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^2+x-30<0
- Derivada de:
-
sint
- Integral de d{x}:
- sint
-
Expresiones idénticas
- sint< cero
- seno de t menos 0
- seno de t menos cero
-
Expresiones con funciones
- sint
- sint>√3/2
- sint<-√2/2
- sint>-√3
- sint<1/2
- sint>1/2
sint<0 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\sin{\left(t \right)} < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(t \right)} = 0$$
Resolvemos:
Tenemos la ecuación
$$\sin{\left(t \right)} = 0$$
cambiamos
$$\sin{\left(t \right)} - 1 = 0$$
$$\sin{\left(t \right)} - 1 = 0$$
Sustituimos
$$w = \sin{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 1$$
Obtenemos la respuesta: w = 1
hacemos cambio inverso
$$\sin{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 62.8318530717959$$
$$x_{2} = 81.6814089933346$$
$$x_{3} = -53.4070751110265$$
$$x_{4} = 59.6902604182061$$
$$x_{5} = 69.1150383789755$$
$$x_{6} = 37.6991118430775$$
$$x_{7} = -40.8407044966673$$
$$x_{8} = -113.097335529233$$
$$x_{9} = -15.707963267949$$
$$x_{10} = 53.4070751110265$$
$$x_{11} = 15.707963267949$$
$$x_{12} = 56.5486677646163$$
$$x_{13} = -34.5575191894877$$
$$x_{14} = 43.9822971502571$$
$$x_{15} = -87.9645943005142$$
$$x_{16} = 84.8230016469244$$
$$x_{17} = 34.5575191894877$$
$$x_{18} = 100.530964914873$$
$$x_{19} = 12.5663706143592$$
$$x_{20} = -84.8230016469244$$
$$x_{21} = 78.5398163397448$$
$$x_{22} = -91.106186954104$$
$$x_{23} = 25.1327412287183$$
$$x_{24} = 9.42477796076938$$
$$x_{25} = -2642.07942166902$$
$$x_{26} = 75.398223686155$$
$$x_{27} = 65.9734457253857$$
$$x_{28} = -25.1327412287183$$
$$x_{29} = 18.8495559215388$$
$$x_{30} = -69.1150383789755$$
$$x_{31} = -28.2743338823081$$
$$x_{32} = -31.4159265358979$$
$$x_{33} = 40.8407044966673$$
$$x_{34} = -6.28318530717959$$
$$x_{35} = -47.1238898038469$$
$$x_{36} = 3.14159265358979$$
$$x_{37} = -62.8318530717959$$
$$x_{38} = -59.6902604182061$$
$$x_{39} = -37.6991118430775$$
$$x_{40} = -81.6814089933346$$
$$x_{41} = -100.530964914873$$
$$x_{42} = -9.42477796076938$$
$$x_{43} = 94.2477796076938$$
$$x_{44} = 31.4159265358979$$
$$x_{45} = 0$$
$$x_{46} = -50.2654824574367$$
$$x_{47} = -21.9911485751286$$
$$x_{48} = -267.035375555132$$
$$x_{49} = 91.106186954104$$
$$x_{50} = 87.9645943005142$$
$$x_{51} = 50.2654824574367$$
$$x_{52} = -43.9822971502571$$
$$x_{53} = -12.5663706143592$$
$$x_{54} = 72.2566310325652$$
$$x_{55} = -78.5398163397448$$
$$x_{56} = -232.477856365645$$
$$x_{57} = -56.5486677646163$$
$$x_{58} = -18.8495559215388$$
$$x_{59} = 97.3893722612836$$
$$x_{60} = 21.9911485751286$$
$$x_{61} = -97.3893722612836$$
$$x_{62} = 47.1238898038469$$
$$x_{63} = -3.14159265358979$$
$$x_{64} = -65.9734457253857$$
$$x_{65} = 28.2743338823081$$
$$x_{66} = -94.2477796076938$$
$$x_{67} = -75.398223686155$$
$$x_{68} = -72.2566310325652$$
$$x_{69} = 6.28318530717959$$
$$x_{1} = 62.8318530717959$$
$$x_{2} = 81.6814089933346$$
$$x_{3} = -53.4070751110265$$
$$x_{4} = 59.6902604182061$$
$$x_{5} = 69.1150383789755$$
$$x_{6} = 37.6991118430775$$
$$x_{7} = -40.8407044966673$$
$$x_{8} = -113.097335529233$$
$$x_{9} = -15.707963267949$$
$$x_{10} = 53.4070751110265$$
$$x_{11} = 15.707963267949$$
$$x_{12} = 56.5486677646163$$
$$x_{13} = -34.5575191894877$$
$$x_{14} = 43.9822971502571$$
$$x_{15} = -87.9645943005142$$
$$x_{16} = 84.8230016469244$$
$$x_{17} = 34.5575191894877$$
$$x_{18} = 100.530964914873$$
$$x_{19} = 12.5663706143592$$
$$x_{20} = -84.8230016469244$$
$$x_{21} = 78.5398163397448$$
$$x_{22} = -91.106186954104$$
$$x_{23} = 25.1327412287183$$
$$x_{24} = 9.42477796076938$$
$$x_{25} = -2642.07942166902$$
$$x_{26} = 75.398223686155$$
$$x_{27} = 65.9734457253857$$
$$x_{28} = -25.1327412287183$$
$$x_{29} = 18.8495559215388$$
$$x_{30} = -69.1150383789755$$
$$x_{31} = -28.2743338823081$$
$$x_{32} = -31.4159265358979$$
$$x_{33} = 40.8407044966673$$
$$x_{34} = -6.28318530717959$$
$$x_{35} = -47.1238898038469$$
$$x_{36} = 3.14159265358979$$
$$x_{37} = -62.8318530717959$$
$$x_{38} = -59.6902604182061$$
$$x_{39} = -37.6991118430775$$
$$x_{40} = -81.6814089933346$$
$$x_{41} = -100.530964914873$$
$$x_{42} = -9.42477796076938$$
$$x_{43} = 94.2477796076938$$
$$x_{44} = 31.4159265358979$$
$$x_{45} = 0$$
$$x_{46} = -50.2654824574367$$
$$x_{47} = -21.9911485751286$$
$$x_{48} = -267.035375555132$$
$$x_{49} = 91.106186954104$$
$$x_{50} = 87.9645943005142$$
$$x_{51} = 50.2654824574367$$
$$x_{52} = -43.9822971502571$$
$$x_{53} = -12.5663706143592$$
$$x_{54} = 72.2566310325652$$
$$x_{55} = -78.5398163397448$$
$$x_{56} = -232.477856365645$$
$$x_{57} = -56.5486677646163$$
$$x_{58} = -18.8495559215388$$
$$x_{59} = 97.3893722612836$$
$$x_{60} = 21.9911485751286$$
$$x_{61} = -97.3893722612836$$
$$x_{62} = 47.1238898038469$$
$$x_{63} = -3.14159265358979$$
$$x_{64} = -65.9734457253857$$
$$x_{65} = 28.2743338823081$$
$$x_{66} = -94.2477796076938$$
$$x_{67} = -75.398223686155$$
$$x_{68} = -72.2566310325652$$
$$x_{69} = 6.28318530717959$$
Las raíces dadas
$$x_{25} = -2642.07942166902$$
$$x_{48} = -267.035375555132$$
$$x_{56} = -232.477856365645$$
$$x_{8} = -113.097335529233$$
$$x_{41} = -100.530964914873$$
$$x_{61} = -97.3893722612836$$
$$x_{66} = -94.2477796076938$$
$$x_{22} = -91.106186954104$$
$$x_{15} = -87.9645943005142$$
$$x_{20} = -84.8230016469244$$
$$x_{40} = -81.6814089933346$$
$$x_{55} = -78.5398163397448$$
$$x_{67} = -75.398223686155$$
$$x_{68} = -72.2566310325652$$
$$x_{30} = -69.1150383789755$$
$$x_{64} = -65.9734457253857$$
$$x_{37} = -62.8318530717959$$
$$x_{38} = -59.6902604182061$$
$$x_{57} = -56.5486677646163$$
$$x_{3} = -53.4070751110265$$
$$x_{46} = -50.2654824574367$$
$$x_{35} = -47.1238898038469$$
$$x_{52} = -43.9822971502571$$
$$x_{7} = -40.8407044966673$$
$$x_{39} = -37.6991118430775$$
$$x_{13} = -34.5575191894877$$
$$x_{32} = -31.4159265358979$$
$$x_{31} = -28.2743338823081$$
$$x_{28} = -25.1327412287183$$
$$x_{47} = -21.9911485751286$$
$$x_{58} = -18.8495559215388$$
$$x_{9} = -15.707963267949$$
$$x_{53} = -12.5663706143592$$
$$x_{42} = -9.42477796076938$$
$$x_{34} = -6.28318530717959$$
$$x_{63} = -3.14159265358979$$
$$x_{45} = 0$$
$$x_{36} = 3.14159265358979$$
$$x_{69} = 6.28318530717959$$
$$x_{24} = 9.42477796076938$$
$$x_{19} = 12.5663706143592$$
$$x_{11} = 15.707963267949$$
$$x_{29} = 18.8495559215388$$
$$x_{60} = 21.9911485751286$$
$$x_{23} = 25.1327412287183$$
$$x_{65} = 28.2743338823081$$
$$x_{44} = 31.4159265358979$$
$$x_{17} = 34.5575191894877$$
$$x_{6} = 37.6991118430775$$
$$x_{33} = 40.8407044966673$$
$$x_{14} = 43.9822971502571$$
$$x_{62} = 47.1238898038469$$
$$x_{51} = 50.2654824574367$$
$$x_{10} = 53.4070751110265$$
$$x_{12} = 56.5486677646163$$
$$x_{4} = 59.6902604182061$$
$$x_{1} = 62.8318530717959$$
$$x_{27} = 65.9734457253857$$
$$x_{5} = 69.1150383789755$$
$$x_{54} = 72.2566310325652$$
$$x_{26} = 75.398223686155$$
$$x_{21} = 78.5398163397448$$
$$x_{2} = 81.6814089933346$$
$$x_{16} = 84.8230016469244$$
$$x_{50} = 87.9645943005142$$
$$x_{49} = 91.106186954104$$
$$x_{43} = 94.2477796076938$$
$$x_{59} = 97.3893722612836$$
$$x_{18} = 100.530964914873$$
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
$$x_{0} = x_{25} - \frac{1}{10}$$
=
$$-2642.07942166902 + - \frac{1}{10}$$
=
$$-2642.17942166902$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} < 0$$
$$\sin{\left(t \right)} < 0$$
Entonces
$$x < -2642.07942166902$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -2642.07942166902 \wedge x < -267.035375555132$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -2642.07942166902 \wedge x < -267.035375555132$$
$$x > -232.477856365645 \wedge x < -113.097335529233$$
$$x > -100.530964914873 \wedge x < -97.3893722612836$$
$$x > -94.2477796076938 \wedge x < -91.106186954104$$
$$x > -87.9645943005142 \wedge x < -84.8230016469244$$
$$x > -81.6814089933346 \wedge x < -78.5398163397448$$
$$x > -75.398223686155 \wedge x < -72.2566310325652$$
$$x > -69.1150383789755 \wedge x < -65.9734457253857$$
$$x > -62.8318530717959 \wedge x < -59.6902604182061$$
$$x > -56.5486677646163 \wedge x < -53.4070751110265$$
$$x > -50.2654824574367 \wedge x < -47.1238898038469$$
$$x > -43.9822971502571 \wedge x < -40.8407044966673$$
$$x > -37.6991118430775 \wedge x < -34.5575191894877$$
$$x > -31.4159265358979 \wedge x < -28.2743338823081$$
$$x > -25.1327412287183 \wedge x < -21.9911485751286$$
$$x > -18.8495559215388 \wedge x < -15.707963267949$$
$$x > -12.5663706143592 \wedge x < -9.42477796076938$$
$$x > -6.28318530717959 \wedge x < -3.14159265358979$$
$$x > 0 \wedge x < 3.14159265358979$$
$$x > 6.28318530717959 \wedge x < 9.42477796076938$$
$$x > 12.5663706143592 \wedge x < 15.707963267949$$
$$x > 18.8495559215388 \wedge x < 21.9911485751286$$
$$x > 25.1327412287183 \wedge x < 28.2743338823081$$
$$x > 31.4159265358979 \wedge x < 34.5575191894877$$
$$x > 37.6991118430775 \wedge x < 40.8407044966673$$
$$x > 43.9822971502571 \wedge x < 47.1238898038469$$
$$x > 50.2654824574367 \wedge x < 53.4070751110265$$
$$x > 56.5486677646163 \wedge x < 59.6902604182061$$
$$x > 62.8318530717959 \wedge x < 65.9734457253857$$
$$x > 69.1150383789755 \wedge x < 72.2566310325652$$
$$x > 75.398223686155 \wedge x < 78.5398163397448$$
$$x > 81.6814089933346 \wedge x < 84.8230016469244$$
$$x > 87.9645943005142 \wedge x < 91.106186954104$$
$$x > 94.2477796076938 \wedge x < 97.3893722612836$$
$$x > 100.530964914873$$
$$\sin{\left(t \right)} < 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(t \right)} = 0$$
Resolvemos:
Tenemos la ecuación
$$\sin{\left(t \right)} = 0$$
cambiamos
$$\sin{\left(t \right)} - 1 = 0$$
$$\sin{\left(t \right)} - 1 = 0$$
Sustituimos
$$w = \sin{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = 1$$
Obtenemos la respuesta: w = 1
hacemos cambio inverso
$$\sin{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = 62.8318530717959$$
$$x_{2} = 81.6814089933346$$
$$x_{3} = -53.4070751110265$$
$$x_{4} = 59.6902604182061$$
$$x_{5} = 69.1150383789755$$
$$x_{6} = 37.6991118430775$$
$$x_{7} = -40.8407044966673$$
$$x_{8} = -113.097335529233$$
$$x_{9} = -15.707963267949$$
$$x_{10} = 53.4070751110265$$
$$x_{11} = 15.707963267949$$
$$x_{12} = 56.5486677646163$$
$$x_{13} = -34.5575191894877$$
$$x_{14} = 43.9822971502571$$
$$x_{15} = -87.9645943005142$$
$$x_{16} = 84.8230016469244$$
$$x_{17} = 34.5575191894877$$
$$x_{18} = 100.530964914873$$
$$x_{19} = 12.5663706143592$$
$$x_{20} = -84.8230016469244$$
$$x_{21} = 78.5398163397448$$
$$x_{22} = -91.106186954104$$
$$x_{23} = 25.1327412287183$$
$$x_{24} = 9.42477796076938$$
$$x_{25} = -2642.07942166902$$
$$x_{26} = 75.398223686155$$
$$x_{27} = 65.9734457253857$$
$$x_{28} = -25.1327412287183$$
$$x_{29} = 18.8495559215388$$
$$x_{30} = -69.1150383789755$$
$$x_{31} = -28.2743338823081$$
$$x_{32} = -31.4159265358979$$
$$x_{33} = 40.8407044966673$$
$$x_{34} = -6.28318530717959$$
$$x_{35} = -47.1238898038469$$
$$x_{36} = 3.14159265358979$$
$$x_{37} = -62.8318530717959$$
$$x_{38} = -59.6902604182061$$
$$x_{39} = -37.6991118430775$$
$$x_{40} = -81.6814089933346$$
$$x_{41} = -100.530964914873$$
$$x_{42} = -9.42477796076938$$
$$x_{43} = 94.2477796076938$$
$$x_{44} = 31.4159265358979$$
$$x_{45} = 0$$
$$x_{46} = -50.2654824574367$$
$$x_{47} = -21.9911485751286$$
$$x_{48} = -267.035375555132$$
$$x_{49} = 91.106186954104$$
$$x_{50} = 87.9645943005142$$
$$x_{51} = 50.2654824574367$$
$$x_{52} = -43.9822971502571$$
$$x_{53} = -12.5663706143592$$
$$x_{54} = 72.2566310325652$$
$$x_{55} = -78.5398163397448$$
$$x_{56} = -232.477856365645$$
$$x_{57} = -56.5486677646163$$
$$x_{58} = -18.8495559215388$$
$$x_{59} = 97.3893722612836$$
$$x_{60} = 21.9911485751286$$
$$x_{61} = -97.3893722612836$$
$$x_{62} = 47.1238898038469$$
$$x_{63} = -3.14159265358979$$
$$x_{64} = -65.9734457253857$$
$$x_{65} = 28.2743338823081$$
$$x_{66} = -94.2477796076938$$
$$x_{67} = -75.398223686155$$
$$x_{68} = -72.2566310325652$$
$$x_{69} = 6.28318530717959$$
$$x_{1} = 62.8318530717959$$
$$x_{2} = 81.6814089933346$$
$$x_{3} = -53.4070751110265$$
$$x_{4} = 59.6902604182061$$
$$x_{5} = 69.1150383789755$$
$$x_{6} = 37.6991118430775$$
$$x_{7} = -40.8407044966673$$
$$x_{8} = -113.097335529233$$
$$x_{9} = -15.707963267949$$
$$x_{10} = 53.4070751110265$$
$$x_{11} = 15.707963267949$$
$$x_{12} = 56.5486677646163$$
$$x_{13} = -34.5575191894877$$
$$x_{14} = 43.9822971502571$$
$$x_{15} = -87.9645943005142$$
$$x_{16} = 84.8230016469244$$
$$x_{17} = 34.5575191894877$$
$$x_{18} = 100.530964914873$$
$$x_{19} = 12.5663706143592$$
$$x_{20} = -84.8230016469244$$
$$x_{21} = 78.5398163397448$$
$$x_{22} = -91.106186954104$$
$$x_{23} = 25.1327412287183$$
$$x_{24} = 9.42477796076938$$
$$x_{25} = -2642.07942166902$$
$$x_{26} = 75.398223686155$$
$$x_{27} = 65.9734457253857$$
$$x_{28} = -25.1327412287183$$
$$x_{29} = 18.8495559215388$$
$$x_{30} = -69.1150383789755$$
$$x_{31} = -28.2743338823081$$
$$x_{32} = -31.4159265358979$$
$$x_{33} = 40.8407044966673$$
$$x_{34} = -6.28318530717959$$
$$x_{35} = -47.1238898038469$$
$$x_{36} = 3.14159265358979$$
$$x_{37} = -62.8318530717959$$
$$x_{38} = -59.6902604182061$$
$$x_{39} = -37.6991118430775$$
$$x_{40} = -81.6814089933346$$
$$x_{41} = -100.530964914873$$
$$x_{42} = -9.42477796076938$$
$$x_{43} = 94.2477796076938$$
$$x_{44} = 31.4159265358979$$
$$x_{45} = 0$$
$$x_{46} = -50.2654824574367$$
$$x_{47} = -21.9911485751286$$
$$x_{48} = -267.035375555132$$
$$x_{49} = 91.106186954104$$
$$x_{50} = 87.9645943005142$$
$$x_{51} = 50.2654824574367$$
$$x_{52} = -43.9822971502571$$
$$x_{53} = -12.5663706143592$$
$$x_{54} = 72.2566310325652$$
$$x_{55} = -78.5398163397448$$
$$x_{56} = -232.477856365645$$
$$x_{57} = -56.5486677646163$$
$$x_{58} = -18.8495559215388$$
$$x_{59} = 97.3893722612836$$
$$x_{60} = 21.9911485751286$$
$$x_{61} = -97.3893722612836$$
$$x_{62} = 47.1238898038469$$
$$x_{63} = -3.14159265358979$$
$$x_{64} = -65.9734457253857$$
$$x_{65} = 28.2743338823081$$
$$x_{66} = -94.2477796076938$$
$$x_{67} = -75.398223686155$$
$$x_{68} = -72.2566310325652$$
$$x_{69} = 6.28318530717959$$
Las raíces dadas
$$x_{25} = -2642.07942166902$$
$$x_{48} = -267.035375555132$$
$$x_{56} = -232.477856365645$$
$$x_{8} = -113.097335529233$$
$$x_{41} = -100.530964914873$$
$$x_{61} = -97.3893722612836$$
$$x_{66} = -94.2477796076938$$
$$x_{22} = -91.106186954104$$
$$x_{15} = -87.9645943005142$$
$$x_{20} = -84.8230016469244$$
$$x_{40} = -81.6814089933346$$
$$x_{55} = -78.5398163397448$$
$$x_{67} = -75.398223686155$$
$$x_{68} = -72.2566310325652$$
$$x_{30} = -69.1150383789755$$
$$x_{64} = -65.9734457253857$$
$$x_{37} = -62.8318530717959$$
$$x_{38} = -59.6902604182061$$
$$x_{57} = -56.5486677646163$$
$$x_{3} = -53.4070751110265$$
$$x_{46} = -50.2654824574367$$
$$x_{35} = -47.1238898038469$$
$$x_{52} = -43.9822971502571$$
$$x_{7} = -40.8407044966673$$
$$x_{39} = -37.6991118430775$$
$$x_{13} = -34.5575191894877$$
$$x_{32} = -31.4159265358979$$
$$x_{31} = -28.2743338823081$$
$$x_{28} = -25.1327412287183$$
$$x_{47} = -21.9911485751286$$
$$x_{58} = -18.8495559215388$$
$$x_{9} = -15.707963267949$$
$$x_{53} = -12.5663706143592$$
$$x_{42} = -9.42477796076938$$
$$x_{34} = -6.28318530717959$$
$$x_{63} = -3.14159265358979$$
$$x_{45} = 0$$
$$x_{36} = 3.14159265358979$$
$$x_{69} = 6.28318530717959$$
$$x_{24} = 9.42477796076938$$
$$x_{19} = 12.5663706143592$$
$$x_{11} = 15.707963267949$$
$$x_{29} = 18.8495559215388$$
$$x_{60} = 21.9911485751286$$
$$x_{23} = 25.1327412287183$$
$$x_{65} = 28.2743338823081$$
$$x_{44} = 31.4159265358979$$
$$x_{17} = 34.5575191894877$$
$$x_{6} = 37.6991118430775$$
$$x_{33} = 40.8407044966673$$
$$x_{14} = 43.9822971502571$$
$$x_{62} = 47.1238898038469$$
$$x_{51} = 50.2654824574367$$
$$x_{10} = 53.4070751110265$$
$$x_{12} = 56.5486677646163$$
$$x_{4} = 59.6902604182061$$
$$x_{1} = 62.8318530717959$$
$$x_{27} = 65.9734457253857$$
$$x_{5} = 69.1150383789755$$
$$x_{54} = 72.2566310325652$$
$$x_{26} = 75.398223686155$$
$$x_{21} = 78.5398163397448$$
$$x_{2} = 81.6814089933346$$
$$x_{16} = 84.8230016469244$$
$$x_{50} = 87.9645943005142$$
$$x_{49} = 91.106186954104$$
$$x_{43} = 94.2477796076938$$
$$x_{59} = 97.3893722612836$$
$$x_{18} = 100.530964914873$$
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
$$x_{0} = x_{25} - \frac{1}{10}$$
=
$$-2642.07942166902 + - \frac{1}{10}$$
=
$$-2642.17942166902$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} < 0$$
$$\sin{\left(t \right)} < 0$$
sin(t) < 0
Entonces
$$x < -2642.07942166902$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -2642.07942166902 \wedge x < -267.035375555132$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------ο-------ο-------
x25 x48 x56 x8 x41 x61 x66 x22 x15 x20 x40 x55 x67 x68 x30 x64 x37 x38 x57 x3 x46 x35 x52 x7 x39 x13 x32 x31 x28 x47 x58 x9 x53 x42 x34 x63 x45 x36 x69 x24 x19 x11 x29 x60 x23 x65 x44 x17 x6 x33 x14 x62 x51 x10 x12 x4 x1 x27 x5 x54 x26 x21 x2 x16 x50 x49 x43 x59 x18Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -2642.07942166902 \wedge x < -267.035375555132$$
$$x > -232.477856365645 \wedge x < -113.097335529233$$
$$x > -100.530964914873 \wedge x < -97.3893722612836$$
$$x > -94.2477796076938 \wedge x < -91.106186954104$$
$$x > -87.9645943005142 \wedge x < -84.8230016469244$$
$$x > -81.6814089933346 \wedge x < -78.5398163397448$$
$$x > -75.398223686155 \wedge x < -72.2566310325652$$
$$x > -69.1150383789755 \wedge x < -65.9734457253857$$
$$x > -62.8318530717959 \wedge x < -59.6902604182061$$
$$x > -56.5486677646163 \wedge x < -53.4070751110265$$
$$x > -50.2654824574367 \wedge x < -47.1238898038469$$
$$x > -43.9822971502571 \wedge x < -40.8407044966673$$
$$x > -37.6991118430775 \wedge x < -34.5575191894877$$
$$x > -31.4159265358979 \wedge x < -28.2743338823081$$
$$x > -25.1327412287183 \wedge x < -21.9911485751286$$
$$x > -18.8495559215388 \wedge x < -15.707963267949$$
$$x > -12.5663706143592 \wedge x < -9.42477796076938$$
$$x > -6.28318530717959 \wedge x < -3.14159265358979$$
$$x > 0 \wedge x < 3.14159265358979$$
$$x > 6.28318530717959 \wedge x < 9.42477796076938$$
$$x > 12.5663706143592 \wedge x < 15.707963267949$$
$$x > 18.8495559215388 \wedge x < 21.9911485751286$$
$$x > 25.1327412287183 \wedge x < 28.2743338823081$$
$$x > 31.4159265358979 \wedge x < 34.5575191894877$$
$$x > 37.6991118430775 \wedge x < 40.8407044966673$$
$$x > 43.9822971502571 \wedge x < 47.1238898038469$$
$$x > 50.2654824574367 \wedge x < 53.4070751110265$$
$$x > 56.5486677646163 \wedge x < 59.6902604182061$$
$$x > 62.8318530717959 \wedge x < 65.9734457253857$$
$$x > 69.1150383789755 \wedge x < 72.2566310325652$$
$$x > 75.398223686155 \wedge x < 78.5398163397448$$
$$x > 81.6814089933346 \wedge x < 84.8230016469244$$
$$x > 87.9645943005142 \wedge x < 91.106186954104$$
$$x > 94.2477796076938 \wedge x < 97.3893722612836$$
$$x > 100.530964914873$$