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^2-4x+3<0
-
x^2-3x+2<0
-
-x^2+x+6>0
-
-x^2-x+12>0
- Derivada de:
-
sint
- Integral de d{x}:
- sint
- Suma de la serie:
-
0,4
-
Expresiones idénticas
- sint< cero , cuatro
- seno de t menos 0,4
- seno de t menos cero , cuatro
-
Expresiones con funciones
- sint
- sint<1/2
- sint>1/2
- sint<1/3
- sint>1/3
- sint>-1/2
sint<0,4 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\sin{\left(t \right)} < \frac{2}{5}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(t \right)} = \frac{2}{5}$$
Resolvemos:
Tenemos la ecuación
$$\sin{\left(t \right)} = \frac{2}{5}$$
cambiamos
$$\sin{\left(t \right)} - \frac{2}{5} = 0$$
$$\sin{\left(t \right)} - \frac{2}{5} = 0$$
Sustituimos
$$w = \sin{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{2}{5}$$
Obtenemos la respuesta: w = 2/5
hacemos cambio inverso
$$\sin{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = -87.5530774544467$$
$$x_{2} = 40.4291876505998$$
$$x_{3} = 82.0929258394021$$
$$x_{4} = -22.402665421196$$
$$x_{5} = -41.2522213427348$$
$$x_{6} = 6.69470215324707$$
$$x_{7} = -16.1194801140165$$
$$x_{8} = 12.9778874604267$$
$$x_{9} = 46.7123729577794$$
$$x_{10} = 75.8097405322225$$
$$x_{11} = -72.6681478786327$$
$$x_{12} = -68.703521532908$$
$$x_{13} = 63.2433699178634$$
$$x_{14} = -31.0044096898304$$
$$x_{15} = -62.4203362257284$$
$$x_{16} = -66.3849625714531$$
$$x_{17} = -93.8362627616263$$
$$x_{18} = 15.2964464218815$$
$$x_{19} = -43.5707803041896$$
$$x_{20} = -3.55310949965728$$
$$x_{21} = -81.2698921472671$$
$$x_{22} = 71.8451141864978$$
$$x_{23} = -28.6858507283756$$
$$x_{24} = -60.1017772642736$$
$$x_{25} = 84.4114848008569$$
$$x_{26} = -37.28759499701$$
$$x_{27} = 94.6592964537613$$
$$x_{28} = -91.5177038001715$$
$$x_{29} = 44.3938139963246$$
$$x_{30} = 34.1460023434202$$
$$x_{31} = 100.942481760941$$
$$x_{32} = -47.5354066499144$$
$$x_{33} = -74.9867068400875$$
$$x_{34} = 59.2787435721386$$
$$x_{35} = -34.9690360355552$$
$$x_{36} = 56.9601846106838$$
$$x_{37} = -85.2345184929919$$
$$x_{38} = 27.8628170362407$$
$$x_{39} = 65.5619288793182$$
$$x_{40} = -78.9513331858123$$
$$x_{41} = -18.4380390754713$$
$$x_{42} = -100.119448068806$$
$$x_{43} = 2.73007580752231$$
$$x_{44} = -49.8539656113692$$
$$x_{45} = -9.83629480683687$$
$$x_{46} = 0.411516846067488$$
$$x_{47} = 78.1282994936773$$
$$x_{48} = 697.845085943002$$
$$x_{49} = 52.995558264959$$
$$x_{50} = 21.5796317290611$$
$$x_{51} = -12.1548537682917$$
$$x_{52} = 19.2610727676062$$
$$x_{53} = 38.110628689145$$
$$x_{54} = 50.6769993035042$$
$$x_{55} = 88.3761111465817$$
$$x_{56} = 90.6946701080365$$
$$x_{57} = 96.9778554152161$$
$$x_{58} = -97.8008891073511$$
$$x_{59} = 25.5442580747858$$
$$x_{60} = -56.1371509185488$$
$$x_{61} = 9.01326111470189$$
$$x_{62} = -53.818591957094$$
$$x_{63} = -24.7212243826509$$
$$x_{64} = -5.8716684611121$$
$$x_{65} = 69.5265552250429$$
$$x_{66} = 31.8274433819654$$
$$x_{1} = -87.5530774544467$$
$$x_{2} = 40.4291876505998$$
$$x_{3} = 82.0929258394021$$
$$x_{4} = -22.402665421196$$
$$x_{5} = -41.2522213427348$$
$$x_{6} = 6.69470215324707$$
$$x_{7} = -16.1194801140165$$
$$x_{8} = 12.9778874604267$$
$$x_{9} = 46.7123729577794$$
$$x_{10} = 75.8097405322225$$
$$x_{11} = -72.6681478786327$$
$$x_{12} = -68.703521532908$$
$$x_{13} = 63.2433699178634$$
$$x_{14} = -31.0044096898304$$
$$x_{15} = -62.4203362257284$$
$$x_{16} = -66.3849625714531$$
$$x_{17} = -93.8362627616263$$
$$x_{18} = 15.2964464218815$$
$$x_{19} = -43.5707803041896$$
$$x_{20} = -3.55310949965728$$
$$x_{21} = -81.2698921472671$$
$$x_{22} = 71.8451141864978$$
$$x_{23} = -28.6858507283756$$
$$x_{24} = -60.1017772642736$$
$$x_{25} = 84.4114848008569$$
$$x_{26} = -37.28759499701$$
$$x_{27} = 94.6592964537613$$
$$x_{28} = -91.5177038001715$$
$$x_{29} = 44.3938139963246$$
$$x_{30} = 34.1460023434202$$
$$x_{31} = 100.942481760941$$
$$x_{32} = -47.5354066499144$$
$$x_{33} = -74.9867068400875$$
$$x_{34} = 59.2787435721386$$
$$x_{35} = -34.9690360355552$$
$$x_{36} = 56.9601846106838$$
$$x_{37} = -85.2345184929919$$
$$x_{38} = 27.8628170362407$$
$$x_{39} = 65.5619288793182$$
$$x_{40} = -78.9513331858123$$
$$x_{41} = -18.4380390754713$$
$$x_{42} = -100.119448068806$$
$$x_{43} = 2.73007580752231$$
$$x_{44} = -49.8539656113692$$
$$x_{45} = -9.83629480683687$$
$$x_{46} = 0.411516846067488$$
$$x_{47} = 78.1282994936773$$
$$x_{48} = 697.845085943002$$
$$x_{49} = 52.995558264959$$
$$x_{50} = 21.5796317290611$$
$$x_{51} = -12.1548537682917$$
$$x_{52} = 19.2610727676062$$
$$x_{53} = 38.110628689145$$
$$x_{54} = 50.6769993035042$$
$$x_{55} = 88.3761111465817$$
$$x_{56} = 90.6946701080365$$
$$x_{57} = 96.9778554152161$$
$$x_{58} = -97.8008891073511$$
$$x_{59} = 25.5442580747858$$
$$x_{60} = -56.1371509185488$$
$$x_{61} = 9.01326111470189$$
$$x_{62} = -53.818591957094$$
$$x_{63} = -24.7212243826509$$
$$x_{64} = -5.8716684611121$$
$$x_{65} = 69.5265552250429$$
$$x_{66} = 31.8274433819654$$
Las raíces dadas
$$x_{42} = -100.119448068806$$
$$x_{58} = -97.8008891073511$$
$$x_{17} = -93.8362627616263$$
$$x_{28} = -91.5177038001715$$
$$x_{1} = -87.5530774544467$$
$$x_{37} = -85.2345184929919$$
$$x_{21} = -81.2698921472671$$
$$x_{40} = -78.9513331858123$$
$$x_{33} = -74.9867068400875$$
$$x_{11} = -72.6681478786327$$
$$x_{12} = -68.703521532908$$
$$x_{16} = -66.3849625714531$$
$$x_{15} = -62.4203362257284$$
$$x_{24} = -60.1017772642736$$
$$x_{60} = -56.1371509185488$$
$$x_{62} = -53.818591957094$$
$$x_{44} = -49.8539656113692$$
$$x_{32} = -47.5354066499144$$
$$x_{19} = -43.5707803041896$$
$$x_{5} = -41.2522213427348$$
$$x_{26} = -37.28759499701$$
$$x_{35} = -34.9690360355552$$
$$x_{14} = -31.0044096898304$$
$$x_{23} = -28.6858507283756$$
$$x_{63} = -24.7212243826509$$
$$x_{4} = -22.402665421196$$
$$x_{41} = -18.4380390754713$$
$$x_{7} = -16.1194801140165$$
$$x_{51} = -12.1548537682917$$
$$x_{45} = -9.83629480683687$$
$$x_{64} = -5.8716684611121$$
$$x_{20} = -3.55310949965728$$
$$x_{46} = 0.411516846067488$$
$$x_{43} = 2.73007580752231$$
$$x_{6} = 6.69470215324707$$
$$x_{61} = 9.01326111470189$$
$$x_{8} = 12.9778874604267$$
$$x_{18} = 15.2964464218815$$
$$x_{52} = 19.2610727676062$$
$$x_{50} = 21.5796317290611$$
$$x_{59} = 25.5442580747858$$
$$x_{38} = 27.8628170362407$$
$$x_{66} = 31.8274433819654$$
$$x_{30} = 34.1460023434202$$
$$x_{53} = 38.110628689145$$
$$x_{2} = 40.4291876505998$$
$$x_{29} = 44.3938139963246$$
$$x_{9} = 46.7123729577794$$
$$x_{54} = 50.6769993035042$$
$$x_{49} = 52.995558264959$$
$$x_{36} = 56.9601846106838$$
$$x_{34} = 59.2787435721386$$
$$x_{13} = 63.2433699178634$$
$$x_{39} = 65.5619288793182$$
$$x_{65} = 69.5265552250429$$
$$x_{22} = 71.8451141864978$$
$$x_{10} = 75.8097405322225$$
$$x_{47} = 78.1282994936773$$
$$x_{3} = 82.0929258394021$$
$$x_{25} = 84.4114848008569$$
$$x_{55} = 88.3761111465817$$
$$x_{56} = 90.6946701080365$$
$$x_{27} = 94.6592964537613$$
$$x_{57} = 96.9778554152161$$
$$x_{31} = 100.942481760941$$
$$x_{48} = 697.845085943002$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{42}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{42} - \frac{1}{10}$$
=
$$-100.119448068806 + - \frac{1}{10}$$
=
$$-100.219448068806$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} < \frac{2}{5}$$
$$\sin{\left(t \right)} < \frac{2}{5}$$
Entonces
$$x < -100.119448068806$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -100.119448068806 \wedge x < -97.8008891073511$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -100.119448068806 \wedge x < -97.8008891073511$$
$$x > -93.8362627616263 \wedge x < -91.5177038001715$$
$$x > -87.5530774544467 \wedge x < -85.2345184929919$$
$$x > -81.2698921472671 \wedge x < -78.9513331858123$$
$$x > -74.9867068400875 \wedge x < -72.6681478786327$$
$$x > -68.703521532908 \wedge x < -66.3849625714531$$
$$x > -62.4203362257284 \wedge x < -60.1017772642736$$
$$x > -56.1371509185488 \wedge x < -53.818591957094$$
$$x > -49.8539656113692 \wedge x < -47.5354066499144$$
$$x > -43.5707803041896 \wedge x < -41.2522213427348$$
$$x > -37.28759499701 \wedge x < -34.9690360355552$$
$$x > -31.0044096898304 \wedge x < -28.6858507283756$$
$$x > -24.7212243826509 \wedge x < -22.402665421196$$
$$x > -18.4380390754713 \wedge x < -16.1194801140165$$
$$x > -12.1548537682917 \wedge x < -9.83629480683687$$
$$x > -5.8716684611121 \wedge x < -3.55310949965728$$
$$x > 0.411516846067488 \wedge x < 2.73007580752231$$
$$x > 6.69470215324707 \wedge x < 9.01326111470189$$
$$x > 12.9778874604267 \wedge x < 15.2964464218815$$
$$x > 19.2610727676062 \wedge x < 21.5796317290611$$
$$x > 25.5442580747858 \wedge x < 27.8628170362407$$
$$x > 31.8274433819654 \wedge x < 34.1460023434202$$
$$x > 38.110628689145 \wedge x < 40.4291876505998$$
$$x > 44.3938139963246 \wedge x < 46.7123729577794$$
$$x > 50.6769993035042 \wedge x < 52.995558264959$$
$$x > 56.9601846106838 \wedge x < 59.2787435721386$$
$$x > 63.2433699178634 \wedge x < 65.5619288793182$$
$$x > 69.5265552250429 \wedge x < 71.8451141864978$$
$$x > 75.8097405322225 \wedge x < 78.1282994936773$$
$$x > 82.0929258394021 \wedge x < 84.4114848008569$$
$$x > 88.3761111465817 \wedge x < 90.6946701080365$$
$$x > 94.6592964537613 \wedge x < 96.9778554152161$$
$$x > 100.942481760941 \wedge x < 697.845085943002$$
$$\sin{\left(t \right)} < \frac{2}{5}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\sin{\left(t \right)} = \frac{2}{5}$$
Resolvemos:
Tenemos la ecuación
$$\sin{\left(t \right)} = \frac{2}{5}$$
cambiamos
$$\sin{\left(t \right)} - \frac{2}{5} = 0$$
$$\sin{\left(t \right)} - \frac{2}{5} = 0$$
Sustituimos
$$w = \sin{\left(t \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{2}{5}$$
Obtenemos la respuesta: w = 2/5
hacemos cambio inverso
$$\sin{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = -87.5530774544467$$
$$x_{2} = 40.4291876505998$$
$$x_{3} = 82.0929258394021$$
$$x_{4} = -22.402665421196$$
$$x_{5} = -41.2522213427348$$
$$x_{6} = 6.69470215324707$$
$$x_{7} = -16.1194801140165$$
$$x_{8} = 12.9778874604267$$
$$x_{9} = 46.7123729577794$$
$$x_{10} = 75.8097405322225$$
$$x_{11} = -72.6681478786327$$
$$x_{12} = -68.703521532908$$
$$x_{13} = 63.2433699178634$$
$$x_{14} = -31.0044096898304$$
$$x_{15} = -62.4203362257284$$
$$x_{16} = -66.3849625714531$$
$$x_{17} = -93.8362627616263$$
$$x_{18} = 15.2964464218815$$
$$x_{19} = -43.5707803041896$$
$$x_{20} = -3.55310949965728$$
$$x_{21} = -81.2698921472671$$
$$x_{22} = 71.8451141864978$$
$$x_{23} = -28.6858507283756$$
$$x_{24} = -60.1017772642736$$
$$x_{25} = 84.4114848008569$$
$$x_{26} = -37.28759499701$$
$$x_{27} = 94.6592964537613$$
$$x_{28} = -91.5177038001715$$
$$x_{29} = 44.3938139963246$$
$$x_{30} = 34.1460023434202$$
$$x_{31} = 100.942481760941$$
$$x_{32} = -47.5354066499144$$
$$x_{33} = -74.9867068400875$$
$$x_{34} = 59.2787435721386$$
$$x_{35} = -34.9690360355552$$
$$x_{36} = 56.9601846106838$$
$$x_{37} = -85.2345184929919$$
$$x_{38} = 27.8628170362407$$
$$x_{39} = 65.5619288793182$$
$$x_{40} = -78.9513331858123$$
$$x_{41} = -18.4380390754713$$
$$x_{42} = -100.119448068806$$
$$x_{43} = 2.73007580752231$$
$$x_{44} = -49.8539656113692$$
$$x_{45} = -9.83629480683687$$
$$x_{46} = 0.411516846067488$$
$$x_{47} = 78.1282994936773$$
$$x_{48} = 697.845085943002$$
$$x_{49} = 52.995558264959$$
$$x_{50} = 21.5796317290611$$
$$x_{51} = -12.1548537682917$$
$$x_{52} = 19.2610727676062$$
$$x_{53} = 38.110628689145$$
$$x_{54} = 50.6769993035042$$
$$x_{55} = 88.3761111465817$$
$$x_{56} = 90.6946701080365$$
$$x_{57} = 96.9778554152161$$
$$x_{58} = -97.8008891073511$$
$$x_{59} = 25.5442580747858$$
$$x_{60} = -56.1371509185488$$
$$x_{61} = 9.01326111470189$$
$$x_{62} = -53.818591957094$$
$$x_{63} = -24.7212243826509$$
$$x_{64} = -5.8716684611121$$
$$x_{65} = 69.5265552250429$$
$$x_{66} = 31.8274433819654$$
$$x_{1} = -87.5530774544467$$
$$x_{2} = 40.4291876505998$$
$$x_{3} = 82.0929258394021$$
$$x_{4} = -22.402665421196$$
$$x_{5} = -41.2522213427348$$
$$x_{6} = 6.69470215324707$$
$$x_{7} = -16.1194801140165$$
$$x_{8} = 12.9778874604267$$
$$x_{9} = 46.7123729577794$$
$$x_{10} = 75.8097405322225$$
$$x_{11} = -72.6681478786327$$
$$x_{12} = -68.703521532908$$
$$x_{13} = 63.2433699178634$$
$$x_{14} = -31.0044096898304$$
$$x_{15} = -62.4203362257284$$
$$x_{16} = -66.3849625714531$$
$$x_{17} = -93.8362627616263$$
$$x_{18} = 15.2964464218815$$
$$x_{19} = -43.5707803041896$$
$$x_{20} = -3.55310949965728$$
$$x_{21} = -81.2698921472671$$
$$x_{22} = 71.8451141864978$$
$$x_{23} = -28.6858507283756$$
$$x_{24} = -60.1017772642736$$
$$x_{25} = 84.4114848008569$$
$$x_{26} = -37.28759499701$$
$$x_{27} = 94.6592964537613$$
$$x_{28} = -91.5177038001715$$
$$x_{29} = 44.3938139963246$$
$$x_{30} = 34.1460023434202$$
$$x_{31} = 100.942481760941$$
$$x_{32} = -47.5354066499144$$
$$x_{33} = -74.9867068400875$$
$$x_{34} = 59.2787435721386$$
$$x_{35} = -34.9690360355552$$
$$x_{36} = 56.9601846106838$$
$$x_{37} = -85.2345184929919$$
$$x_{38} = 27.8628170362407$$
$$x_{39} = 65.5619288793182$$
$$x_{40} = -78.9513331858123$$
$$x_{41} = -18.4380390754713$$
$$x_{42} = -100.119448068806$$
$$x_{43} = 2.73007580752231$$
$$x_{44} = -49.8539656113692$$
$$x_{45} = -9.83629480683687$$
$$x_{46} = 0.411516846067488$$
$$x_{47} = 78.1282994936773$$
$$x_{48} = 697.845085943002$$
$$x_{49} = 52.995558264959$$
$$x_{50} = 21.5796317290611$$
$$x_{51} = -12.1548537682917$$
$$x_{52} = 19.2610727676062$$
$$x_{53} = 38.110628689145$$
$$x_{54} = 50.6769993035042$$
$$x_{55} = 88.3761111465817$$
$$x_{56} = 90.6946701080365$$
$$x_{57} = 96.9778554152161$$
$$x_{58} = -97.8008891073511$$
$$x_{59} = 25.5442580747858$$
$$x_{60} = -56.1371509185488$$
$$x_{61} = 9.01326111470189$$
$$x_{62} = -53.818591957094$$
$$x_{63} = -24.7212243826509$$
$$x_{64} = -5.8716684611121$$
$$x_{65} = 69.5265552250429$$
$$x_{66} = 31.8274433819654$$
Las raíces dadas
$$x_{42} = -100.119448068806$$
$$x_{58} = -97.8008891073511$$
$$x_{17} = -93.8362627616263$$
$$x_{28} = -91.5177038001715$$
$$x_{1} = -87.5530774544467$$
$$x_{37} = -85.2345184929919$$
$$x_{21} = -81.2698921472671$$
$$x_{40} = -78.9513331858123$$
$$x_{33} = -74.9867068400875$$
$$x_{11} = -72.6681478786327$$
$$x_{12} = -68.703521532908$$
$$x_{16} = -66.3849625714531$$
$$x_{15} = -62.4203362257284$$
$$x_{24} = -60.1017772642736$$
$$x_{60} = -56.1371509185488$$
$$x_{62} = -53.818591957094$$
$$x_{44} = -49.8539656113692$$
$$x_{32} = -47.5354066499144$$
$$x_{19} = -43.5707803041896$$
$$x_{5} = -41.2522213427348$$
$$x_{26} = -37.28759499701$$
$$x_{35} = -34.9690360355552$$
$$x_{14} = -31.0044096898304$$
$$x_{23} = -28.6858507283756$$
$$x_{63} = -24.7212243826509$$
$$x_{4} = -22.402665421196$$
$$x_{41} = -18.4380390754713$$
$$x_{7} = -16.1194801140165$$
$$x_{51} = -12.1548537682917$$
$$x_{45} = -9.83629480683687$$
$$x_{64} = -5.8716684611121$$
$$x_{20} = -3.55310949965728$$
$$x_{46} = 0.411516846067488$$
$$x_{43} = 2.73007580752231$$
$$x_{6} = 6.69470215324707$$
$$x_{61} = 9.01326111470189$$
$$x_{8} = 12.9778874604267$$
$$x_{18} = 15.2964464218815$$
$$x_{52} = 19.2610727676062$$
$$x_{50} = 21.5796317290611$$
$$x_{59} = 25.5442580747858$$
$$x_{38} = 27.8628170362407$$
$$x_{66} = 31.8274433819654$$
$$x_{30} = 34.1460023434202$$
$$x_{53} = 38.110628689145$$
$$x_{2} = 40.4291876505998$$
$$x_{29} = 44.3938139963246$$
$$x_{9} = 46.7123729577794$$
$$x_{54} = 50.6769993035042$$
$$x_{49} = 52.995558264959$$
$$x_{36} = 56.9601846106838$$
$$x_{34} = 59.2787435721386$$
$$x_{13} = 63.2433699178634$$
$$x_{39} = 65.5619288793182$$
$$x_{65} = 69.5265552250429$$
$$x_{22} = 71.8451141864978$$
$$x_{10} = 75.8097405322225$$
$$x_{47} = 78.1282994936773$$
$$x_{3} = 82.0929258394021$$
$$x_{25} = 84.4114848008569$$
$$x_{55} = 88.3761111465817$$
$$x_{56} = 90.6946701080365$$
$$x_{27} = 94.6592964537613$$
$$x_{57} = 96.9778554152161$$
$$x_{31} = 100.942481760941$$
$$x_{48} = 697.845085943002$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{42}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{42} - \frac{1}{10}$$
=
$$-100.119448068806 + - \frac{1}{10}$$
=
$$-100.219448068806$$
lo sustituimos en la expresión
$$\sin{\left(t \right)} < \frac{2}{5}$$
$$\sin{\left(t \right)} < \frac{2}{5}$$
sin(t) < 2/5
Entonces
$$x < -100.119448068806$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -100.119448068806 \wedge x < -97.8008891073511$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x42 x58 x17 x28 x1 x37 x21 x40 x33 x11 x12 x16 x15 x24 x60 x62 x44 x32 x19 x5 x26 x35 x14 x23 x63 x4 x41 x7 x51 x45 x64 x20 x46 x43 x6 x61 x8 x18 x52 x50 x59 x38 x66 x30 x53 x2 x29 x9 x54 x49 x36 x34 x13 x39 x65 x22 x10 x47 x3 x25 x55 x56 x27 x57 x31 x48Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -100.119448068806 \wedge x < -97.8008891073511$$
$$x > -93.8362627616263 \wedge x < -91.5177038001715$$
$$x > -87.5530774544467 \wedge x < -85.2345184929919$$
$$x > -81.2698921472671 \wedge x < -78.9513331858123$$
$$x > -74.9867068400875 \wedge x < -72.6681478786327$$
$$x > -68.703521532908 \wedge x < -66.3849625714531$$
$$x > -62.4203362257284 \wedge x < -60.1017772642736$$
$$x > -56.1371509185488 \wedge x < -53.818591957094$$
$$x > -49.8539656113692 \wedge x < -47.5354066499144$$
$$x > -43.5707803041896 \wedge x < -41.2522213427348$$
$$x > -37.28759499701 \wedge x < -34.9690360355552$$
$$x > -31.0044096898304 \wedge x < -28.6858507283756$$
$$x > -24.7212243826509 \wedge x < -22.402665421196$$
$$x > -18.4380390754713 \wedge x < -16.1194801140165$$
$$x > -12.1548537682917 \wedge x < -9.83629480683687$$
$$x > -5.8716684611121 \wedge x < -3.55310949965728$$
$$x > 0.411516846067488 \wedge x < 2.73007580752231$$
$$x > 6.69470215324707 \wedge x < 9.01326111470189$$
$$x > 12.9778874604267 \wedge x < 15.2964464218815$$
$$x > 19.2610727676062 \wedge x < 21.5796317290611$$
$$x > 25.5442580747858 \wedge x < 27.8628170362407$$
$$x > 31.8274433819654 \wedge x < 34.1460023434202$$
$$x > 38.110628689145 \wedge x < 40.4291876505998$$
$$x > 44.3938139963246 \wedge x < 46.7123729577794$$
$$x > 50.6769993035042 \wedge x < 52.995558264959$$
$$x > 56.9601846106838 \wedge x < 59.2787435721386$$
$$x > 63.2433699178634 \wedge x < 65.5619288793182$$
$$x > 69.5265552250429 \wedge x < 71.8451141864978$$
$$x > 75.8097405322225 \wedge x < 78.1282994936773$$
$$x > 82.0929258394021 \wedge x < 84.4114848008569$$
$$x > 88.3761111465817 \wedge x < 90.6946701080365$$
$$x > 94.6592964537613 \wedge x < 96.9778554152161$$
$$x > 100.942481760941 \wedge x < 697.845085943002$$
Respuesta rápida
[src]
/ / / ____\\ / / ____\ \\ | | |2*\/ 21 || | |2*\/ 21 | || Or|And|0 <= t, t < atan|--------||, And|t <= 2*pi, pi - atan|--------| < t|| \ \ \ 21 // \ \ 21 / //
$$\left(0 \leq t \wedge t < \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}\right) \vee \left(t \leq 2 \pi \wedge \pi - \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)} < t\right)$$
((0 <= t)∧(t < atan(2*sqrt(21)/21)))∨((t <= 2*pi)∧(pi - atan(2*sqrt(21)/21) < t))
Respuesta rápida 2
[src]
/ ____\ / ____\
|2*\/ 21 | |2*\/ 21 |
[0, atan|--------|) U (pi - atan|--------|, 2*pi]
\ 21 / \ 21 /
$$x\ in\ \left[0, \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}\right) \cup \left(\pi - \operatorname{atan}{\left(\frac{2 \sqrt{21}}{21} \right)}, 2 \pi\right]$$
x in Union(Interval.Ropen(0, atan(2*sqrt(21)/21)), Interval.Lopen(pi - atan(2*sqrt(21)/21), 2*pi))