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- 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-7)(x+8)>0
-
-x^2-10x-24>0
-
4x-4>9x+6
-
3+x/4+2-x/3<0
-
Expresiones idénticas
- (pi*abs(sin(pi*x)))/(tres *(cos(pi*x)^(dos / tres)))< uno
- ( número pi multiplicar por abs( seno de ( número pi multiplicar por x))) dividir por (3 multiplicar por ( coseno de ( número pi multiplicar por x) en el grado (2 dividir por 3))) menos 1
- ( número pi multiplicar por abs( seno de ( número pi multiplicar por x))) dividir por (tres multiplicar por ( coseno de ( número pi multiplicar por x) en el grado (dos dividir por tres))) menos uno
- (pi*abs(sin(pi*x)))/(3*(cos(pi*x)(2/3)))<1
- pi*abssinpi*x/3*cospi*x2/3<1
- (piabs(sin(pix)))/(3(cos(pix)^(2/3)))<1
- (piabs(sin(pix)))/(3(cos(pix)(2/3)))<1
- piabssinpix/3cospix2/3<1
- piabssinpix/3cospix^2/3<1
- (pi*abs(sin(pi*x))) dividir por (3*(cos(pi*x)^(2 dividir por 3)))<1
-
Expresiones con funciones
- Seno sin
- sin(x)>√(3/2)
- sin(x/2)>-1/2
- sin(x/2)<-1
- sin(x^2)>=1/2
- sin(x)=>-1
- Coseno cos
- cos(nx)>=x^2+1
- cos(x)*cos(pi*1/6)-sin(x)*sin(pi*1/6)>(sqrt(3))*1/2
- cos(2p-x)>=-sqrt2/2
- cos(x)/2<0
- cos(2x)<=-sqrt(3/2)
(pi*abs(sin(pi*x)))/(3*(cos(pi*x)^(2/3)))<1 desigualdades
Solución
Ha introducido
[src]
pi*|sin(pi*x)|
-------------- < 1
2/3
3*cos (pi*x)
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} < 1$$
(pi*Abs(sin(pi*x)))/((3*cos(pi*x)^(2/3))) < 1
Solución detallada
Se da la desigualdad:
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} < 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} = 1$$
Resolvemos:
$$x_{1} = -53.7366477934335$$
$$x_{2} = 90.2633522065665$$
$$x_{3} = 62.2633522065665$$
$$x_{4} = -23.7366477934335$$
$$x_{5} = -97.7366477934335$$
$$x_{6} = -55.7366477934335$$
$$x_{7} = -83.7366477934335$$
$$x_{8} = 38.2633522065665$$
$$x_{9} = -11.7366477934335$$
$$x_{10} = 40.2633522065665$$
$$x_{11} = 28.2633522065665$$
$$x_{12} = -15.7366477934335$$
$$x_{13} = 48.2633522065665$$
$$x_{14} = -65.7366477934335$$
$$x_{15} = -7.73664779343354$$
$$x_{16} = -35.7366477934335$$
$$x_{17} = 80.2633522065665$$
$$x_{18} = 82.2633522065665$$
$$x_{19} = -59.7366477934335$$
$$x_{20} = -79.7366477934335$$
$$x_{21} = -25.7366477934335$$
$$x_{22} = 32.2633522065665$$
$$x_{23} = 2.26335220656646$$
$$x_{24} = 14.2633522065665$$
$$x_{25} = -77.7366477934335$$
$$x_{26} = -69.7366477934335$$
$$x_{27} = 4.26335220656646$$
$$x_{28} = 66.2633522065665$$
$$x_{29} = -81.7366477934335$$
$$x_{30} = -49.7366477934335$$
$$x_{31} = 20.2633522065665$$
$$x_{32} = -21.7366477934335$$
$$x_{33} = -91.7366477934335$$
$$x_{34} = 26.2633522065665$$
$$x_{35} = 22.2633522065665$$
$$x_{36} = -13.7366477934335$$
$$x_{37} = -51.7366477934335$$
$$x_{38} = -47.7366477934335$$
$$x_{39} = -41.7366477934335$$
$$x_{40} = -61.7366477934335$$
$$x_{41} = 50.2633522065665$$
$$x_{42} = 92.2633522065665$$
$$x_{43} = 98.2633522065665$$
$$x_{44} = -89.7366477934335$$
$$x_{45} = 70.2633522065665$$
$$x_{46} = -37.7366477934335$$
$$x_{47} = -87.7366477934335$$
$$x_{48} = -67.7366477934335$$
$$x_{49} = -43.7366477934335$$
$$x_{50} = -75.7366477934335$$
$$x_{51} = 0.26335220656646$$
$$x_{52} = -95.7366477934335$$
$$x_{53} = 96.2633522065665$$
$$x_{54} = 16.2633522065665$$
$$x_{55} = 12.2633522065665$$
$$x_{56} = 84.2633522065665$$
$$x_{57} = -17.7366477934335$$
$$x_{58} = 24.2633522065665$$
$$x_{59} = 88.2633522065665$$
$$x_{60} = -85.7366477934335$$
$$x_{61} = 78.2633522065665$$
$$x_{62} = 18.2633522065665$$
$$x_{63} = 72.2633522065665$$
$$x_{64} = 68.2633522065665$$
$$x_{65} = 56.2633522065665$$
$$x_{66} = 36.2633522065665$$
$$x_{67} = -9.73664779343354$$
$$x_{68} = -99.7366477934335$$
$$x_{69} = -1.73664779343354$$
$$x_{70} = -39.7366477934335$$
$$x_{71} = 58.2633522065665$$
$$x_{72} = -31.7366477934335$$
$$x_{73} = -71.7366477934335$$
$$x_{74} = 100.263352206566$$
$$x_{75} = 42.2633522065665$$
$$x_{76} = 64.2633522065665$$
$$x_{77} = 10.2633522065665$$
$$x_{78} = 46.2633522065665$$
$$x_{79} = 34.2633522065665$$
$$x_{80} = -29.7366477934335$$
$$x_{81} = 86.2633522065665$$
$$x_{82} = -33.7366477934335$$
$$x_{83} = -45.7366477934335$$
$$x_{84} = 54.2633522065665$$
$$x_{85} = -63.7366477934335$$
$$x_{86} = -57.7366477934335$$
$$x_{87} = 52.2633522065665$$
$$x_{88} = -3.73664779343354$$
$$x_{89} = 44.2633522065665$$
$$x_{90} = 94.2633522065665$$
$$x_{91} = -73.7366477934335$$
$$x_{92} = -19.7366477934335$$
$$x_{93} = -93.7366477934335$$
$$x_{94} = -5.73664779343354$$
$$x_{95} = -27.7366477934335$$
$$x_{96} = 76.2633522065665$$
$$x_{97} = 8.26335220656646$$
$$x_{98} = 30.2633522065665$$
$$x_{99} = 6.26335220656646$$
$$x_{100} = 60.2633522065665$$
$$x_{101} = 74.2633522065665$$
$$x_{1} = -53.7366477934335$$
$$x_{2} = 90.2633522065665$$
$$x_{3} = 62.2633522065665$$
$$x_{4} = -23.7366477934335$$
$$x_{5} = -97.7366477934335$$
$$x_{6} = -55.7366477934335$$
$$x_{7} = -83.7366477934335$$
$$x_{8} = 38.2633522065665$$
$$x_{9} = -11.7366477934335$$
$$x_{10} = 40.2633522065665$$
$$x_{11} = 28.2633522065665$$
$$x_{12} = -15.7366477934335$$
$$x_{13} = 48.2633522065665$$
$$x_{14} = -65.7366477934335$$
$$x_{15} = -7.73664779343354$$
$$x_{16} = -35.7366477934335$$
$$x_{17} = 80.2633522065665$$
$$x_{18} = 82.2633522065665$$
$$x_{19} = -59.7366477934335$$
$$x_{20} = -79.7366477934335$$
$$x_{21} = -25.7366477934335$$
$$x_{22} = 32.2633522065665$$
$$x_{23} = 2.26335220656646$$
$$x_{24} = 14.2633522065665$$
$$x_{25} = -77.7366477934335$$
$$x_{26} = -69.7366477934335$$
$$x_{27} = 4.26335220656646$$
$$x_{28} = 66.2633522065665$$
$$x_{29} = -81.7366477934335$$
$$x_{30} = -49.7366477934335$$
$$x_{31} = 20.2633522065665$$
$$x_{32} = -21.7366477934335$$
$$x_{33} = -91.7366477934335$$
$$x_{34} = 26.2633522065665$$
$$x_{35} = 22.2633522065665$$
$$x_{36} = -13.7366477934335$$
$$x_{37} = -51.7366477934335$$
$$x_{38} = -47.7366477934335$$
$$x_{39} = -41.7366477934335$$
$$x_{40} = -61.7366477934335$$
$$x_{41} = 50.2633522065665$$
$$x_{42} = 92.2633522065665$$
$$x_{43} = 98.2633522065665$$
$$x_{44} = -89.7366477934335$$
$$x_{45} = 70.2633522065665$$
$$x_{46} = -37.7366477934335$$
$$x_{47} = -87.7366477934335$$
$$x_{48} = -67.7366477934335$$
$$x_{49} = -43.7366477934335$$
$$x_{50} = -75.7366477934335$$
$$x_{51} = 0.26335220656646$$
$$x_{52} = -95.7366477934335$$
$$x_{53} = 96.2633522065665$$
$$x_{54} = 16.2633522065665$$
$$x_{55} = 12.2633522065665$$
$$x_{56} = 84.2633522065665$$
$$x_{57} = -17.7366477934335$$
$$x_{58} = 24.2633522065665$$
$$x_{59} = 88.2633522065665$$
$$x_{60} = -85.7366477934335$$
$$x_{61} = 78.2633522065665$$
$$x_{62} = 18.2633522065665$$
$$x_{63} = 72.2633522065665$$
$$x_{64} = 68.2633522065665$$
$$x_{65} = 56.2633522065665$$
$$x_{66} = 36.2633522065665$$
$$x_{67} = -9.73664779343354$$
$$x_{68} = -99.7366477934335$$
$$x_{69} = -1.73664779343354$$
$$x_{70} = -39.7366477934335$$
$$x_{71} = 58.2633522065665$$
$$x_{72} = -31.7366477934335$$
$$x_{73} = -71.7366477934335$$
$$x_{74} = 100.263352206566$$
$$x_{75} = 42.2633522065665$$
$$x_{76} = 64.2633522065665$$
$$x_{77} = 10.2633522065665$$
$$x_{78} = 46.2633522065665$$
$$x_{79} = 34.2633522065665$$
$$x_{80} = -29.7366477934335$$
$$x_{81} = 86.2633522065665$$
$$x_{82} = -33.7366477934335$$
$$x_{83} = -45.7366477934335$$
$$x_{84} = 54.2633522065665$$
$$x_{85} = -63.7366477934335$$
$$x_{86} = -57.7366477934335$$
$$x_{87} = 52.2633522065665$$
$$x_{88} = -3.73664779343354$$
$$x_{89} = 44.2633522065665$$
$$x_{90} = 94.2633522065665$$
$$x_{91} = -73.7366477934335$$
$$x_{92} = -19.7366477934335$$
$$x_{93} = -93.7366477934335$$
$$x_{94} = -5.73664779343354$$
$$x_{95} = -27.7366477934335$$
$$x_{96} = 76.2633522065665$$
$$x_{97} = 8.26335220656646$$
$$x_{98} = 30.2633522065665$$
$$x_{99} = 6.26335220656646$$
$$x_{100} = 60.2633522065665$$
$$x_{101} = 74.2633522065665$$
Las raíces dadas
$$x_{68} = -99.7366477934335$$
$$x_{5} = -97.7366477934335$$
$$x_{52} = -95.7366477934335$$
$$x_{93} = -93.7366477934335$$
$$x_{33} = -91.7366477934335$$
$$x_{44} = -89.7366477934335$$
$$x_{47} = -87.7366477934335$$
$$x_{60} = -85.7366477934335$$
$$x_{7} = -83.7366477934335$$
$$x_{29} = -81.7366477934335$$
$$x_{20} = -79.7366477934335$$
$$x_{25} = -77.7366477934335$$
$$x_{50} = -75.7366477934335$$
$$x_{91} = -73.7366477934335$$
$$x_{73} = -71.7366477934335$$
$$x_{26} = -69.7366477934335$$
$$x_{48} = -67.7366477934335$$
$$x_{14} = -65.7366477934335$$
$$x_{85} = -63.7366477934335$$
$$x_{40} = -61.7366477934335$$
$$x_{19} = -59.7366477934335$$
$$x_{86} = -57.7366477934335$$
$$x_{6} = -55.7366477934335$$
$$x_{1} = -53.7366477934335$$
$$x_{37} = -51.7366477934335$$
$$x_{30} = -49.7366477934335$$
$$x_{38} = -47.7366477934335$$
$$x_{83} = -45.7366477934335$$
$$x_{49} = -43.7366477934335$$
$$x_{39} = -41.7366477934335$$
$$x_{70} = -39.7366477934335$$
$$x_{46} = -37.7366477934335$$
$$x_{16} = -35.7366477934335$$
$$x_{82} = -33.7366477934335$$
$$x_{72} = -31.7366477934335$$
$$x_{80} = -29.7366477934335$$
$$x_{95} = -27.7366477934335$$
$$x_{21} = -25.7366477934335$$
$$x_{4} = -23.7366477934335$$
$$x_{32} = -21.7366477934335$$
$$x_{92} = -19.7366477934335$$
$$x_{57} = -17.7366477934335$$
$$x_{12} = -15.7366477934335$$
$$x_{36} = -13.7366477934335$$
$$x_{9} = -11.7366477934335$$
$$x_{67} = -9.73664779343354$$
$$x_{15} = -7.73664779343354$$
$$x_{94} = -5.73664779343354$$
$$x_{88} = -3.73664779343354$$
$$x_{69} = -1.73664779343354$$
$$x_{51} = 0.26335220656646$$
$$x_{23} = 2.26335220656646$$
$$x_{27} = 4.26335220656646$$
$$x_{99} = 6.26335220656646$$
$$x_{97} = 8.26335220656646$$
$$x_{77} = 10.2633522065665$$
$$x_{55} = 12.2633522065665$$
$$x_{24} = 14.2633522065665$$
$$x_{54} = 16.2633522065665$$
$$x_{62} = 18.2633522065665$$
$$x_{31} = 20.2633522065665$$
$$x_{35} = 22.2633522065665$$
$$x_{58} = 24.2633522065665$$
$$x_{34} = 26.2633522065665$$
$$x_{11} = 28.2633522065665$$
$$x_{98} = 30.2633522065665$$
$$x_{22} = 32.2633522065665$$
$$x_{79} = 34.2633522065665$$
$$x_{66} = 36.2633522065665$$
$$x_{8} = 38.2633522065665$$
$$x_{10} = 40.2633522065665$$
$$x_{75} = 42.2633522065665$$
$$x_{89} = 44.2633522065665$$
$$x_{78} = 46.2633522065665$$
$$x_{13} = 48.2633522065665$$
$$x_{41} = 50.2633522065665$$
$$x_{87} = 52.2633522065665$$
$$x_{84} = 54.2633522065665$$
$$x_{65} = 56.2633522065665$$
$$x_{71} = 58.2633522065665$$
$$x_{100} = 60.2633522065665$$
$$x_{3} = 62.2633522065665$$
$$x_{76} = 64.2633522065665$$
$$x_{28} = 66.2633522065665$$
$$x_{64} = 68.2633522065665$$
$$x_{45} = 70.2633522065665$$
$$x_{63} = 72.2633522065665$$
$$x_{101} = 74.2633522065665$$
$$x_{96} = 76.2633522065665$$
$$x_{61} = 78.2633522065665$$
$$x_{17} = 80.2633522065665$$
$$x_{18} = 82.2633522065665$$
$$x_{56} = 84.2633522065665$$
$$x_{81} = 86.2633522065665$$
$$x_{59} = 88.2633522065665$$
$$x_{2} = 90.2633522065665$$
$$x_{42} = 92.2633522065665$$
$$x_{90} = 94.2633522065665$$
$$x_{53} = 96.2633522065665$$
$$x_{43} = 98.2633522065665$$
$$x_{74} = 100.263352206566$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{68}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{68} - \frac{1}{10}$$
=
$$-99.7366477934335 + - \frac{1}{10}$$
=
$$-99.8366477934335$$
lo sustituimos en la expresión
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} < 1$$
$$\frac{\pi \left|{\sin{\left(\left(-99.8366477934335\right) \pi \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\left(-99.8366477934335\right) \pi \right)}} < 1$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -99.7366477934335$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -99.7366477934335$$
$$x > -97.7366477934335 \wedge x < -95.7366477934335$$
$$x > -93.7366477934335 \wedge x < -91.7366477934335$$
$$x > -89.7366477934335 \wedge x < -87.7366477934335$$
$$x > -85.7366477934335 \wedge x < -83.7366477934335$$
$$x > -81.7366477934335 \wedge x < -79.7366477934335$$
$$x > -77.7366477934335 \wedge x < -75.7366477934335$$
$$x > -73.7366477934335 \wedge x < -71.7366477934335$$
$$x > -69.7366477934335 \wedge x < -67.7366477934335$$
$$x > -65.7366477934335 \wedge x < -63.7366477934335$$
$$x > -61.7366477934335 \wedge x < -59.7366477934335$$
$$x > -57.7366477934335 \wedge x < -55.7366477934335$$
$$x > -53.7366477934335 \wedge x < -51.7366477934335$$
$$x > -49.7366477934335 \wedge x < -47.7366477934335$$
$$x > -45.7366477934335 \wedge x < -43.7366477934335$$
$$x > -41.7366477934335 \wedge x < -39.7366477934335$$
$$x > -37.7366477934335 \wedge x < -35.7366477934335$$
$$x > -33.7366477934335 \wedge x < -31.7366477934335$$
$$x > -29.7366477934335 \wedge x < -27.7366477934335$$
$$x > -25.7366477934335 \wedge x < -23.7366477934335$$
$$x > -21.7366477934335 \wedge x < -19.7366477934335$$
$$x > -17.7366477934335 \wedge x < -15.7366477934335$$
$$x > -13.7366477934335 \wedge x < -11.7366477934335$$
$$x > -9.73664779343354 \wedge x < -7.73664779343354$$
$$x > -5.73664779343354 \wedge x < -3.73664779343354$$
$$x > -1.73664779343354 \wedge x < 0.26335220656646$$
$$x > 2.26335220656646 \wedge x < 4.26335220656646$$
$$x > 6.26335220656646 \wedge x < 8.26335220656646$$
$$x > 10.2633522065665 \wedge x < 12.2633522065665$$
$$x > 14.2633522065665 \wedge x < 16.2633522065665$$
$$x > 18.2633522065665 \wedge x < 20.2633522065665$$
$$x > 22.2633522065665 \wedge x < 24.2633522065665$$
$$x > 26.2633522065665 \wedge x < 28.2633522065665$$
$$x > 30.2633522065665 \wedge x < 32.2633522065665$$
$$x > 34.2633522065665 \wedge x < 36.2633522065665$$
$$x > 38.2633522065665 \wedge x < 40.2633522065665$$
$$x > 42.2633522065665 \wedge x < 44.2633522065665$$
$$x > 46.2633522065665 \wedge x < 48.2633522065665$$
$$x > 50.2633522065665 \wedge x < 52.2633522065665$$
$$x > 54.2633522065665 \wedge x < 56.2633522065665$$
$$x > 58.2633522065665 \wedge x < 60.2633522065665$$
$$x > 62.2633522065665 \wedge x < 64.2633522065665$$
$$x > 66.2633522065665 \wedge x < 68.2633522065665$$
$$x > 70.2633522065665 \wedge x < 72.2633522065665$$
$$x > 74.2633522065665 \wedge x < 76.2633522065665$$
$$x > 78.2633522065665 \wedge x < 80.2633522065665$$
$$x > 82.2633522065665 \wedge x < 84.2633522065665$$
$$x > 86.2633522065665 \wedge x < 88.2633522065665$$
$$x > 90.2633522065665 \wedge x < 92.2633522065665$$
$$x > 94.2633522065665 \wedge x < 96.2633522065665$$
$$x > 98.2633522065665 \wedge x < 100.263352206566$$
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} < 1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} = 1$$
Resolvemos:
$$x_{1} = -53.7366477934335$$
$$x_{2} = 90.2633522065665$$
$$x_{3} = 62.2633522065665$$
$$x_{4} = -23.7366477934335$$
$$x_{5} = -97.7366477934335$$
$$x_{6} = -55.7366477934335$$
$$x_{7} = -83.7366477934335$$
$$x_{8} = 38.2633522065665$$
$$x_{9} = -11.7366477934335$$
$$x_{10} = 40.2633522065665$$
$$x_{11} = 28.2633522065665$$
$$x_{12} = -15.7366477934335$$
$$x_{13} = 48.2633522065665$$
$$x_{14} = -65.7366477934335$$
$$x_{15} = -7.73664779343354$$
$$x_{16} = -35.7366477934335$$
$$x_{17} = 80.2633522065665$$
$$x_{18} = 82.2633522065665$$
$$x_{19} = -59.7366477934335$$
$$x_{20} = -79.7366477934335$$
$$x_{21} = -25.7366477934335$$
$$x_{22} = 32.2633522065665$$
$$x_{23} = 2.26335220656646$$
$$x_{24} = 14.2633522065665$$
$$x_{25} = -77.7366477934335$$
$$x_{26} = -69.7366477934335$$
$$x_{27} = 4.26335220656646$$
$$x_{28} = 66.2633522065665$$
$$x_{29} = -81.7366477934335$$
$$x_{30} = -49.7366477934335$$
$$x_{31} = 20.2633522065665$$
$$x_{32} = -21.7366477934335$$
$$x_{33} = -91.7366477934335$$
$$x_{34} = 26.2633522065665$$
$$x_{35} = 22.2633522065665$$
$$x_{36} = -13.7366477934335$$
$$x_{37} = -51.7366477934335$$
$$x_{38} = -47.7366477934335$$
$$x_{39} = -41.7366477934335$$
$$x_{40} = -61.7366477934335$$
$$x_{41} = 50.2633522065665$$
$$x_{42} = 92.2633522065665$$
$$x_{43} = 98.2633522065665$$
$$x_{44} = -89.7366477934335$$
$$x_{45} = 70.2633522065665$$
$$x_{46} = -37.7366477934335$$
$$x_{47} = -87.7366477934335$$
$$x_{48} = -67.7366477934335$$
$$x_{49} = -43.7366477934335$$
$$x_{50} = -75.7366477934335$$
$$x_{51} = 0.26335220656646$$
$$x_{52} = -95.7366477934335$$
$$x_{53} = 96.2633522065665$$
$$x_{54} = 16.2633522065665$$
$$x_{55} = 12.2633522065665$$
$$x_{56} = 84.2633522065665$$
$$x_{57} = -17.7366477934335$$
$$x_{58} = 24.2633522065665$$
$$x_{59} = 88.2633522065665$$
$$x_{60} = -85.7366477934335$$
$$x_{61} = 78.2633522065665$$
$$x_{62} = 18.2633522065665$$
$$x_{63} = 72.2633522065665$$
$$x_{64} = 68.2633522065665$$
$$x_{65} = 56.2633522065665$$
$$x_{66} = 36.2633522065665$$
$$x_{67} = -9.73664779343354$$
$$x_{68} = -99.7366477934335$$
$$x_{69} = -1.73664779343354$$
$$x_{70} = -39.7366477934335$$
$$x_{71} = 58.2633522065665$$
$$x_{72} = -31.7366477934335$$
$$x_{73} = -71.7366477934335$$
$$x_{74} = 100.263352206566$$
$$x_{75} = 42.2633522065665$$
$$x_{76} = 64.2633522065665$$
$$x_{77} = 10.2633522065665$$
$$x_{78} = 46.2633522065665$$
$$x_{79} = 34.2633522065665$$
$$x_{80} = -29.7366477934335$$
$$x_{81} = 86.2633522065665$$
$$x_{82} = -33.7366477934335$$
$$x_{83} = -45.7366477934335$$
$$x_{84} = 54.2633522065665$$
$$x_{85} = -63.7366477934335$$
$$x_{86} = -57.7366477934335$$
$$x_{87} = 52.2633522065665$$
$$x_{88} = -3.73664779343354$$
$$x_{89} = 44.2633522065665$$
$$x_{90} = 94.2633522065665$$
$$x_{91} = -73.7366477934335$$
$$x_{92} = -19.7366477934335$$
$$x_{93} = -93.7366477934335$$
$$x_{94} = -5.73664779343354$$
$$x_{95} = -27.7366477934335$$
$$x_{96} = 76.2633522065665$$
$$x_{97} = 8.26335220656646$$
$$x_{98} = 30.2633522065665$$
$$x_{99} = 6.26335220656646$$
$$x_{100} = 60.2633522065665$$
$$x_{101} = 74.2633522065665$$
$$x_{1} = -53.7366477934335$$
$$x_{2} = 90.2633522065665$$
$$x_{3} = 62.2633522065665$$
$$x_{4} = -23.7366477934335$$
$$x_{5} = -97.7366477934335$$
$$x_{6} = -55.7366477934335$$
$$x_{7} = -83.7366477934335$$
$$x_{8} = 38.2633522065665$$
$$x_{9} = -11.7366477934335$$
$$x_{10} = 40.2633522065665$$
$$x_{11} = 28.2633522065665$$
$$x_{12} = -15.7366477934335$$
$$x_{13} = 48.2633522065665$$
$$x_{14} = -65.7366477934335$$
$$x_{15} = -7.73664779343354$$
$$x_{16} = -35.7366477934335$$
$$x_{17} = 80.2633522065665$$
$$x_{18} = 82.2633522065665$$
$$x_{19} = -59.7366477934335$$
$$x_{20} = -79.7366477934335$$
$$x_{21} = -25.7366477934335$$
$$x_{22} = 32.2633522065665$$
$$x_{23} = 2.26335220656646$$
$$x_{24} = 14.2633522065665$$
$$x_{25} = -77.7366477934335$$
$$x_{26} = -69.7366477934335$$
$$x_{27} = 4.26335220656646$$
$$x_{28} = 66.2633522065665$$
$$x_{29} = -81.7366477934335$$
$$x_{30} = -49.7366477934335$$
$$x_{31} = 20.2633522065665$$
$$x_{32} = -21.7366477934335$$
$$x_{33} = -91.7366477934335$$
$$x_{34} = 26.2633522065665$$
$$x_{35} = 22.2633522065665$$
$$x_{36} = -13.7366477934335$$
$$x_{37} = -51.7366477934335$$
$$x_{38} = -47.7366477934335$$
$$x_{39} = -41.7366477934335$$
$$x_{40} = -61.7366477934335$$
$$x_{41} = 50.2633522065665$$
$$x_{42} = 92.2633522065665$$
$$x_{43} = 98.2633522065665$$
$$x_{44} = -89.7366477934335$$
$$x_{45} = 70.2633522065665$$
$$x_{46} = -37.7366477934335$$
$$x_{47} = -87.7366477934335$$
$$x_{48} = -67.7366477934335$$
$$x_{49} = -43.7366477934335$$
$$x_{50} = -75.7366477934335$$
$$x_{51} = 0.26335220656646$$
$$x_{52} = -95.7366477934335$$
$$x_{53} = 96.2633522065665$$
$$x_{54} = 16.2633522065665$$
$$x_{55} = 12.2633522065665$$
$$x_{56} = 84.2633522065665$$
$$x_{57} = -17.7366477934335$$
$$x_{58} = 24.2633522065665$$
$$x_{59} = 88.2633522065665$$
$$x_{60} = -85.7366477934335$$
$$x_{61} = 78.2633522065665$$
$$x_{62} = 18.2633522065665$$
$$x_{63} = 72.2633522065665$$
$$x_{64} = 68.2633522065665$$
$$x_{65} = 56.2633522065665$$
$$x_{66} = 36.2633522065665$$
$$x_{67} = -9.73664779343354$$
$$x_{68} = -99.7366477934335$$
$$x_{69} = -1.73664779343354$$
$$x_{70} = -39.7366477934335$$
$$x_{71} = 58.2633522065665$$
$$x_{72} = -31.7366477934335$$
$$x_{73} = -71.7366477934335$$
$$x_{74} = 100.263352206566$$
$$x_{75} = 42.2633522065665$$
$$x_{76} = 64.2633522065665$$
$$x_{77} = 10.2633522065665$$
$$x_{78} = 46.2633522065665$$
$$x_{79} = 34.2633522065665$$
$$x_{80} = -29.7366477934335$$
$$x_{81} = 86.2633522065665$$
$$x_{82} = -33.7366477934335$$
$$x_{83} = -45.7366477934335$$
$$x_{84} = 54.2633522065665$$
$$x_{85} = -63.7366477934335$$
$$x_{86} = -57.7366477934335$$
$$x_{87} = 52.2633522065665$$
$$x_{88} = -3.73664779343354$$
$$x_{89} = 44.2633522065665$$
$$x_{90} = 94.2633522065665$$
$$x_{91} = -73.7366477934335$$
$$x_{92} = -19.7366477934335$$
$$x_{93} = -93.7366477934335$$
$$x_{94} = -5.73664779343354$$
$$x_{95} = -27.7366477934335$$
$$x_{96} = 76.2633522065665$$
$$x_{97} = 8.26335220656646$$
$$x_{98} = 30.2633522065665$$
$$x_{99} = 6.26335220656646$$
$$x_{100} = 60.2633522065665$$
$$x_{101} = 74.2633522065665$$
Las raíces dadas
$$x_{68} = -99.7366477934335$$
$$x_{5} = -97.7366477934335$$
$$x_{52} = -95.7366477934335$$
$$x_{93} = -93.7366477934335$$
$$x_{33} = -91.7366477934335$$
$$x_{44} = -89.7366477934335$$
$$x_{47} = -87.7366477934335$$
$$x_{60} = -85.7366477934335$$
$$x_{7} = -83.7366477934335$$
$$x_{29} = -81.7366477934335$$
$$x_{20} = -79.7366477934335$$
$$x_{25} = -77.7366477934335$$
$$x_{50} = -75.7366477934335$$
$$x_{91} = -73.7366477934335$$
$$x_{73} = -71.7366477934335$$
$$x_{26} = -69.7366477934335$$
$$x_{48} = -67.7366477934335$$
$$x_{14} = -65.7366477934335$$
$$x_{85} = -63.7366477934335$$
$$x_{40} = -61.7366477934335$$
$$x_{19} = -59.7366477934335$$
$$x_{86} = -57.7366477934335$$
$$x_{6} = -55.7366477934335$$
$$x_{1} = -53.7366477934335$$
$$x_{37} = -51.7366477934335$$
$$x_{30} = -49.7366477934335$$
$$x_{38} = -47.7366477934335$$
$$x_{83} = -45.7366477934335$$
$$x_{49} = -43.7366477934335$$
$$x_{39} = -41.7366477934335$$
$$x_{70} = -39.7366477934335$$
$$x_{46} = -37.7366477934335$$
$$x_{16} = -35.7366477934335$$
$$x_{82} = -33.7366477934335$$
$$x_{72} = -31.7366477934335$$
$$x_{80} = -29.7366477934335$$
$$x_{95} = -27.7366477934335$$
$$x_{21} = -25.7366477934335$$
$$x_{4} = -23.7366477934335$$
$$x_{32} = -21.7366477934335$$
$$x_{92} = -19.7366477934335$$
$$x_{57} = -17.7366477934335$$
$$x_{12} = -15.7366477934335$$
$$x_{36} = -13.7366477934335$$
$$x_{9} = -11.7366477934335$$
$$x_{67} = -9.73664779343354$$
$$x_{15} = -7.73664779343354$$
$$x_{94} = -5.73664779343354$$
$$x_{88} = -3.73664779343354$$
$$x_{69} = -1.73664779343354$$
$$x_{51} = 0.26335220656646$$
$$x_{23} = 2.26335220656646$$
$$x_{27} = 4.26335220656646$$
$$x_{99} = 6.26335220656646$$
$$x_{97} = 8.26335220656646$$
$$x_{77} = 10.2633522065665$$
$$x_{55} = 12.2633522065665$$
$$x_{24} = 14.2633522065665$$
$$x_{54} = 16.2633522065665$$
$$x_{62} = 18.2633522065665$$
$$x_{31} = 20.2633522065665$$
$$x_{35} = 22.2633522065665$$
$$x_{58} = 24.2633522065665$$
$$x_{34} = 26.2633522065665$$
$$x_{11} = 28.2633522065665$$
$$x_{98} = 30.2633522065665$$
$$x_{22} = 32.2633522065665$$
$$x_{79} = 34.2633522065665$$
$$x_{66} = 36.2633522065665$$
$$x_{8} = 38.2633522065665$$
$$x_{10} = 40.2633522065665$$
$$x_{75} = 42.2633522065665$$
$$x_{89} = 44.2633522065665$$
$$x_{78} = 46.2633522065665$$
$$x_{13} = 48.2633522065665$$
$$x_{41} = 50.2633522065665$$
$$x_{87} = 52.2633522065665$$
$$x_{84} = 54.2633522065665$$
$$x_{65} = 56.2633522065665$$
$$x_{71} = 58.2633522065665$$
$$x_{100} = 60.2633522065665$$
$$x_{3} = 62.2633522065665$$
$$x_{76} = 64.2633522065665$$
$$x_{28} = 66.2633522065665$$
$$x_{64} = 68.2633522065665$$
$$x_{45} = 70.2633522065665$$
$$x_{63} = 72.2633522065665$$
$$x_{101} = 74.2633522065665$$
$$x_{96} = 76.2633522065665$$
$$x_{61} = 78.2633522065665$$
$$x_{17} = 80.2633522065665$$
$$x_{18} = 82.2633522065665$$
$$x_{56} = 84.2633522065665$$
$$x_{81} = 86.2633522065665$$
$$x_{59} = 88.2633522065665$$
$$x_{2} = 90.2633522065665$$
$$x_{42} = 92.2633522065665$$
$$x_{90} = 94.2633522065665$$
$$x_{53} = 96.2633522065665$$
$$x_{43} = 98.2633522065665$$
$$x_{74} = 100.263352206566$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{68}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{68} - \frac{1}{10}$$
=
$$-99.7366477934335 + - \frac{1}{10}$$
=
$$-99.8366477934335$$
lo sustituimos en la expresión
$$\frac{\pi \left|{\sin{\left(\pi x \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\pi x \right)}} < 1$$
$$\frac{\pi \left|{\sin{\left(\left(-99.8366477934335\right) \pi \right)}}\right|}{3 \cos^{\frac{2}{3}}{\left(\left(-99.8366477934335\right) \pi \right)}} < 1$$
-pi*sin(1.83664779343353*pi)
-----------------------------
2/3 < 1
3*cos (1.83664779343353*pi)
significa que una de las soluciones de nuestra ecuación será con:
$$x < -99.7366477934335$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------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-------
x68 x5 x52 x93 x33 x44 x47 x60 x7 x29 x20 x25 x50 x91 x73 x26 x48 x14 x85 x40 x19 x86 x6 x1 x37 x30 x38 x83 x49 x39 x70 x46 x16 x82 x72 x80 x95 x21 x4 x32 x92 x57 x12 x36 x9 x67 x15 x94 x88 x69 x51 x23 x27 x99 x97 x77 x55 x24 x54 x62 x31 x35 x58 x34 x11 x98 x22 x79 x66 x8 x10 x75 x89 x78 x13 x41 x87 x84 x65 x71 x100 x3 x76 x28 x64 x45 x63 x101 x96 x61 x17 x18 x56 x81 x59 x2 x42 x90 x53 x43 x74Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -99.7366477934335$$
$$x > -97.7366477934335 \wedge x < -95.7366477934335$$
$$x > -93.7366477934335 \wedge x < -91.7366477934335$$
$$x > -89.7366477934335 \wedge x < -87.7366477934335$$
$$x > -85.7366477934335 \wedge x < -83.7366477934335$$
$$x > -81.7366477934335 \wedge x < -79.7366477934335$$
$$x > -77.7366477934335 \wedge x < -75.7366477934335$$
$$x > -73.7366477934335 \wedge x < -71.7366477934335$$
$$x > -69.7366477934335 \wedge x < -67.7366477934335$$
$$x > -65.7366477934335 \wedge x < -63.7366477934335$$
$$x > -61.7366477934335 \wedge x < -59.7366477934335$$
$$x > -57.7366477934335 \wedge x < -55.7366477934335$$
$$x > -53.7366477934335 \wedge x < -51.7366477934335$$
$$x > -49.7366477934335 \wedge x < -47.7366477934335$$
$$x > -45.7366477934335 \wedge x < -43.7366477934335$$
$$x > -41.7366477934335 \wedge x < -39.7366477934335$$
$$x > -37.7366477934335 \wedge x < -35.7366477934335$$
$$x > -33.7366477934335 \wedge x < -31.7366477934335$$
$$x > -29.7366477934335 \wedge x < -27.7366477934335$$
$$x > -25.7366477934335 \wedge x < -23.7366477934335$$
$$x > -21.7366477934335 \wedge x < -19.7366477934335$$
$$x > -17.7366477934335 \wedge x < -15.7366477934335$$
$$x > -13.7366477934335 \wedge x < -11.7366477934335$$
$$x > -9.73664779343354 \wedge x < -7.73664779343354$$
$$x > -5.73664779343354 \wedge x < -3.73664779343354$$
$$x > -1.73664779343354 \wedge x < 0.26335220656646$$
$$x > 2.26335220656646 \wedge x < 4.26335220656646$$
$$x > 6.26335220656646 \wedge x < 8.26335220656646$$
$$x > 10.2633522065665 \wedge x < 12.2633522065665$$
$$x > 14.2633522065665 \wedge x < 16.2633522065665$$
$$x > 18.2633522065665 \wedge x < 20.2633522065665$$
$$x > 22.2633522065665 \wedge x < 24.2633522065665$$
$$x > 26.2633522065665 \wedge x < 28.2633522065665$$
$$x > 30.2633522065665 \wedge x < 32.2633522065665$$
$$x > 34.2633522065665 \wedge x < 36.2633522065665$$
$$x > 38.2633522065665 \wedge x < 40.2633522065665$$
$$x > 42.2633522065665 \wedge x < 44.2633522065665$$
$$x > 46.2633522065665 \wedge x < 48.2633522065665$$
$$x > 50.2633522065665 \wedge x < 52.2633522065665$$
$$x > 54.2633522065665 \wedge x < 56.2633522065665$$
$$x > 58.2633522065665 \wedge x < 60.2633522065665$$
$$x > 62.2633522065665 \wedge x < 64.2633522065665$$
$$x > 66.2633522065665 \wedge x < 68.2633522065665$$
$$x > 70.2633522065665 \wedge x < 72.2633522065665$$
$$x > 74.2633522065665 \wedge x < 76.2633522065665$$
$$x > 78.2633522065665 \wedge x < 80.2633522065665$$
$$x > 82.2633522065665 \wedge x < 84.2633522065665$$
$$x > 86.2633522065665 \wedge x < 88.2633522065665$$
$$x > 90.2633522065665 \wedge x < 92.2633522065665$$
$$x > 94.2633522065665 \wedge x < 96.2633522065665$$
$$x > 98.2633522065665 \wedge x < 100.263352206566$$
Solución de la desigualdad en el gráfico