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:
-
6-3x<19-(x-7)
-
x-1>x/(2-x)
-
-2x+5<=-3x-3
-
5x^2-8x+3>0
- Derivada de:
-
-1
- Límite de la función:
-
-1
- Forma canónica:
- -1
-
Expresiones idénticas
- cos(siete *p)/ cinco - uno <- uno
- coseno de (7 multiplicar por p) dividir por 5 menos 1 menos menos 1
- coseno de (siete multiplicar por p) dividir por cinco menos uno menos menos uno
- cos(7p)/5-1<-1
- cos7p/5-1<-1
- cos(7*p) dividir por 5-1<-1
-
Expresiones semejantes
- cos(7*p)/5-1<+1
- cos(7*p)/5+1<-1
-
Expresiones con funciones
- Coseno cos
- cos(pi/2-(3/x))>=1/2
- cos(x/2)+sqrt(2)/2>=0
- cos(x)>-2/2
- cos(x)>3\4
- cos^2x/2<3
cos(7*p)/5-1<-1 desigualdades
Solución
Ha introducido
[src]
cos(7*p) -------- - 1 < -1 5
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
cos(7*p)/5 - 1 < -1
Solución detallada
Se da la desigualdad:
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = -1$$
Resolvemos:
Tenemos la ecuación
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = -1$$
cambiamos
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = 0$$
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = 0$$
Sustituimos
$$w = \cos{\left(7 p \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{w}{5} = 1$$
Dividamos ambos miembros de la ecuación en 1/5
Obtenemos la respuesta: w = 5
hacemos cambio inverso
$$\cos{\left(7 p \right)} = w$$
sustituimos w:
$$x_{1} = -7.85398163397448$$
$$x_{2} = 78.3154168644884$$
$$x_{3} = 66.1978452006421$$
$$x_{4} = 41.9627018729494$$
$$x_{5} = 15.9323627432054$$
$$x_{6} = 30.2939291596159$$
$$x_{7} = -29.845130209103$$
$$x_{8} = -15.9323627432054$$
$$x_{9} = 85.9449990232065$$
$$x_{10} = 28.0499344070517$$
$$x_{11} = -47.7970882296161$$
$$x_{12} = 70.2370357552575$$
$$x_{13} = -81.905808468591$$
$$x_{14} = 58.1194640914112$$
$$x_{15} = 22.215548050385$$
$$x_{16} = -73.8274273593601$$
$$x_{17} = -35.6795165657698$$
$$x_{18} = -2.01959527730772$$
$$x_{19} = 24.0107438524363$$
$$x_{20} = -21.7667490998721$$
$$x_{21} = 50.0410829821803$$
$$x_{22} = -50.0410829821803$$
$$x_{23} = -94.0233801324374$$
$$x_{24} = -98.0625706870528$$
$$x_{25} = -24.0107438524363$$
$$x_{26} = -43.7578976750007$$
$$x_{27} = -85.9449990232065$$
$$x_{28} = -41.9627018729494$$
$$x_{29} = -6.05878583192317$$
$$x_{30} = 72.0322315573088$$
$$x_{31} = -87.7401948252578$$
$$x_{32} = 37.4747123678211$$
$$x_{33} = 4.26359002987186$$
$$x_{34} = 54.0802735367957$$
$$x_{35} = -89.9841895778219$$
$$x_{36} = 0.224399475256414$$
$$x_{37} = 67.9930410026934$$
$$x_{38} = 96.2673748850015$$
$$x_{39} = 52.2850777347444$$
$$x_{40} = 44.2066966255135$$
$$x_{41} = 48.245887180129$$
$$x_{42} = -55.875469338847$$
$$x_{43} = -39.7187071203852$$
$$x_{44} = 2.01959527730772$$
$$x_{45} = 26.2547386050004$$
$$x_{46} = 88.1889937757706$$
$$x_{47} = -77.8666179139756$$
$$x_{48} = -99.8577664891041$$
$$x_{49} = -65.7490462501292$$
$$x_{50} = 62.1586546460266$$
$$x_{51} = -72.0322315573088$$
$$x_{52} = 56.7730672398727$$
$$x_{53} = -3.81479107935903$$
$$x_{54} = 80.1106126665397$$
$$x_{55} = -13.6883679906412$$
$$x_{56} = -46.0018924275648$$
$$x_{57} = 46.0018924275648$$
$$x_{58} = 19.9715532978208$$
$$x_{59} = 32.0891249616672$$
$$x_{60} = -80.5594116170526$$
$$x_{61} = -67.9930410026934$$
$$x_{62} = -28.0499344070517$$
$$x_{63} = 98.0625706870528$$
$$x_{64} = 3.81479107935903$$
$$x_{65} = 10.0979763865386$$
$$x_{66} = -95.8185759344887$$
$$x_{67} = -91.7793853798732$$
$$x_{68} = -69.7882368047447$$
$$x_{69} = 18.1763574957695$$
$$x_{70} = 40.1675060708981$$
$$x_{71} = -83.7010042706423$$
$$x_{72} = 6.05878583192317$$
$$x_{73} = 8.30278058448731$$
$$x_{74} = -63.9538504480779$$
$$x_{75} = -61.7098556955138$$
$$x_{76} = 74.276226309873$$
$$x_{77} = -32.53792391218$$
$$x_{78} = -76.0714221119243$$
$$x_{79} = 100.306565439617$$
$$x_{80} = 89.9841895778219$$
$$x_{81} = -33.8843207637185$$
$$x_{82} = 76.0714221119243$$
$$x_{83} = -51.8362787842316$$
$$x_{84} = -19.9715532978208$$
$$x_{85} = -11.8931721885899$$
$$x_{86} = 36.1283155162826$$
$$x_{87} = 84.1498032211552$$
$$x_{88} = 94.0233801324374$$
$$x_{89} = -25.8059396544876$$
$$x_{90} = 92.2281843303861$$
$$x_{91} = -59.9146598934625$$
$$x_{92} = -17.7275585452567$$
$$x_{93} = -37.9235113183339$$
$$x_{94} = 14.1371669411541$$
$$x_{95} = 63.9538504480779$$
$$x_{1} = -7.85398163397448$$
$$x_{2} = 78.3154168644884$$
$$x_{3} = 66.1978452006421$$
$$x_{4} = 41.9627018729494$$
$$x_{5} = 15.9323627432054$$
$$x_{6} = 30.2939291596159$$
$$x_{7} = -29.845130209103$$
$$x_{8} = -15.9323627432054$$
$$x_{9} = 85.9449990232065$$
$$x_{10} = 28.0499344070517$$
$$x_{11} = -47.7970882296161$$
$$x_{12} = 70.2370357552575$$
$$x_{13} = -81.905808468591$$
$$x_{14} = 58.1194640914112$$
$$x_{15} = 22.215548050385$$
$$x_{16} = -73.8274273593601$$
$$x_{17} = -35.6795165657698$$
$$x_{18} = -2.01959527730772$$
$$x_{19} = 24.0107438524363$$
$$x_{20} = -21.7667490998721$$
$$x_{21} = 50.0410829821803$$
$$x_{22} = -50.0410829821803$$
$$x_{23} = -94.0233801324374$$
$$x_{24} = -98.0625706870528$$
$$x_{25} = -24.0107438524363$$
$$x_{26} = -43.7578976750007$$
$$x_{27} = -85.9449990232065$$
$$x_{28} = -41.9627018729494$$
$$x_{29} = -6.05878583192317$$
$$x_{30} = 72.0322315573088$$
$$x_{31} = -87.7401948252578$$
$$x_{32} = 37.4747123678211$$
$$x_{33} = 4.26359002987186$$
$$x_{34} = 54.0802735367957$$
$$x_{35} = -89.9841895778219$$
$$x_{36} = 0.224399475256414$$
$$x_{37} = 67.9930410026934$$
$$x_{38} = 96.2673748850015$$
$$x_{39} = 52.2850777347444$$
$$x_{40} = 44.2066966255135$$
$$x_{41} = 48.245887180129$$
$$x_{42} = -55.875469338847$$
$$x_{43} = -39.7187071203852$$
$$x_{44} = 2.01959527730772$$
$$x_{45} = 26.2547386050004$$
$$x_{46} = 88.1889937757706$$
$$x_{47} = -77.8666179139756$$
$$x_{48} = -99.8577664891041$$
$$x_{49} = -65.7490462501292$$
$$x_{50} = 62.1586546460266$$
$$x_{51} = -72.0322315573088$$
$$x_{52} = 56.7730672398727$$
$$x_{53} = -3.81479107935903$$
$$x_{54} = 80.1106126665397$$
$$x_{55} = -13.6883679906412$$
$$x_{56} = -46.0018924275648$$
$$x_{57} = 46.0018924275648$$
$$x_{58} = 19.9715532978208$$
$$x_{59} = 32.0891249616672$$
$$x_{60} = -80.5594116170526$$
$$x_{61} = -67.9930410026934$$
$$x_{62} = -28.0499344070517$$
$$x_{63} = 98.0625706870528$$
$$x_{64} = 3.81479107935903$$
$$x_{65} = 10.0979763865386$$
$$x_{66} = -95.8185759344887$$
$$x_{67} = -91.7793853798732$$
$$x_{68} = -69.7882368047447$$
$$x_{69} = 18.1763574957695$$
$$x_{70} = 40.1675060708981$$
$$x_{71} = -83.7010042706423$$
$$x_{72} = 6.05878583192317$$
$$x_{73} = 8.30278058448731$$
$$x_{74} = -63.9538504480779$$
$$x_{75} = -61.7098556955138$$
$$x_{76} = 74.276226309873$$
$$x_{77} = -32.53792391218$$
$$x_{78} = -76.0714221119243$$
$$x_{79} = 100.306565439617$$
$$x_{80} = 89.9841895778219$$
$$x_{81} = -33.8843207637185$$
$$x_{82} = 76.0714221119243$$
$$x_{83} = -51.8362787842316$$
$$x_{84} = -19.9715532978208$$
$$x_{85} = -11.8931721885899$$
$$x_{86} = 36.1283155162826$$
$$x_{87} = 84.1498032211552$$
$$x_{88} = 94.0233801324374$$
$$x_{89} = -25.8059396544876$$
$$x_{90} = 92.2281843303861$$
$$x_{91} = -59.9146598934625$$
$$x_{92} = -17.7275585452567$$
$$x_{93} = -37.9235113183339$$
$$x_{94} = 14.1371669411541$$
$$x_{95} = 63.9538504480779$$
Las raíces dadas
$$x_{48} = -99.8577664891041$$
$$x_{24} = -98.0625706870528$$
$$x_{66} = -95.8185759344887$$
$$x_{23} = -94.0233801324374$$
$$x_{67} = -91.7793853798732$$
$$x_{35} = -89.9841895778219$$
$$x_{31} = -87.7401948252578$$
$$x_{27} = -85.9449990232065$$
$$x_{71} = -83.7010042706423$$
$$x_{13} = -81.905808468591$$
$$x_{60} = -80.5594116170526$$
$$x_{47} = -77.8666179139756$$
$$x_{78} = -76.0714221119243$$
$$x_{16} = -73.8274273593601$$
$$x_{51} = -72.0322315573088$$
$$x_{68} = -69.7882368047447$$
$$x_{61} = -67.9930410026934$$
$$x_{49} = -65.7490462501292$$
$$x_{74} = -63.9538504480779$$
$$x_{75} = -61.7098556955138$$
$$x_{91} = -59.9146598934625$$
$$x_{42} = -55.875469338847$$
$$x_{83} = -51.8362787842316$$
$$x_{22} = -50.0410829821803$$
$$x_{11} = -47.7970882296161$$
$$x_{56} = -46.0018924275648$$
$$x_{26} = -43.7578976750007$$
$$x_{28} = -41.9627018729494$$
$$x_{43} = -39.7187071203852$$
$$x_{93} = -37.9235113183339$$
$$x_{17} = -35.6795165657698$$
$$x_{81} = -33.8843207637185$$
$$x_{77} = -32.53792391218$$
$$x_{7} = -29.845130209103$$
$$x_{62} = -28.0499344070517$$
$$x_{89} = -25.8059396544876$$
$$x_{25} = -24.0107438524363$$
$$x_{20} = -21.7667490998721$$
$$x_{84} = -19.9715532978208$$
$$x_{92} = -17.7275585452567$$
$$x_{8} = -15.9323627432054$$
$$x_{55} = -13.6883679906412$$
$$x_{85} = -11.8931721885899$$
$$x_{1} = -7.85398163397448$$
$$x_{29} = -6.05878583192317$$
$$x_{53} = -3.81479107935903$$
$$x_{18} = -2.01959527730772$$
$$x_{36} = 0.224399475256414$$
$$x_{44} = 2.01959527730772$$
$$x_{64} = 3.81479107935903$$
$$x_{33} = 4.26359002987186$$
$$x_{72} = 6.05878583192317$$
$$x_{73} = 8.30278058448731$$
$$x_{65} = 10.0979763865386$$
$$x_{94} = 14.1371669411541$$
$$x_{5} = 15.9323627432054$$
$$x_{69} = 18.1763574957695$$
$$x_{58} = 19.9715532978208$$
$$x_{15} = 22.215548050385$$
$$x_{19} = 24.0107438524363$$
$$x_{45} = 26.2547386050004$$
$$x_{10} = 28.0499344070517$$
$$x_{6} = 30.2939291596159$$
$$x_{59} = 32.0891249616672$$
$$x_{86} = 36.1283155162826$$
$$x_{32} = 37.4747123678211$$
$$x_{70} = 40.1675060708981$$
$$x_{4} = 41.9627018729494$$
$$x_{40} = 44.2066966255135$$
$$x_{57} = 46.0018924275648$$
$$x_{41} = 48.245887180129$$
$$x_{21} = 50.0410829821803$$
$$x_{39} = 52.2850777347444$$
$$x_{34} = 54.0802735367957$$
$$x_{52} = 56.7730672398727$$
$$x_{14} = 58.1194640914112$$
$$x_{50} = 62.1586546460266$$
$$x_{95} = 63.9538504480779$$
$$x_{3} = 66.1978452006421$$
$$x_{37} = 67.9930410026934$$
$$x_{12} = 70.2370357552575$$
$$x_{30} = 72.0322315573088$$
$$x_{76} = 74.276226309873$$
$$x_{82} = 76.0714221119243$$
$$x_{2} = 78.3154168644884$$
$$x_{54} = 80.1106126665397$$
$$x_{87} = 84.1498032211552$$
$$x_{9} = 85.9449990232065$$
$$x_{46} = 88.1889937757706$$
$$x_{80} = 89.9841895778219$$
$$x_{90} = 92.2281843303861$$
$$x_{88} = 94.0233801324374$$
$$x_{38} = 96.2673748850015$$
$$x_{63} = 98.0625706870528$$
$$x_{79} = 100.306565439617$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{48}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{48} - \frac{1}{10}$$
=
$$-99.8577664891041 + - \frac{1}{10}$$
=
$$-99.9577664891041$$
lo sustituimos en la expresión
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
Entonces
$$x < -99.8577664891041$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.8577664891041 \wedge x < -98.0625706870528$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.8577664891041 \wedge x < -98.0625706870528$$
$$x > -95.8185759344887 \wedge x < -94.0233801324374$$
$$x > -91.7793853798732 \wedge x < -89.9841895778219$$
$$x > -87.7401948252578 \wedge x < -85.9449990232065$$
$$x > -83.7010042706423 \wedge x < -81.905808468591$$
$$x > -80.5594116170526 \wedge x < -77.8666179139756$$
$$x > -76.0714221119243 \wedge x < -73.8274273593601$$
$$x > -72.0322315573088 \wedge x < -69.7882368047447$$
$$x > -67.9930410026934 \wedge x < -65.7490462501292$$
$$x > -63.9538504480779 \wedge x < -61.7098556955138$$
$$x > -59.9146598934625 \wedge x < -55.875469338847$$
$$x > -51.8362787842316 \wedge x < -50.0410829821803$$
$$x > -47.7970882296161 \wedge x < -46.0018924275648$$
$$x > -43.7578976750007 \wedge x < -41.9627018729494$$
$$x > -39.7187071203852 \wedge x < -37.9235113183339$$
$$x > -35.6795165657698 \wedge x < -33.8843207637185$$
$$x > -32.53792391218 \wedge x < -29.845130209103$$
$$x > -28.0499344070517 \wedge x < -25.8059396544876$$
$$x > -24.0107438524363 \wedge x < -21.7667490998721$$
$$x > -19.9715532978208 \wedge x < -17.7275585452567$$
$$x > -15.9323627432054 \wedge x < -13.6883679906412$$
$$x > -11.8931721885899 \wedge x < -7.85398163397448$$
$$x > -6.05878583192317 \wedge x < -3.81479107935903$$
$$x > -2.01959527730772 \wedge x < 0.224399475256414$$
$$x > 2.01959527730772 \wedge x < 3.81479107935903$$
$$x > 4.26359002987186 \wedge x < 6.05878583192317$$
$$x > 8.30278058448731 \wedge x < 10.0979763865386$$
$$x > 14.1371669411541 \wedge x < 15.9323627432054$$
$$x > 18.1763574957695 \wedge x < 19.9715532978208$$
$$x > 22.215548050385 \wedge x < 24.0107438524363$$
$$x > 26.2547386050004 \wedge x < 28.0499344070517$$
$$x > 30.2939291596159 \wedge x < 32.0891249616672$$
$$x > 36.1283155162826 \wedge x < 37.4747123678211$$
$$x > 40.1675060708981 \wedge x < 41.9627018729494$$
$$x > 44.2066966255135 \wedge x < 46.0018924275648$$
$$x > 48.245887180129 \wedge x < 50.0410829821803$$
$$x > 52.2850777347444 \wedge x < 54.0802735367957$$
$$x > 56.7730672398727 \wedge x < 58.1194640914112$$
$$x > 62.1586546460266 \wedge x < 63.9538504480779$$
$$x > 66.1978452006421 \wedge x < 67.9930410026934$$
$$x > 70.2370357552575 \wedge x < 72.0322315573088$$
$$x > 74.276226309873 \wedge x < 76.0714221119243$$
$$x > 78.3154168644884 \wedge x < 80.1106126665397$$
$$x > 84.1498032211552 \wedge x < 85.9449990232065$$
$$x > 88.1889937757706 \wedge x < 89.9841895778219$$
$$x > 92.2281843303861 \wedge x < 94.0233801324374$$
$$x > 96.2673748850015 \wedge x < 98.0625706870528$$
$$x > 100.306565439617$$
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = -1$$
Resolvemos:
Tenemos la ecuación
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = -1$$
cambiamos
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = 0$$
$$\frac{\cos{\left(7 p \right)}}{5} - 1 = 0$$
Sustituimos
$$w = \cos{\left(7 p \right)}$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$\frac{w}{5} = 1$$
Dividamos ambos miembros de la ecuación en 1/5
w = 1 / (1/5)
Obtenemos la respuesta: w = 5
hacemos cambio inverso
$$\cos{\left(7 p \right)} = w$$
sustituimos w:
$$x_{1} = -7.85398163397448$$
$$x_{2} = 78.3154168644884$$
$$x_{3} = 66.1978452006421$$
$$x_{4} = 41.9627018729494$$
$$x_{5} = 15.9323627432054$$
$$x_{6} = 30.2939291596159$$
$$x_{7} = -29.845130209103$$
$$x_{8} = -15.9323627432054$$
$$x_{9} = 85.9449990232065$$
$$x_{10} = 28.0499344070517$$
$$x_{11} = -47.7970882296161$$
$$x_{12} = 70.2370357552575$$
$$x_{13} = -81.905808468591$$
$$x_{14} = 58.1194640914112$$
$$x_{15} = 22.215548050385$$
$$x_{16} = -73.8274273593601$$
$$x_{17} = -35.6795165657698$$
$$x_{18} = -2.01959527730772$$
$$x_{19} = 24.0107438524363$$
$$x_{20} = -21.7667490998721$$
$$x_{21} = 50.0410829821803$$
$$x_{22} = -50.0410829821803$$
$$x_{23} = -94.0233801324374$$
$$x_{24} = -98.0625706870528$$
$$x_{25} = -24.0107438524363$$
$$x_{26} = -43.7578976750007$$
$$x_{27} = -85.9449990232065$$
$$x_{28} = -41.9627018729494$$
$$x_{29} = -6.05878583192317$$
$$x_{30} = 72.0322315573088$$
$$x_{31} = -87.7401948252578$$
$$x_{32} = 37.4747123678211$$
$$x_{33} = 4.26359002987186$$
$$x_{34} = 54.0802735367957$$
$$x_{35} = -89.9841895778219$$
$$x_{36} = 0.224399475256414$$
$$x_{37} = 67.9930410026934$$
$$x_{38} = 96.2673748850015$$
$$x_{39} = 52.2850777347444$$
$$x_{40} = 44.2066966255135$$
$$x_{41} = 48.245887180129$$
$$x_{42} = -55.875469338847$$
$$x_{43} = -39.7187071203852$$
$$x_{44} = 2.01959527730772$$
$$x_{45} = 26.2547386050004$$
$$x_{46} = 88.1889937757706$$
$$x_{47} = -77.8666179139756$$
$$x_{48} = -99.8577664891041$$
$$x_{49} = -65.7490462501292$$
$$x_{50} = 62.1586546460266$$
$$x_{51} = -72.0322315573088$$
$$x_{52} = 56.7730672398727$$
$$x_{53} = -3.81479107935903$$
$$x_{54} = 80.1106126665397$$
$$x_{55} = -13.6883679906412$$
$$x_{56} = -46.0018924275648$$
$$x_{57} = 46.0018924275648$$
$$x_{58} = 19.9715532978208$$
$$x_{59} = 32.0891249616672$$
$$x_{60} = -80.5594116170526$$
$$x_{61} = -67.9930410026934$$
$$x_{62} = -28.0499344070517$$
$$x_{63} = 98.0625706870528$$
$$x_{64} = 3.81479107935903$$
$$x_{65} = 10.0979763865386$$
$$x_{66} = -95.8185759344887$$
$$x_{67} = -91.7793853798732$$
$$x_{68} = -69.7882368047447$$
$$x_{69} = 18.1763574957695$$
$$x_{70} = 40.1675060708981$$
$$x_{71} = -83.7010042706423$$
$$x_{72} = 6.05878583192317$$
$$x_{73} = 8.30278058448731$$
$$x_{74} = -63.9538504480779$$
$$x_{75} = -61.7098556955138$$
$$x_{76} = 74.276226309873$$
$$x_{77} = -32.53792391218$$
$$x_{78} = -76.0714221119243$$
$$x_{79} = 100.306565439617$$
$$x_{80} = 89.9841895778219$$
$$x_{81} = -33.8843207637185$$
$$x_{82} = 76.0714221119243$$
$$x_{83} = -51.8362787842316$$
$$x_{84} = -19.9715532978208$$
$$x_{85} = -11.8931721885899$$
$$x_{86} = 36.1283155162826$$
$$x_{87} = 84.1498032211552$$
$$x_{88} = 94.0233801324374$$
$$x_{89} = -25.8059396544876$$
$$x_{90} = 92.2281843303861$$
$$x_{91} = -59.9146598934625$$
$$x_{92} = -17.7275585452567$$
$$x_{93} = -37.9235113183339$$
$$x_{94} = 14.1371669411541$$
$$x_{95} = 63.9538504480779$$
$$x_{1} = -7.85398163397448$$
$$x_{2} = 78.3154168644884$$
$$x_{3} = 66.1978452006421$$
$$x_{4} = 41.9627018729494$$
$$x_{5} = 15.9323627432054$$
$$x_{6} = 30.2939291596159$$
$$x_{7} = -29.845130209103$$
$$x_{8} = -15.9323627432054$$
$$x_{9} = 85.9449990232065$$
$$x_{10} = 28.0499344070517$$
$$x_{11} = -47.7970882296161$$
$$x_{12} = 70.2370357552575$$
$$x_{13} = -81.905808468591$$
$$x_{14} = 58.1194640914112$$
$$x_{15} = 22.215548050385$$
$$x_{16} = -73.8274273593601$$
$$x_{17} = -35.6795165657698$$
$$x_{18} = -2.01959527730772$$
$$x_{19} = 24.0107438524363$$
$$x_{20} = -21.7667490998721$$
$$x_{21} = 50.0410829821803$$
$$x_{22} = -50.0410829821803$$
$$x_{23} = -94.0233801324374$$
$$x_{24} = -98.0625706870528$$
$$x_{25} = -24.0107438524363$$
$$x_{26} = -43.7578976750007$$
$$x_{27} = -85.9449990232065$$
$$x_{28} = -41.9627018729494$$
$$x_{29} = -6.05878583192317$$
$$x_{30} = 72.0322315573088$$
$$x_{31} = -87.7401948252578$$
$$x_{32} = 37.4747123678211$$
$$x_{33} = 4.26359002987186$$
$$x_{34} = 54.0802735367957$$
$$x_{35} = -89.9841895778219$$
$$x_{36} = 0.224399475256414$$
$$x_{37} = 67.9930410026934$$
$$x_{38} = 96.2673748850015$$
$$x_{39} = 52.2850777347444$$
$$x_{40} = 44.2066966255135$$
$$x_{41} = 48.245887180129$$
$$x_{42} = -55.875469338847$$
$$x_{43} = -39.7187071203852$$
$$x_{44} = 2.01959527730772$$
$$x_{45} = 26.2547386050004$$
$$x_{46} = 88.1889937757706$$
$$x_{47} = -77.8666179139756$$
$$x_{48} = -99.8577664891041$$
$$x_{49} = -65.7490462501292$$
$$x_{50} = 62.1586546460266$$
$$x_{51} = -72.0322315573088$$
$$x_{52} = 56.7730672398727$$
$$x_{53} = -3.81479107935903$$
$$x_{54} = 80.1106126665397$$
$$x_{55} = -13.6883679906412$$
$$x_{56} = -46.0018924275648$$
$$x_{57} = 46.0018924275648$$
$$x_{58} = 19.9715532978208$$
$$x_{59} = 32.0891249616672$$
$$x_{60} = -80.5594116170526$$
$$x_{61} = -67.9930410026934$$
$$x_{62} = -28.0499344070517$$
$$x_{63} = 98.0625706870528$$
$$x_{64} = 3.81479107935903$$
$$x_{65} = 10.0979763865386$$
$$x_{66} = -95.8185759344887$$
$$x_{67} = -91.7793853798732$$
$$x_{68} = -69.7882368047447$$
$$x_{69} = 18.1763574957695$$
$$x_{70} = 40.1675060708981$$
$$x_{71} = -83.7010042706423$$
$$x_{72} = 6.05878583192317$$
$$x_{73} = 8.30278058448731$$
$$x_{74} = -63.9538504480779$$
$$x_{75} = -61.7098556955138$$
$$x_{76} = 74.276226309873$$
$$x_{77} = -32.53792391218$$
$$x_{78} = -76.0714221119243$$
$$x_{79} = 100.306565439617$$
$$x_{80} = 89.9841895778219$$
$$x_{81} = -33.8843207637185$$
$$x_{82} = 76.0714221119243$$
$$x_{83} = -51.8362787842316$$
$$x_{84} = -19.9715532978208$$
$$x_{85} = -11.8931721885899$$
$$x_{86} = 36.1283155162826$$
$$x_{87} = 84.1498032211552$$
$$x_{88} = 94.0233801324374$$
$$x_{89} = -25.8059396544876$$
$$x_{90} = 92.2281843303861$$
$$x_{91} = -59.9146598934625$$
$$x_{92} = -17.7275585452567$$
$$x_{93} = -37.9235113183339$$
$$x_{94} = 14.1371669411541$$
$$x_{95} = 63.9538504480779$$
Las raíces dadas
$$x_{48} = -99.8577664891041$$
$$x_{24} = -98.0625706870528$$
$$x_{66} = -95.8185759344887$$
$$x_{23} = -94.0233801324374$$
$$x_{67} = -91.7793853798732$$
$$x_{35} = -89.9841895778219$$
$$x_{31} = -87.7401948252578$$
$$x_{27} = -85.9449990232065$$
$$x_{71} = -83.7010042706423$$
$$x_{13} = -81.905808468591$$
$$x_{60} = -80.5594116170526$$
$$x_{47} = -77.8666179139756$$
$$x_{78} = -76.0714221119243$$
$$x_{16} = -73.8274273593601$$
$$x_{51} = -72.0322315573088$$
$$x_{68} = -69.7882368047447$$
$$x_{61} = -67.9930410026934$$
$$x_{49} = -65.7490462501292$$
$$x_{74} = -63.9538504480779$$
$$x_{75} = -61.7098556955138$$
$$x_{91} = -59.9146598934625$$
$$x_{42} = -55.875469338847$$
$$x_{83} = -51.8362787842316$$
$$x_{22} = -50.0410829821803$$
$$x_{11} = -47.7970882296161$$
$$x_{56} = -46.0018924275648$$
$$x_{26} = -43.7578976750007$$
$$x_{28} = -41.9627018729494$$
$$x_{43} = -39.7187071203852$$
$$x_{93} = -37.9235113183339$$
$$x_{17} = -35.6795165657698$$
$$x_{81} = -33.8843207637185$$
$$x_{77} = -32.53792391218$$
$$x_{7} = -29.845130209103$$
$$x_{62} = -28.0499344070517$$
$$x_{89} = -25.8059396544876$$
$$x_{25} = -24.0107438524363$$
$$x_{20} = -21.7667490998721$$
$$x_{84} = -19.9715532978208$$
$$x_{92} = -17.7275585452567$$
$$x_{8} = -15.9323627432054$$
$$x_{55} = -13.6883679906412$$
$$x_{85} = -11.8931721885899$$
$$x_{1} = -7.85398163397448$$
$$x_{29} = -6.05878583192317$$
$$x_{53} = -3.81479107935903$$
$$x_{18} = -2.01959527730772$$
$$x_{36} = 0.224399475256414$$
$$x_{44} = 2.01959527730772$$
$$x_{64} = 3.81479107935903$$
$$x_{33} = 4.26359002987186$$
$$x_{72} = 6.05878583192317$$
$$x_{73} = 8.30278058448731$$
$$x_{65} = 10.0979763865386$$
$$x_{94} = 14.1371669411541$$
$$x_{5} = 15.9323627432054$$
$$x_{69} = 18.1763574957695$$
$$x_{58} = 19.9715532978208$$
$$x_{15} = 22.215548050385$$
$$x_{19} = 24.0107438524363$$
$$x_{45} = 26.2547386050004$$
$$x_{10} = 28.0499344070517$$
$$x_{6} = 30.2939291596159$$
$$x_{59} = 32.0891249616672$$
$$x_{86} = 36.1283155162826$$
$$x_{32} = 37.4747123678211$$
$$x_{70} = 40.1675060708981$$
$$x_{4} = 41.9627018729494$$
$$x_{40} = 44.2066966255135$$
$$x_{57} = 46.0018924275648$$
$$x_{41} = 48.245887180129$$
$$x_{21} = 50.0410829821803$$
$$x_{39} = 52.2850777347444$$
$$x_{34} = 54.0802735367957$$
$$x_{52} = 56.7730672398727$$
$$x_{14} = 58.1194640914112$$
$$x_{50} = 62.1586546460266$$
$$x_{95} = 63.9538504480779$$
$$x_{3} = 66.1978452006421$$
$$x_{37} = 67.9930410026934$$
$$x_{12} = 70.2370357552575$$
$$x_{30} = 72.0322315573088$$
$$x_{76} = 74.276226309873$$
$$x_{82} = 76.0714221119243$$
$$x_{2} = 78.3154168644884$$
$$x_{54} = 80.1106126665397$$
$$x_{87} = 84.1498032211552$$
$$x_{9} = 85.9449990232065$$
$$x_{46} = 88.1889937757706$$
$$x_{80} = 89.9841895778219$$
$$x_{90} = 92.2281843303861$$
$$x_{88} = 94.0233801324374$$
$$x_{38} = 96.2673748850015$$
$$x_{63} = 98.0625706870528$$
$$x_{79} = 100.306565439617$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{48}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{48} - \frac{1}{10}$$
=
$$-99.8577664891041 + - \frac{1}{10}$$
=
$$-99.9577664891041$$
lo sustituimos en la expresión
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
$$\frac{\cos{\left(7 p \right)}}{5} - 1 < -1$$
cos(7*p)
-1 + -------- < -1
5 Entonces
$$x < -99.8577664891041$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x > -99.8577664891041 \wedge x < -98.0625706870528$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------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-------
x48 x24 x66 x23 x67 x35 x31 x27 x71 x13 x60 x47 x78 x16 x51 x68 x61 x49 x74 x75 x91 x42 x83 x22 x11 x56 x26 x28 x43 x93 x17 x81 x77 x7 x62 x89 x25 x20 x84 x92 x8 x55 x85 x1 x29 x53 x18 x36 x44 x64 x33 x72 x73 x65 x94 x5 x69 x58 x15 x19 x45 x10 x6 x59 x86 x32 x70 x4 x40 x57 x41 x21 x39 x34 x52 x14 x50 x95 x3 x37 x12 x30 x76 x82 x2 x54 x87 x9 x46 x80 x90 x88 x38 x63 x79Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x > -99.8577664891041 \wedge x < -98.0625706870528$$
$$x > -95.8185759344887 \wedge x < -94.0233801324374$$
$$x > -91.7793853798732 \wedge x < -89.9841895778219$$
$$x > -87.7401948252578 \wedge x < -85.9449990232065$$
$$x > -83.7010042706423 \wedge x < -81.905808468591$$
$$x > -80.5594116170526 \wedge x < -77.8666179139756$$
$$x > -76.0714221119243 \wedge x < -73.8274273593601$$
$$x > -72.0322315573088 \wedge x < -69.7882368047447$$
$$x > -67.9930410026934 \wedge x < -65.7490462501292$$
$$x > -63.9538504480779 \wedge x < -61.7098556955138$$
$$x > -59.9146598934625 \wedge x < -55.875469338847$$
$$x > -51.8362787842316 \wedge x < -50.0410829821803$$
$$x > -47.7970882296161 \wedge x < -46.0018924275648$$
$$x > -43.7578976750007 \wedge x < -41.9627018729494$$
$$x > -39.7187071203852 \wedge x < -37.9235113183339$$
$$x > -35.6795165657698 \wedge x < -33.8843207637185$$
$$x > -32.53792391218 \wedge x < -29.845130209103$$
$$x > -28.0499344070517 \wedge x < -25.8059396544876$$
$$x > -24.0107438524363 \wedge x < -21.7667490998721$$
$$x > -19.9715532978208 \wedge x < -17.7275585452567$$
$$x > -15.9323627432054 \wedge x < -13.6883679906412$$
$$x > -11.8931721885899 \wedge x < -7.85398163397448$$
$$x > -6.05878583192317 \wedge x < -3.81479107935903$$
$$x > -2.01959527730772 \wedge x < 0.224399475256414$$
$$x > 2.01959527730772 \wedge x < 3.81479107935903$$
$$x > 4.26359002987186 \wedge x < 6.05878583192317$$
$$x > 8.30278058448731 \wedge x < 10.0979763865386$$
$$x > 14.1371669411541 \wedge x < 15.9323627432054$$
$$x > 18.1763574957695 \wedge x < 19.9715532978208$$
$$x > 22.215548050385 \wedge x < 24.0107438524363$$
$$x > 26.2547386050004 \wedge x < 28.0499344070517$$
$$x > 30.2939291596159 \wedge x < 32.0891249616672$$
$$x > 36.1283155162826 \wedge x < 37.4747123678211$$
$$x > 40.1675060708981 \wedge x < 41.9627018729494$$
$$x > 44.2066966255135 \wedge x < 46.0018924275648$$
$$x > 48.245887180129 \wedge x < 50.0410829821803$$
$$x > 52.2850777347444 \wedge x < 54.0802735367957$$
$$x > 56.7730672398727 \wedge x < 58.1194640914112$$
$$x > 62.1586546460266 \wedge x < 63.9538504480779$$
$$x > 66.1978452006421 \wedge x < 67.9930410026934$$
$$x > 70.2370357552575 \wedge x < 72.0322315573088$$
$$x > 74.276226309873 \wedge x < 76.0714221119243$$
$$x > 78.3154168644884 \wedge x < 80.1106126665397$$
$$x > 84.1498032211552 \wedge x < 85.9449990232065$$
$$x > 88.1889937757706 \wedge x < 89.9841895778219$$
$$x > 92.2281843303861 \wedge x < 94.0233801324374$$
$$x > 96.2673748850015 \wedge x < 98.0625706870528$$
$$x > 100.306565439617$$