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+64)*(x-5)>0
-
-x^2+4x+5>0
-
(x+1)*(x-19)>0
-
x^2+23x<=0
-
Expresiones idénticas
- dos *sin2x- siete *sin(x)+ tres > cero
- 2 multiplicar por seno de 2x menos 7 multiplicar por seno de (x) más 3 más 0
- dos multiplicar por seno de 2x menos siete multiplicar por seno de (x) más tres más cero
- 2sin2x-7sin(x)+3>0
- 2sin2x-7sinx+3>0
-
Expresiones semejantes
- 2*sin2x+7*sin(x)+3>0
- 2*sin2x-7*sin(x)-3>0
- 2*sin2x-7*sinx+3>0
-
Expresiones con funciones
- Seno sin
- sin(x)^2>3/5
- sin(x)cos(x)>sqrt(3)/4
- sin(pi/4+x/2)>=1
- sin(3*x-pi/5)<=sqrt(3)/2
- sin(x+pi*1/4)>0
2*sin2x-7*sin(x)+3>0 desigualdades
Solución
Ha introducido
[src]
2*sin(2*x) - 7*sin(x) + 3 > 0
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0$$
-7*sin(x) + 2*sin(2*x) + 3 > 0
Solución detallada
Se da la desigualdad:
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 = 0$$
Resolvemos:
$$x_{1} = -87.1690749807234$$
$$x_{2} = -36.9035925232867$$
$$x_{3} = 95.0432989274846$$
$$x_{4} = -66.2537559502919$$
$$x_{5} = 25.9282605485092$$
$$x_{6} = -74.6027043663642$$
$$x_{7} = 63.6273723915867$$
$$x_{8} = -49.4699631376459$$
$$x_{9} = -59.9705706431123$$
$$x_{10} = 57.3441870844071$$
$$x_{11} = -28.5546441072143$$
$$x_{12} = -3.421902878496$$
$$x_{13} = 13.36188993415$$
$$x_{14} = -99.7354455950826$$
$$x_{15} = -72.5369412574715$$
$$x_{16} = -30.6204072161071$$
$$x_{17} = 38.4946311628683$$
$$x_{18} = -24.3372219089275$$
$$x_{19} = -9.70508818567559$$
$$x_{20} = 65.6931355004795$$
$$x_{21} = -11.7708512945684$$
$$x_{22} = -80.8858896735438$$
$$x_{23} = 88.760113620305$$
$$x_{24} = 32.2114458556888$$
$$x_{25} = 90.8258767291978$$
$$x_{26} = -41.1210147215735$$
$$x_{27} = -91.3864971790102$$
$$x_{28} = 27.9940236574019$$
$$x_{29} = -18.0540366017479$$
$$x_{30} = -62.036333752005$$
$$x_{31} = 34.2772089645815$$
$$x_{32} = 84.5426914220182$$
$$x_{33} = 78.2595061148386$$
$$x_{34} = -78.820126564651$$
$$x_{35} = -47.4042000287531$$
$$x_{36} = 51.0610017772275$$
$$x_{37} = 97.1090620363774$$
$$x_{38} = 76.1937430059459$$
$$x_{39} = 40.5603942717611$$
$$x_{40} = -43.1867778304663$$
$$x_{41} = -97.6696824861898$$
$$x_{42} = 53.1267648861203$$
$$x_{43} = -93.452260287903$$
$$x_{44} = 21.7108383502223$$
$$x_{45} = 2.86128242868359$$
$$x_{46} = -68.3195190591846$$
$$x_{47} = -22.2714588000348$$
$$x_{48} = -15.9882734928552$$
$$x_{49} = 9.14446773586317$$
$$x_{50} = 44.7778164700479$$
$$x_{51} = 14194.5111282385$$
$$x_{52} = 69.9105576987663$$
$$x_{53} = 101.326484234664$$
$$x_{54} = 46.8435795789407$$
$$x_{55} = 15.4276530430428$$
$$x_{56} = 71.976320807659$$
$$x_{57} = 7.07870462697041$$
$$x_{58} = 0.795519319790823$$
$$x_{59} = -34.8378294143939$$
$$x_{60} = 82.4769283131254$$
$$x_{61} = -53.6873853359327$$
$$x_{62} = -5.48766598738876$$
$$x_{63} = -55.7531484448255$$
$$x_{64} = 59.4099501932999$$
$$x_{65} = 19.6450752413296$$
$$x_{1} = -87.1690749807234$$
$$x_{2} = -36.9035925232867$$
$$x_{3} = 95.0432989274846$$
$$x_{4} = -66.2537559502919$$
$$x_{5} = 25.9282605485092$$
$$x_{6} = -74.6027043663642$$
$$x_{7} = 63.6273723915867$$
$$x_{8} = -49.4699631376459$$
$$x_{9} = -59.9705706431123$$
$$x_{10} = 57.3441870844071$$
$$x_{11} = -28.5546441072143$$
$$x_{12} = -3.421902878496$$
$$x_{13} = 13.36188993415$$
$$x_{14} = -99.7354455950826$$
$$x_{15} = -72.5369412574715$$
$$x_{16} = -30.6204072161071$$
$$x_{17} = 38.4946311628683$$
$$x_{18} = -24.3372219089275$$
$$x_{19} = -9.70508818567559$$
$$x_{20} = 65.6931355004795$$
$$x_{21} = -11.7708512945684$$
$$x_{22} = -80.8858896735438$$
$$x_{23} = 88.760113620305$$
$$x_{24} = 32.2114458556888$$
$$x_{25} = 90.8258767291978$$
$$x_{26} = -41.1210147215735$$
$$x_{27} = -91.3864971790102$$
$$x_{28} = 27.9940236574019$$
$$x_{29} = -18.0540366017479$$
$$x_{30} = -62.036333752005$$
$$x_{31} = 34.2772089645815$$
$$x_{32} = 84.5426914220182$$
$$x_{33} = 78.2595061148386$$
$$x_{34} = -78.820126564651$$
$$x_{35} = -47.4042000287531$$
$$x_{36} = 51.0610017772275$$
$$x_{37} = 97.1090620363774$$
$$x_{38} = 76.1937430059459$$
$$x_{39} = 40.5603942717611$$
$$x_{40} = -43.1867778304663$$
$$x_{41} = -97.6696824861898$$
$$x_{42} = 53.1267648861203$$
$$x_{43} = -93.452260287903$$
$$x_{44} = 21.7108383502223$$
$$x_{45} = 2.86128242868359$$
$$x_{46} = -68.3195190591846$$
$$x_{47} = -22.2714588000348$$
$$x_{48} = -15.9882734928552$$
$$x_{49} = 9.14446773586317$$
$$x_{50} = 44.7778164700479$$
$$x_{51} = 14194.5111282385$$
$$x_{52} = 69.9105576987663$$
$$x_{53} = 101.326484234664$$
$$x_{54} = 46.8435795789407$$
$$x_{55} = 15.4276530430428$$
$$x_{56} = 71.976320807659$$
$$x_{57} = 7.07870462697041$$
$$x_{58} = 0.795519319790823$$
$$x_{59} = -34.8378294143939$$
$$x_{60} = 82.4769283131254$$
$$x_{61} = -53.6873853359327$$
$$x_{62} = -5.48766598738876$$
$$x_{63} = -55.7531484448255$$
$$x_{64} = 59.4099501932999$$
$$x_{65} = 19.6450752413296$$
Las raíces dadas
$$x_{14} = -99.7354455950826$$
$$x_{41} = -97.6696824861898$$
$$x_{43} = -93.452260287903$$
$$x_{27} = -91.3864971790102$$
$$x_{1} = -87.1690749807234$$
$$x_{22} = -80.8858896735438$$
$$x_{34} = -78.820126564651$$
$$x_{6} = -74.6027043663642$$
$$x_{15} = -72.5369412574715$$
$$x_{46} = -68.3195190591846$$
$$x_{4} = -66.2537559502919$$
$$x_{30} = -62.036333752005$$
$$x_{9} = -59.9705706431123$$
$$x_{63} = -55.7531484448255$$
$$x_{61} = -53.6873853359327$$
$$x_{8} = -49.4699631376459$$
$$x_{35} = -47.4042000287531$$
$$x_{40} = -43.1867778304663$$
$$x_{26} = -41.1210147215735$$
$$x_{2} = -36.9035925232867$$
$$x_{59} = -34.8378294143939$$
$$x_{16} = -30.6204072161071$$
$$x_{11} = -28.5546441072143$$
$$x_{18} = -24.3372219089275$$
$$x_{47} = -22.2714588000348$$
$$x_{29} = -18.0540366017479$$
$$x_{48} = -15.9882734928552$$
$$x_{21} = -11.7708512945684$$
$$x_{19} = -9.70508818567559$$
$$x_{62} = -5.48766598738876$$
$$x_{12} = -3.421902878496$$
$$x_{58} = 0.795519319790823$$
$$x_{45} = 2.86128242868359$$
$$x_{57} = 7.07870462697041$$
$$x_{49} = 9.14446773586317$$
$$x_{13} = 13.36188993415$$
$$x_{55} = 15.4276530430428$$
$$x_{65} = 19.6450752413296$$
$$x_{44} = 21.7108383502223$$
$$x_{5} = 25.9282605485092$$
$$x_{28} = 27.9940236574019$$
$$x_{24} = 32.2114458556888$$
$$x_{31} = 34.2772089645815$$
$$x_{17} = 38.4946311628683$$
$$x_{39} = 40.5603942717611$$
$$x_{50} = 44.7778164700479$$
$$x_{54} = 46.8435795789407$$
$$x_{36} = 51.0610017772275$$
$$x_{42} = 53.1267648861203$$
$$x_{10} = 57.3441870844071$$
$$x_{64} = 59.4099501932999$$
$$x_{7} = 63.6273723915867$$
$$x_{20} = 65.6931355004795$$
$$x_{52} = 69.9105576987663$$
$$x_{56} = 71.976320807659$$
$$x_{38} = 76.1937430059459$$
$$x_{33} = 78.2595061148386$$
$$x_{60} = 82.4769283131254$$
$$x_{32} = 84.5426914220182$$
$$x_{23} = 88.760113620305$$
$$x_{25} = 90.8258767291978$$
$$x_{3} = 95.0432989274846$$
$$x_{37} = 97.1090620363774$$
$$x_{53} = 101.326484234664$$
$$x_{51} = 14194.5111282385$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{14}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{14} - \frac{1}{10}$$
=
$$-99.7354455950826 + - \frac{1}{10}$$
=
$$-99.8354455950826$$
lo sustituimos en la expresión
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0$$
$$\left(- 7 \sin{\left(-99.8354455950826 \right)} + 2 \sin{\left(\left(-99.8354455950826\right) 2 \right)}\right) + 3 > 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -99.7354455950826$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -99.7354455950826$$
$$x > -97.6696824861898 \wedge x < -93.452260287903$$
$$x > -91.3864971790102 \wedge x < -87.1690749807234$$
$$x > -80.8858896735438 \wedge x < -78.820126564651$$
$$x > -74.6027043663642 \wedge x < -72.5369412574715$$
$$x > -68.3195190591846 \wedge x < -66.2537559502919$$
$$x > -62.036333752005 \wedge x < -59.9705706431123$$
$$x > -55.7531484448255 \wedge x < -53.6873853359327$$
$$x > -49.4699631376459 \wedge x < -47.4042000287531$$
$$x > -43.1867778304663 \wedge x < -41.1210147215735$$
$$x > -36.9035925232867 \wedge x < -34.8378294143939$$
$$x > -30.6204072161071 \wedge x < -28.5546441072143$$
$$x > -24.3372219089275 \wedge x < -22.2714588000348$$
$$x > -18.0540366017479 \wedge x < -15.9882734928552$$
$$x > -11.7708512945684 \wedge x < -9.70508818567559$$
$$x > -5.48766598738876 \wedge x < -3.421902878496$$
$$x > 0.795519319790823 \wedge x < 2.86128242868359$$
$$x > 7.07870462697041 \wedge x < 9.14446773586317$$
$$x > 13.36188993415 \wedge x < 15.4276530430428$$
$$x > 19.6450752413296 \wedge x < 21.7108383502223$$
$$x > 25.9282605485092 \wedge x < 27.9940236574019$$
$$x > 32.2114458556888 \wedge x < 34.2772089645815$$
$$x > 38.4946311628683 \wedge x < 40.5603942717611$$
$$x > 44.7778164700479 \wedge x < 46.8435795789407$$
$$x > 51.0610017772275 \wedge x < 53.1267648861203$$
$$x > 57.3441870844071 \wedge x < 59.4099501932999$$
$$x > 63.6273723915867 \wedge x < 65.6931355004795$$
$$x > 69.9105576987663 \wedge x < 71.976320807659$$
$$x > 76.1937430059459 \wedge x < 78.2595061148386$$
$$x > 82.4769283131254 \wedge x < 84.5426914220182$$
$$x > 88.760113620305 \wedge x < 90.8258767291978$$
$$x > 95.0432989274846 \wedge x < 97.1090620363774$$
$$x > 101.326484234664 \wedge x < 14194.5111282385$$
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 = 0$$
Resolvemos:
$$x_{1} = -87.1690749807234$$
$$x_{2} = -36.9035925232867$$
$$x_{3} = 95.0432989274846$$
$$x_{4} = -66.2537559502919$$
$$x_{5} = 25.9282605485092$$
$$x_{6} = -74.6027043663642$$
$$x_{7} = 63.6273723915867$$
$$x_{8} = -49.4699631376459$$
$$x_{9} = -59.9705706431123$$
$$x_{10} = 57.3441870844071$$
$$x_{11} = -28.5546441072143$$
$$x_{12} = -3.421902878496$$
$$x_{13} = 13.36188993415$$
$$x_{14} = -99.7354455950826$$
$$x_{15} = -72.5369412574715$$
$$x_{16} = -30.6204072161071$$
$$x_{17} = 38.4946311628683$$
$$x_{18} = -24.3372219089275$$
$$x_{19} = -9.70508818567559$$
$$x_{20} = 65.6931355004795$$
$$x_{21} = -11.7708512945684$$
$$x_{22} = -80.8858896735438$$
$$x_{23} = 88.760113620305$$
$$x_{24} = 32.2114458556888$$
$$x_{25} = 90.8258767291978$$
$$x_{26} = -41.1210147215735$$
$$x_{27} = -91.3864971790102$$
$$x_{28} = 27.9940236574019$$
$$x_{29} = -18.0540366017479$$
$$x_{30} = -62.036333752005$$
$$x_{31} = 34.2772089645815$$
$$x_{32} = 84.5426914220182$$
$$x_{33} = 78.2595061148386$$
$$x_{34} = -78.820126564651$$
$$x_{35} = -47.4042000287531$$
$$x_{36} = 51.0610017772275$$
$$x_{37} = 97.1090620363774$$
$$x_{38} = 76.1937430059459$$
$$x_{39} = 40.5603942717611$$
$$x_{40} = -43.1867778304663$$
$$x_{41} = -97.6696824861898$$
$$x_{42} = 53.1267648861203$$
$$x_{43} = -93.452260287903$$
$$x_{44} = 21.7108383502223$$
$$x_{45} = 2.86128242868359$$
$$x_{46} = -68.3195190591846$$
$$x_{47} = -22.2714588000348$$
$$x_{48} = -15.9882734928552$$
$$x_{49} = 9.14446773586317$$
$$x_{50} = 44.7778164700479$$
$$x_{51} = 14194.5111282385$$
$$x_{52} = 69.9105576987663$$
$$x_{53} = 101.326484234664$$
$$x_{54} = 46.8435795789407$$
$$x_{55} = 15.4276530430428$$
$$x_{56} = 71.976320807659$$
$$x_{57} = 7.07870462697041$$
$$x_{58} = 0.795519319790823$$
$$x_{59} = -34.8378294143939$$
$$x_{60} = 82.4769283131254$$
$$x_{61} = -53.6873853359327$$
$$x_{62} = -5.48766598738876$$
$$x_{63} = -55.7531484448255$$
$$x_{64} = 59.4099501932999$$
$$x_{65} = 19.6450752413296$$
$$x_{1} = -87.1690749807234$$
$$x_{2} = -36.9035925232867$$
$$x_{3} = 95.0432989274846$$
$$x_{4} = -66.2537559502919$$
$$x_{5} = 25.9282605485092$$
$$x_{6} = -74.6027043663642$$
$$x_{7} = 63.6273723915867$$
$$x_{8} = -49.4699631376459$$
$$x_{9} = -59.9705706431123$$
$$x_{10} = 57.3441870844071$$
$$x_{11} = -28.5546441072143$$
$$x_{12} = -3.421902878496$$
$$x_{13} = 13.36188993415$$
$$x_{14} = -99.7354455950826$$
$$x_{15} = -72.5369412574715$$
$$x_{16} = -30.6204072161071$$
$$x_{17} = 38.4946311628683$$
$$x_{18} = -24.3372219089275$$
$$x_{19} = -9.70508818567559$$
$$x_{20} = 65.6931355004795$$
$$x_{21} = -11.7708512945684$$
$$x_{22} = -80.8858896735438$$
$$x_{23} = 88.760113620305$$
$$x_{24} = 32.2114458556888$$
$$x_{25} = 90.8258767291978$$
$$x_{26} = -41.1210147215735$$
$$x_{27} = -91.3864971790102$$
$$x_{28} = 27.9940236574019$$
$$x_{29} = -18.0540366017479$$
$$x_{30} = -62.036333752005$$
$$x_{31} = 34.2772089645815$$
$$x_{32} = 84.5426914220182$$
$$x_{33} = 78.2595061148386$$
$$x_{34} = -78.820126564651$$
$$x_{35} = -47.4042000287531$$
$$x_{36} = 51.0610017772275$$
$$x_{37} = 97.1090620363774$$
$$x_{38} = 76.1937430059459$$
$$x_{39} = 40.5603942717611$$
$$x_{40} = -43.1867778304663$$
$$x_{41} = -97.6696824861898$$
$$x_{42} = 53.1267648861203$$
$$x_{43} = -93.452260287903$$
$$x_{44} = 21.7108383502223$$
$$x_{45} = 2.86128242868359$$
$$x_{46} = -68.3195190591846$$
$$x_{47} = -22.2714588000348$$
$$x_{48} = -15.9882734928552$$
$$x_{49} = 9.14446773586317$$
$$x_{50} = 44.7778164700479$$
$$x_{51} = 14194.5111282385$$
$$x_{52} = 69.9105576987663$$
$$x_{53} = 101.326484234664$$
$$x_{54} = 46.8435795789407$$
$$x_{55} = 15.4276530430428$$
$$x_{56} = 71.976320807659$$
$$x_{57} = 7.07870462697041$$
$$x_{58} = 0.795519319790823$$
$$x_{59} = -34.8378294143939$$
$$x_{60} = 82.4769283131254$$
$$x_{61} = -53.6873853359327$$
$$x_{62} = -5.48766598738876$$
$$x_{63} = -55.7531484448255$$
$$x_{64} = 59.4099501932999$$
$$x_{65} = 19.6450752413296$$
Las raíces dadas
$$x_{14} = -99.7354455950826$$
$$x_{41} = -97.6696824861898$$
$$x_{43} = -93.452260287903$$
$$x_{27} = -91.3864971790102$$
$$x_{1} = -87.1690749807234$$
$$x_{22} = -80.8858896735438$$
$$x_{34} = -78.820126564651$$
$$x_{6} = -74.6027043663642$$
$$x_{15} = -72.5369412574715$$
$$x_{46} = -68.3195190591846$$
$$x_{4} = -66.2537559502919$$
$$x_{30} = -62.036333752005$$
$$x_{9} = -59.9705706431123$$
$$x_{63} = -55.7531484448255$$
$$x_{61} = -53.6873853359327$$
$$x_{8} = -49.4699631376459$$
$$x_{35} = -47.4042000287531$$
$$x_{40} = -43.1867778304663$$
$$x_{26} = -41.1210147215735$$
$$x_{2} = -36.9035925232867$$
$$x_{59} = -34.8378294143939$$
$$x_{16} = -30.6204072161071$$
$$x_{11} = -28.5546441072143$$
$$x_{18} = -24.3372219089275$$
$$x_{47} = -22.2714588000348$$
$$x_{29} = -18.0540366017479$$
$$x_{48} = -15.9882734928552$$
$$x_{21} = -11.7708512945684$$
$$x_{19} = -9.70508818567559$$
$$x_{62} = -5.48766598738876$$
$$x_{12} = -3.421902878496$$
$$x_{58} = 0.795519319790823$$
$$x_{45} = 2.86128242868359$$
$$x_{57} = 7.07870462697041$$
$$x_{49} = 9.14446773586317$$
$$x_{13} = 13.36188993415$$
$$x_{55} = 15.4276530430428$$
$$x_{65} = 19.6450752413296$$
$$x_{44} = 21.7108383502223$$
$$x_{5} = 25.9282605485092$$
$$x_{28} = 27.9940236574019$$
$$x_{24} = 32.2114458556888$$
$$x_{31} = 34.2772089645815$$
$$x_{17} = 38.4946311628683$$
$$x_{39} = 40.5603942717611$$
$$x_{50} = 44.7778164700479$$
$$x_{54} = 46.8435795789407$$
$$x_{36} = 51.0610017772275$$
$$x_{42} = 53.1267648861203$$
$$x_{10} = 57.3441870844071$$
$$x_{64} = 59.4099501932999$$
$$x_{7} = 63.6273723915867$$
$$x_{20} = 65.6931355004795$$
$$x_{52} = 69.9105576987663$$
$$x_{56} = 71.976320807659$$
$$x_{38} = 76.1937430059459$$
$$x_{33} = 78.2595061148386$$
$$x_{60} = 82.4769283131254$$
$$x_{32} = 84.5426914220182$$
$$x_{23} = 88.760113620305$$
$$x_{25} = 90.8258767291978$$
$$x_{3} = 95.0432989274846$$
$$x_{37} = 97.1090620363774$$
$$x_{53} = 101.326484234664$$
$$x_{51} = 14194.5111282385$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{14}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{14} - \frac{1}{10}$$
=
$$-99.7354455950826 + - \frac{1}{10}$$
=
$$-99.8354455950826$$
lo sustituimos en la expresión
$$\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0$$
$$\left(- 7 \sin{\left(-99.8354455950826 \right)} + 2 \sin{\left(\left(-99.8354455950826\right) 2 \right)}\right) + 3 > 0$$
0.482284559587646 > 0
significa que una de las soluciones de nuestra ecuación será con:
$$x < -99.7354455950826$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x14 x41 x43 x27 x1 x22 x34 x6 x15 x46 x4 x30 x9 x63 x61 x8 x35 x40 x26 x2 x59 x16 x11 x18 x47 x29 x48 x21 x19 x62 x12 x58 x45 x57 x49 x13 x55 x65 x44 x5 x28 x24 x31 x17 x39 x50 x54 x36 x42 x10 x64 x7 x20 x52 x56 x38 x33 x60 x32 x23 x25 x3 x37 x53 x51Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -99.7354455950826$$
$$x > -97.6696824861898 \wedge x < -93.452260287903$$
$$x > -91.3864971790102 \wedge x < -87.1690749807234$$
$$x > -80.8858896735438 \wedge x < -78.820126564651$$
$$x > -74.6027043663642 \wedge x < -72.5369412574715$$
$$x > -68.3195190591846 \wedge x < -66.2537559502919$$
$$x > -62.036333752005 \wedge x < -59.9705706431123$$
$$x > -55.7531484448255 \wedge x < -53.6873853359327$$
$$x > -49.4699631376459 \wedge x < -47.4042000287531$$
$$x > -43.1867778304663 \wedge x < -41.1210147215735$$
$$x > -36.9035925232867 \wedge x < -34.8378294143939$$
$$x > -30.6204072161071 \wedge x < -28.5546441072143$$
$$x > -24.3372219089275 \wedge x < -22.2714588000348$$
$$x > -18.0540366017479 \wedge x < -15.9882734928552$$
$$x > -11.7708512945684 \wedge x < -9.70508818567559$$
$$x > -5.48766598738876 \wedge x < -3.421902878496$$
$$x > 0.795519319790823 \wedge x < 2.86128242868359$$
$$x > 7.07870462697041 \wedge x < 9.14446773586317$$
$$x > 13.36188993415 \wedge x < 15.4276530430428$$
$$x > 19.6450752413296 \wedge x < 21.7108383502223$$
$$x > 25.9282605485092 \wedge x < 27.9940236574019$$
$$x > 32.2114458556888 \wedge x < 34.2772089645815$$
$$x > 38.4946311628683 \wedge x < 40.5603942717611$$
$$x > 44.7778164700479 \wedge x < 46.8435795789407$$
$$x > 51.0610017772275 \wedge x < 53.1267648861203$$
$$x > 57.3441870844071 \wedge x < 59.4099501932999$$
$$x > 63.6273723915867 \wedge x < 65.6931355004795$$
$$x > 69.9105576987663 \wedge x < 71.976320807659$$
$$x > 76.1937430059459 \wedge x < 78.2595061148386$$
$$x > 82.4769283131254 \wedge x < 84.5426914220182$$
$$x > 88.760113620305 \wedge x < 90.8258767291978$$
$$x > 95.0432989274846 \wedge x < 97.1090620363774$$
$$x > 101.326484234664 \wedge x < 14194.5111282385$$
Solución de la desigualdad en el gráfico
Respuesta rápida
[src]
/ / / ______________________________________________________________________________________________________________________________________\\ / / ______________________________________________________________________________________________________________________________________\ \\ | | | / _________________ || | | / _________________ | || | | | / / ______ || | | / / ______ | || | | | / 218 / 73 2*\/ 1418 14 2374 || | | / 218 / 73 2*\/ 1418 14 2374 | || | | | / --- - 2*3 / -- + ---------- + ------------------------ + ------------------------------------------------------------------------ || | | / --- - 2*3 / -- + ---------- + ------------------------ + ------------------------------------------------------------------------ | || | | | ___________________________________________________________ / 9 \/ 27 27 _________________ ___________________________________________________________ || | | ___________________________________________________________ / 9 \/ 27 27 _________________ ___________________________________________________________ | || | | | / _________________ / / ______ / _________________ || | | / _________________ / / ______ / _________________ | || | | | / / ______ / / 73 2*\/ 1418 / / ______ || | | / / ______ / / 73 2*\/ 1418 / / ______ | || | | | / 109 / 73 2*\/ 1418 14 / 9*3 / -- + ---------- / 109 / 73 2*\/ 1418 14 || | | / 109 / 73 2*\/ 1418 14 / 9*3 / -- + ---------- / 109 / 73 2*\/ 1418 14 | || | | | / --- + 2*3 / -- + ---------- - ------------------------ / \/ 27 27 27* / --- + 2*3 / -- + ---------- - ------------------------ || | | / --- + 2*3 / -- + ---------- - ------------------------ / \/ 27 27 27* / --- + 2*3 / -- + ---------- - ------------------------ | || | | | / 9 \/ 27 27 _________________ / / 9 \/ 27 27 _________________ || | | / 9 \/ 27 27 _________________ / / 9 \/ 27 27 _________________ | || | | | / / ______ / / / ______ || | | / / ______ / / / ______ | || | | | / / 73 2*\/ 1418 / / / 73 2*\/ 1418 || | | / / 73 2*\/ 1418 / / / 73 2*\/ 1418 | || | | | / 9*3 / -- + ---------- / / 9*3 / -- + ---------- || | | / 9*3 / -- + ---------- / / 9*3 / -- + ---------- | || | | |11 \/ \/ 27 27 \/ \/ \/ 27 27 || | |11 \/ \/ 27 27 \/ \/ \/ 27 27 | || Or|And|0 <= x, x < 2*atan|-- + --------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------||, And|x <= 2*pi, 2*atan|-- + --------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------| < x|| \ \ \6 2 2 // \ \6 2 2 / //
$$\left(0 \leq x \wedge x < 2 \operatorname{atan}{\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + \frac{2374}{27 \sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}} + \frac{218}{9}}}{2} + \frac{11}{6} + \frac{\sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}}{2} \right)}\right) \vee \left(x \leq 2 \pi \wedge 2 \operatorname{atan}{\left(\frac{11}{6} + \frac{\sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + \frac{2374}{27 \sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}} + \frac{218}{9}}}{2} \right)} < x\right)$$
((0 <= x)∧(x < 2*atan(11/6 + sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))/2 - sqrt(218/9 - 2*(73/27 + 2*sqrt(1418)/27)^(1/3) + 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)) + 2374/(27*sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))))/2)))∨((x <= 2*pi)∧(2*atan(11/6 + sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))/2 + sqrt(218/9 - 2*(73/27 + 2*sqrt(1418)/27)^(1/3) + 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)) + 2374/(27*sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))))/2) < x))