -31.5058223091142 \wedge x < -28.1737722723591$$
$$x > -25.2450159931248 \wedge x < -21.8614049429289$$
$$x > -18.9989839374818 \wedge x < -15.524751792341$$
$$x > -12.789368792168 \wedge x < -9.1090512714554$$
$$x > -6.71777296700565 \wedge x < -6.71777296700561$$
$$x > 6.71777296700561 \wedge x < 9.1090512714554$$
$$x > 12.789368792168 \wedge x < 15.524751792341$$
$$x > 18.9989839374818 \wedge x < 21.8614049429289$$
$$x > 25.2450159931248 \wedge x < 28.1737722723591$$
$$x > 31.5058223091142 \wedge x < 34.4753849437034$$
$$x > 37.7740594883425 \wedge x < 40.7712756967684$$
$$x > 44.0465558538625 \wedge x < 47.0637557911179$$
$$x > 50.3217189805734 \wedge x < 53.354037820599$$
$$x > 56.5986619801693 \wedge x < 59.6428198653341$$
$$x > 62.8768518560757 \wedge x < 65.9305324449798$$
$$x > 69.1559490497049 \wedge x < 72.217455590799$$
$$x > 75.4357270068736 \wedge x < 78.5037793560876$$
$$x > 81.7160287887195 \wedge x < 84.7896372872959$$
$$x > 87.9967422448965 \wedge x < 91.0751259816486$$
$$x > 94.2777851024745 \wedge x < 97.3603170444132$$
$$x > 100.559095639214 \wedge x < 116.214587809701$$
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
Resolvemos:
$$x_{1} = -87.9967422448965$$
$$x_{2} = 28.1737722723591$$
$$x_{3} = -47.0637557911179$$
$$x_{4} = -100.559095639214$$
$$x_{5} = 15.524751792341$$
$$x_{6} = -81.7160287887195$$
$$x_{7} = 94.2777851024745$$
$$x_{8} = -12.789368792168$$
$$x_{9} = 91.0751259816486$$
$$x_{10} = -6.71777296700565$$
$$x_{11} = -62.8768518560757$$
$$x_{12} = -9.1090512714554$$
$$x_{13} = 62.8768518560757$$
$$x_{14} = -25.2450159931248$$
$$x_{15} = -21.8614049429289$$
$$x_{16} = 31.5058223091142$$
$$x_{17} = -37.7740594883425$$
$$x_{18} = -97.3603170444132$$
$$x_{19} = -40.7712756967684$$
$$x_{20} = 25.2450159931248$$
$$x_{21} = -15.524751792341$$
$$x_{22} = 47.0637557911179$$
$$x_{23} = 97.3603170444132$$
$$x_{24} = 12.789368792168$$
$$x_{25} = -31.5058223091142$$
$$x_{26} = -50.3217189805734$$
$$x_{27} = -65.9305324449798$$
$$x_{28} = -34.4753849437034$$
$$x_{29} = 18.9989839374818$$
$$x_{30} = 59.6428198653341$$
$$x_{31} = 65.9305324449798$$
$$x_{32} = 6.71777296700561$$
$$x_{33} = -94.2777851024745$$
$$x_{34} = 69.1559490497049$$
$$x_{35} = -113.122341393481$$
$$x_{36} = 84.7896372872959$$
$$x_{37} = 56.5986619801693$$
$$x_{38} = 75.4357270068736$$
$$x_{39} = -18.9989839374818$$
$$x_{40} = -44.0465558538625$$
$$x_{41} = 78.5037793560876$$
$$x_{42} = 116.214587809701$$
$$x_{43} = -69.1559490497049$$
$$x_{44} = 53.354037820599$$
$$x_{45} = 100.559095639214$$
$$x_{46} = 44.0465558538625$$
$$x_{47} = 21.8614049429289$$
$$x_{48} = -56.5986619801693$$
$$x_{49} = -6.71777296700561$$
$$x_{50} = 72.217455590799$$
$$x_{51} = -28.1737722723591$$
$$x_{52} = 37.7740594883425$$
$$x_{53} = -91.0751259816486$$
$$x_{54} = -53.354037820599$$
$$x_{55} = 40.7712756967684$$
$$x_{56} = -78.5037793560876$$
$$x_{57} = -75.4357270068736$$
$$x_{58} = 81.7160287887195$$
$$x_{59} = 87.9967422448965$$
$$x_{60} = 9.1090512714554$$
$$x_{61} = 50.3217189805734$$
$$x_{62} = -59.6428198653341$$
$$x_{63} = -72.217455590799$$
$$x_{64} = 34.4753849437034$$
$$x_{65} = -84.7896372872959$$
$$x_{1} = -87.9967422448965$$
$$x_{2} = 28.1737722723591$$
$$x_{3} = -47.0637557911179$$
$$x_{4} = -100.559095639214$$
$$x_{5} = 15.524751792341$$
$$x_{6} = -81.7160287887195$$
$$x_{7} = 94.2777851024745$$
$$x_{8} = -12.789368792168$$
$$x_{9} = 91.0751259816486$$
$$x_{10} = -6.71777296700565$$
$$x_{11} = -62.8768518560757$$
$$x_{12} = -9.1090512714554$$
$$x_{13} = 62.8768518560757$$
$$x_{14} = -25.2450159931248$$
$$x_{15} = -21.8614049429289$$
$$x_{16} = 31.5058223091142$$
$$x_{17} = -37.7740594883425$$
$$x_{18} = -97.3603170444132$$
$$x_{19} = -40.7712756967684$$
$$x_{20} = 25.2450159931248$$
$$x_{21} = -15.524751792341$$
$$x_{22} = 47.0637557911179$$
$$x_{23} = 97.3603170444132$$
$$x_{24} = 12.789368792168$$
$$x_{25} = -31.5058223091142$$
$$x_{26} = -50.3217189805734$$
$$x_{27} = -65.9305324449798$$
$$x_{28} = -34.4753849437034$$
$$x_{29} = 18.9989839374818$$
$$x_{30} = 59.6428198653341$$
$$x_{31} = 65.9305324449798$$
$$x_{32} = 6.71777296700561$$
$$x_{33} = -94.2777851024745$$
$$x_{34} = 69.1559490497049$$
$$x_{35} = -113.122341393481$$
$$x_{36} = 84.7896372872959$$
$$x_{37} = 56.5986619801693$$
$$x_{38} = 75.4357270068736$$
$$x_{39} = -18.9989839374818$$
$$x_{40} = -44.0465558538625$$
$$x_{41} = 78.5037793560876$$
$$x_{42} = 116.214587809701$$
$$x_{43} = -69.1559490497049$$
$$x_{44} = 53.354037820599$$
$$x_{45} = 100.559095639214$$
$$x_{46} = 44.0465558538625$$
$$x_{47} = 21.8614049429289$$
$$x_{48} = -56.5986619801693$$
$$x_{49} = -6.71777296700561$$
$$x_{50} = 72.217455590799$$
$$x_{51} = -28.1737722723591$$
$$x_{52} = 37.7740594883425$$
$$x_{53} = -91.0751259816486$$
$$x_{54} = -53.354037820599$$
$$x_{55} = 40.7712756967684$$
$$x_{56} = -78.5037793560876$$
$$x_{57} = -75.4357270068736$$
$$x_{58} = 81.7160287887195$$
$$x_{59} = 87.9967422448965$$
$$x_{60} = 9.1090512714554$$
$$x_{61} = 50.3217189805734$$
$$x_{62} = -59.6428198653341$$
$$x_{63} = -72.217455590799$$
$$x_{64} = 34.4753849437034$$
$$x_{65} = -84.7896372872959$$
Las raíces dadas
$$x_{35} = -113.122341393481$$
$$x_{4} = -100.559095639214$$
$$x_{18} = -97.3603170444132$$
$$x_{33} = -94.2777851024745$$
$$x_{53} = -91.0751259816486$$
$$x_{1} = -87.9967422448965$$
$$x_{65} = -84.7896372872959$$
$$x_{6} = -81.7160287887195$$
$$x_{56} = -78.5037793560876$$
$$x_{57} = -75.4357270068736$$
$$x_{63} = -72.217455590799$$
$$x_{43} = -69.1559490497049$$
$$x_{27} = -65.9305324449798$$
$$x_{11} = -62.8768518560757$$
$$x_{62} = -59.6428198653341$$
$$x_{48} = -56.5986619801693$$
$$x_{54} = -53.354037820599$$
$$x_{26} = -50.3217189805734$$
$$x_{3} = -47.0637557911179$$
$$x_{40} = -44.0465558538625$$
$$x_{19} = -40.7712756967684$$
$$x_{17} = -37.7740594883425$$
$$x_{28} = -34.4753849437034$$
$$x_{25} = -31.5058223091142$$
$$x_{51} = -28.1737722723591$$
$$x_{14} = -25.2450159931248$$
$$x_{15} = -21.8614049429289$$
$$x_{39} = -18.9989839374818$$
$$x_{21} = -15.524751792341$$
$$x_{8} = -12.789368792168$$
$$x_{12} = -9.1090512714554$$
$$x_{10} = -6.71777296700565$$
$$x_{49} = -6.71777296700561$$
$$x_{32} = 6.71777296700561$$
$$x_{60} = 9.1090512714554$$
$$x_{24} = 12.789368792168$$
$$x_{5} = 15.524751792341$$
$$x_{29} = 18.9989839374818$$
$$x_{47} = 21.8614049429289$$
$$x_{20} = 25.2450159931248$$
$$x_{2} = 28.1737722723591$$
$$x_{16} = 31.5058223091142$$
$$x_{64} = 34.4753849437034$$
$$x_{52} = 37.7740594883425$$
$$x_{55} = 40.7712756967684$$
$$x_{46} = 44.0465558538625$$
$$x_{22} = 47.0637557911179$$
$$x_{61} = 50.3217189805734$$
$$x_{44} = 53.354037820599$$
$$x_{37} = 56.5986619801693$$
$$x_{30} = 59.6428198653341$$
$$x_{13} = 62.8768518560757$$
$$x_{31} = 65.9305324449798$$
$$x_{34} = 69.1559490497049$$
$$x_{50} = 72.217455590799$$
$$x_{38} = 75.4357270068736$$
$$x_{41} = 78.5037793560876$$
$$x_{58} = 81.7160287887195$$
$$x_{36} = 84.7896372872959$$
$$x_{59} = 87.9967422448965$$
$$x_{9} = 91.0751259816486$$
$$x_{7} = 94.2777851024745$$
$$x_{23} = 97.3603170444132$$
$$x_{45} = 100.559095639214$$
$$x_{42} = 116.214587809701$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{35}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{35} - \frac{1}{10}$$
=
$$-113.122341393481 + - \frac{1}{10}$$
=
$$-113.222341393481$$
lo sustituimos en la expresión
$$x \frac{\cos{\left(\pi \right)}}{4} \sin{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(x \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
$$\left(-113.222341393481\right) \frac{\cos{\left(\pi \right)}}{4} \sin{\left(-113.222341393481 \right)} + \frac{\sin{\left(\pi \right)}}{4} \cos{\left(-113.222341393481 \right)} < \frac{\left(-1\right) \sqrt{2}}{2}$$
___
-\/ 2
-3.52915600241859 < -------
2
significa que una de las soluciones de nuestra ecuación será con:
$$x < -113.122341393481$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x35 x4 x18 x33 x53 x1 x65 x6 x56 x57 x63 x43 x27 x11 x62 x48 x54 x26 x3 x40 x19 x17 x28 x25 x51 x14 x15 x39 x21 x8 x12 x10 x49 x32 x60 x24 x5 x29 x47 x20 x2 x16 x64 x52 x55 x46 x22 x61 x44 x37 x30 x13 x31 x34 x50 x38 x41 x58 x36 x59 x9 x7 x23 x45 x42Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -113.122341393481$$
$$x > -100.559095639214 \wedge x < -97.3603170444132$$
$$x > -94.2777851024745 \wedge x < -91.0751259816486$$
$$x > -87.9967422448965 \wedge x < -84.7896372872959$$
$$x > -81.7160287887195 \wedge x < -78.5037793560876$$
$$x > -75.4357270068736 \wedge x < -72.217455590799$$
$$x > -69.1559490497049 \wedge x < -65.9305324449798$$
$$x > -62.8768518560757 \wedge x < -59.6428198653341$$
$$x > -56.5986619801693 \wedge x < -53.354037820599$$
$$x > -50.3217189805734 \wedge x < -47.0637557911179$$
$$x > -44.0465558538625 \wedge x < -40.7712756967684$$
$$x > -37.7740594883425 \wedge x < -34.4753849437034$$
$$x > -31.5058223091142 \wedge x < -28.1737722723591$$
$$x > -25.2450159931248 \wedge x < -21.8614049429289$$
$$x > -18.9989839374818 \wedge x < -15.524751792341$$
$$x > -12.789368792168 \wedge x < -9.1090512714554$$
$$x > -6.71777296700565 \wedge x < -6.71777296700561$$
$$x > 6.71777296700561 \wedge x < 9.1090512714554$$
$$x > 12.789368792168 \wedge x < 15.524751792341$$
$$x > 18.9989839374818 \wedge x < 21.8614049429289$$
$$x > 25.2450159931248 \wedge x < 28.1737722723591$$
$$x > 31.5058223091142 \wedge x < 34.4753849437034$$
$$x > 37.7740594883425 \wedge x < 40.7712756967684$$
$$x > 44.0465558538625 \wedge x < 47.0637557911179$$
$$x > 50.3217189805734 \wedge x < 53.354037820599$$
$$x > 56.5986619801693 \wedge x < 59.6428198653341$$
$$x > 62.8768518560757 \wedge x < 65.9305324449798$$
$$x > 69.1559490497049 \wedge x < 72.217455590799$$
$$x > 75.4357270068736 \wedge x < 78.5037793560876$$
$$x > 81.7160287887195 \wedge x < 84.7896372872959$$
$$x > 87.9967422448965 \wedge x < 91.0751259816486$$
$$x > 94.2777851024745 \wedge x < 97.3603170444132$$
$$x > 100.559095639214 \wedge x < 116.214587809701$$
Solución de la desigualdad en el gráfico
Gráfico