Sr Examen
Otras calculadoras
- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
-
(x+4)*(x-2)<0
-
x^2-17x+72<0
- (4-x)/(x-5)>=1/(1-x)
-
x-5/4-x+1/3>2
- Gráfico de la función y =:
- abs(cos(x))
- Derivada de:
-
1/2
- Suma de la serie:
-
1/2
- Límite de la función:
-
1/2
-
Expresiones idénticas
- abs(cos(x))< uno / dos
- abs( coseno de (x)) menos 1 dividir por 2
- abs( coseno de (x)) menos uno dividir por dos
- abscosx<1/2
- abs(cos(x))<1 dividir por 2
-
Expresiones semejantes
- abs(cosx)<1/2
-
Expresiones con funciones
- abs
- abs(x-3)*(abs(x-4)+abs(x+5)-abs(2x+1))<=0
- abs(x^2-6x)>7
- abs(sin(3*x-pi/10))<=1
- abs(2*x*x)<1
- abs(2*x+4)<=abs(x+3)-1
- Coseno cos
- cos2x<1/2
- cos5x<1/2
- cos(x)<=-√2/2
- cos(x)<0,5
- cos(x)>=sqrt(3)/2
abs(cos(x))<1/2 desigualdades
Solución
Ha introducido
[src]
|cos(x)| < 1/2
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
Abs(cos(x)) < 1/2
Solución detallada
Se da la desigualdad:
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
cambiamos
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
Sustituimos
$$w = \left|{\cos{\left(x \right)}}\right|$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\left|{\cos{\left(x \right)}}\right| = w$$
sustituimos w:
$$x_{1} = -93.2005820564972$$
$$x_{2} = -68.0678408277789$$
$$x_{3} = -79.5870138909414$$
$$x_{4} = 63.8790506229925$$
$$x_{5} = 82.7286065445312$$
$$x_{6} = -85.870199198121$$
$$x_{7} = -4.18879020478639$$
$$x_{8} = 74.3510261349584$$
$$x_{9} = 61.7846555205993$$
$$x_{10} = -35.6047167406843$$
$$x_{11} = 2.0943951023932$$
$$x_{12} = 33.5103216382911$$
$$x_{13} = -76.4454212373516$$
$$x_{14} = -32.4631240870945$$
$$x_{15} = 30.3687289847013$$
$$x_{16} = -63.8790506229925$$
$$x_{17} = 39.7935069454707$$
$$x_{18} = -70.162235930172$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 269.129770657526$$
$$x_{21} = 38.7463093942741$$
$$x_{22} = 76.4454212373516$$
$$x_{23} = -39.7935069454707$$
$$x_{24} = -77.4926187885482$$
$$x_{25} = -96.342174710087$$
$$x_{26} = 85.870199198121$$
$$x_{27} = 98.4365698124802$$
$$x_{28} = -24.0855436775217$$
$$x_{29} = -90.0589894029074$$
$$x_{30} = -41.8879020478639$$
$$x_{31} = -673.348025419412$$
$$x_{32} = 60.7374579694027$$
$$x_{33} = 90.0589894029074$$
$$x_{34} = 275.412955964705$$
$$x_{35} = -2.0943951023932$$
$$x_{36} = 41.8879020478639$$
$$x_{37} = -74.3510261349584$$
$$x_{38} = 26.1799387799149$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -61.7846555205993$$
$$x_{41} = 68.0678408277789$$
$$x_{42} = -13.6135681655558$$
$$x_{43} = -55.5014702134197$$
$$x_{44} = -30.3687289847013$$
$$x_{45} = 77.4926187885482$$
$$x_{46} = -26.1799387799149$$
$$x_{47} = 8.37758040957278$$
$$x_{48} = 52.3598775598299$$
$$x_{49} = -46.0766922526503$$
$$x_{50} = -33.5103216382911$$
$$x_{51} = 16.7551608191456$$
$$x_{52} = -60.7374579694027$$
$$x_{53} = -99.4837673636768$$
$$x_{54} = -27.2271363311115$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 96.342174710087$$
$$x_{57} = -11.5191730631626$$
$$x_{58} = -83.7758040957278$$
$$x_{59} = -54.4542726622231$$
$$x_{60} = 3803.42150594604$$
$$x_{61} = 19.8967534727354$$
$$x_{62} = 48.1710873550435$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = -10.471975511966$$
$$x_{65} = 4.18879020478639$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = 11.5191730631626$$
$$x_{68} = 83.7758040957278$$
$$x_{69} = -42.9350995990605$$
$$x_{70} = -71.2094334813686$$
$$x_{71} = -19.8967534727354$$
$$x_{72} = 54.4542726622231$$
$$x_{73} = 99.4837673636768$$
$$x_{74} = 92.1533845053006$$
$$x_{75} = -48.1710873550435$$
$$x_{76} = 46.0766922526503$$
$$x_{77} = 24.0855436775217$$
$$x_{78} = 10.471975511966$$
$$x_{79} = 17.8023583703422$$
$$x_{80} = -17.8023583703422$$
$$x_{81} = -57.5958653158129$$
$$x_{82} = -92.1533845053006$$
$$x_{83} = -52.3598775598299$$
$$x_{84} = -98.4365698124802$$
$$x_{1} = -93.2005820564972$$
$$x_{2} = -68.0678408277789$$
$$x_{3} = -79.5870138909414$$
$$x_{4} = 63.8790506229925$$
$$x_{5} = 82.7286065445312$$
$$x_{6} = -85.870199198121$$
$$x_{7} = -4.18879020478639$$
$$x_{8} = 74.3510261349584$$
$$x_{9} = 61.7846555205993$$
$$x_{10} = -35.6047167406843$$
$$x_{11} = 2.0943951023932$$
$$x_{12} = 33.5103216382911$$
$$x_{13} = -76.4454212373516$$
$$x_{14} = -32.4631240870945$$
$$x_{15} = 30.3687289847013$$
$$x_{16} = -63.8790506229925$$
$$x_{17} = 39.7935069454707$$
$$x_{18} = -70.162235930172$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 269.129770657526$$
$$x_{21} = 38.7463093942741$$
$$x_{22} = 76.4454212373516$$
$$x_{23} = -39.7935069454707$$
$$x_{24} = -77.4926187885482$$
$$x_{25} = -96.342174710087$$
$$x_{26} = 85.870199198121$$
$$x_{27} = 98.4365698124802$$
$$x_{28} = -24.0855436775217$$
$$x_{29} = -90.0589894029074$$
$$x_{30} = -41.8879020478639$$
$$x_{31} = -673.348025419412$$
$$x_{32} = 60.7374579694027$$
$$x_{33} = 90.0589894029074$$
$$x_{34} = 275.412955964705$$
$$x_{35} = -2.0943951023932$$
$$x_{36} = 41.8879020478639$$
$$x_{37} = -74.3510261349584$$
$$x_{38} = 26.1799387799149$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -61.7846555205993$$
$$x_{41} = 68.0678408277789$$
$$x_{42} = -13.6135681655558$$
$$x_{43} = -55.5014702134197$$
$$x_{44} = -30.3687289847013$$
$$x_{45} = 77.4926187885482$$
$$x_{46} = -26.1799387799149$$
$$x_{47} = 8.37758040957278$$
$$x_{48} = 52.3598775598299$$
$$x_{49} = -46.0766922526503$$
$$x_{50} = -33.5103216382911$$
$$x_{51} = 16.7551608191456$$
$$x_{52} = -60.7374579694027$$
$$x_{53} = -99.4837673636768$$
$$x_{54} = -27.2271363311115$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 96.342174710087$$
$$x_{57} = -11.5191730631626$$
$$x_{58} = -83.7758040957278$$
$$x_{59} = -54.4542726622231$$
$$x_{60} = 3803.42150594604$$
$$x_{61} = 19.8967534727354$$
$$x_{62} = 48.1710873550435$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = -10.471975511966$$
$$x_{65} = 4.18879020478639$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = 11.5191730631626$$
$$x_{68} = 83.7758040957278$$
$$x_{69} = -42.9350995990605$$
$$x_{70} = -71.2094334813686$$
$$x_{71} = -19.8967534727354$$
$$x_{72} = 54.4542726622231$$
$$x_{73} = 99.4837673636768$$
$$x_{74} = 92.1533845053006$$
$$x_{75} = -48.1710873550435$$
$$x_{76} = 46.0766922526503$$
$$x_{77} = 24.0855436775217$$
$$x_{78} = 10.471975511966$$
$$x_{79} = 17.8023583703422$$
$$x_{80} = -17.8023583703422$$
$$x_{81} = -57.5958653158129$$
$$x_{82} = -92.1533845053006$$
$$x_{83} = -52.3598775598299$$
$$x_{84} = -98.4365698124802$$
Las raíces dadas
$$x_{31} = -673.348025419412$$
$$x_{53} = -99.4837673636768$$
$$x_{84} = -98.4365698124802$$
$$x_{25} = -96.342174710087$$
$$x_{1} = -93.2005820564972$$
$$x_{82} = -92.1533845053006$$
$$x_{29} = -90.0589894029074$$
$$x_{6} = -85.870199198121$$
$$x_{58} = -83.7758040957278$$
$$x_{3} = -79.5870138909414$$
$$x_{24} = -77.4926187885482$$
$$x_{13} = -76.4454212373516$$
$$x_{37} = -74.3510261349584$$
$$x_{70} = -71.2094334813686$$
$$x_{18} = -70.162235930172$$
$$x_{2} = -68.0678408277789$$
$$x_{16} = -63.8790506229925$$
$$x_{40} = -61.7846555205993$$
$$x_{52} = -60.7374579694027$$
$$x_{81} = -57.5958653158129$$
$$x_{43} = -55.5014702134197$$
$$x_{59} = -54.4542726622231$$
$$x_{83} = -52.3598775598299$$
$$x_{63} = -49.2182849062401$$
$$x_{75} = -48.1710873550435$$
$$x_{49} = -46.0766922526503$$
$$x_{69} = -42.9350995990605$$
$$x_{30} = -41.8879020478639$$
$$x_{23} = -39.7935069454707$$
$$x_{10} = -35.6047167406843$$
$$x_{50} = -33.5103216382911$$
$$x_{14} = -32.4631240870945$$
$$x_{44} = -30.3687289847013$$
$$x_{54} = -27.2271363311115$$
$$x_{46} = -26.1799387799149$$
$$x_{28} = -24.0855436775217$$
$$x_{71} = -19.8967534727354$$
$$x_{80} = -17.8023583703422$$
$$x_{42} = -13.6135681655558$$
$$x_{57} = -11.5191730631626$$
$$x_{64} = -10.471975511966$$
$$x_{55} = -5.23598775598299$$
$$x_{7} = -4.18879020478639$$
$$x_{35} = -2.0943951023932$$
$$x_{11} = 2.0943951023932$$
$$x_{65} = 4.18879020478639$$
$$x_{47} = 8.37758040957278$$
$$x_{78} = 10.471975511966$$
$$x_{67} = 11.5191730631626$$
$$x_{51} = 16.7551608191456$$
$$x_{79} = 17.8023583703422$$
$$x_{61} = 19.8967534727354$$
$$x_{77} = 24.0855436775217$$
$$x_{38} = 26.1799387799149$$
$$x_{15} = 30.3687289847013$$
$$x_{66} = 32.4631240870945$$
$$x_{12} = 33.5103216382911$$
$$x_{21} = 38.7463093942741$$
$$x_{17} = 39.7935069454707$$
$$x_{36} = 41.8879020478639$$
$$x_{76} = 46.0766922526503$$
$$x_{62} = 48.1710873550435$$
$$x_{48} = 52.3598775598299$$
$$x_{72} = 54.4542726622231$$
$$x_{39} = 55.5014702134197$$
$$x_{32} = 60.7374579694027$$
$$x_{9} = 61.7846555205993$$
$$x_{4} = 63.8790506229925$$
$$x_{41} = 68.0678408277789$$
$$x_{19} = 70.162235930172$$
$$x_{8} = 74.3510261349584$$
$$x_{22} = 76.4454212373516$$
$$x_{45} = 77.4926187885482$$
$$x_{5} = 82.7286065445312$$
$$x_{68} = 83.7758040957278$$
$$x_{26} = 85.870199198121$$
$$x_{33} = 90.0589894029074$$
$$x_{74} = 92.1533845053006$$
$$x_{56} = 96.342174710087$$
$$x_{27} = 98.4365698124802$$
$$x_{73} = 99.4837673636768$$
$$x_{20} = 269.129770657526$$
$$x_{34} = 275.412955964705$$
$$x_{60} = 3803.42150594604$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{31}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{31} - \frac{1}{10}$$
=
$$-673.348025419412 + - \frac{1}{10}$$
=
$$-673.448025419412$$
lo sustituimos en la expresión
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
$$\left|{\cos{\left(-673.448025419412 \right)}}\right| < \frac{1}{2}$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -673.348025419412$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -673.348025419412$$
$$x > -99.4837673636768 \wedge x < -98.4365698124802$$
$$x > -96.342174710087 \wedge x < -93.2005820564972$$
$$x > -92.1533845053006 \wedge x < -90.0589894029074$$
$$x > -85.870199198121 \wedge x < -83.7758040957278$$
$$x > -79.5870138909414 \wedge x < -77.4926187885482$$
$$x > -76.4454212373516 \wedge x < -74.3510261349584$$
$$x > -71.2094334813686 \wedge x < -70.162235930172$$
$$x > -68.0678408277789 \wedge x < -63.8790506229925$$
$$x > -61.7846555205993 \wedge x < -60.7374579694027$$
$$x > -57.5958653158129 \wedge x < -55.5014702134197$$
$$x > -54.4542726622231 \wedge x < -52.3598775598299$$
$$x > -49.2182849062401 \wedge x < -48.1710873550435$$
$$x > -46.0766922526503 \wedge x < -42.9350995990605$$
$$x > -41.8879020478639 \wedge x < -39.7935069454707$$
$$x > -35.6047167406843 \wedge x < -33.5103216382911$$
$$x > -32.4631240870945 \wedge x < -30.3687289847013$$
$$x > -27.2271363311115 \wedge x < -26.1799387799149$$
$$x > -24.0855436775217 \wedge x < -19.8967534727354$$
$$x > -17.8023583703422 \wedge x < -13.6135681655558$$
$$x > -11.5191730631626 \wedge x < -10.471975511966$$
$$x > -5.23598775598299 \wedge x < -4.18879020478639$$
$$x > -2.0943951023932 \wedge x < 2.0943951023932$$
$$x > 4.18879020478639 \wedge x < 8.37758040957278$$
$$x > 10.471975511966 \wedge x < 11.5191730631626$$
$$x > 16.7551608191456 \wedge x < 17.8023583703422$$
$$x > 19.8967534727354 \wedge x < 24.0855436775217$$
$$x > 26.1799387799149 \wedge x < 30.3687289847013$$
$$x > 32.4631240870945 \wedge x < 33.5103216382911$$
$$x > 38.7463093942741 \wedge x < 39.7935069454707$$
$$x > 41.8879020478639 \wedge x < 46.0766922526503$$
$$x > 48.1710873550435 \wedge x < 52.3598775598299$$
$$x > 54.4542726622231 \wedge x < 55.5014702134197$$
$$x > 60.7374579694027 \wedge x < 61.7846555205993$$
$$x > 63.8790506229925 \wedge x < 68.0678408277789$$
$$x > 70.162235930172 \wedge x < 74.3510261349584$$
$$x > 76.4454212373516 \wedge x < 77.4926187885482$$
$$x > 82.7286065445312 \wedge x < 83.7758040957278$$
$$x > 85.870199198121 \wedge x < 90.0589894029074$$
$$x > 92.1533845053006 \wedge x < 96.342174710087$$
$$x > 98.4365698124802 \wedge x < 99.4837673636768$$
$$x > 269.129770657526 \wedge x < 275.412955964705$$
$$x > 3803.42150594604$$
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\left|{\cos{\left(x \right)}}\right| = \frac{1}{2}$$
cambiamos
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
$$\left|{\cos{\left(x \right)}}\right| - \frac{1}{2} = 0$$
Sustituimos
$$w = \left|{\cos{\left(x \right)}}\right|$$
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w = \frac{1}{2}$$
Obtenemos la respuesta: w = 1/2
hacemos cambio inverso
$$\left|{\cos{\left(x \right)}}\right| = w$$
sustituimos w:
$$x_{1} = -93.2005820564972$$
$$x_{2} = -68.0678408277789$$
$$x_{3} = -79.5870138909414$$
$$x_{4} = 63.8790506229925$$
$$x_{5} = 82.7286065445312$$
$$x_{6} = -85.870199198121$$
$$x_{7} = -4.18879020478639$$
$$x_{8} = 74.3510261349584$$
$$x_{9} = 61.7846555205993$$
$$x_{10} = -35.6047167406843$$
$$x_{11} = 2.0943951023932$$
$$x_{12} = 33.5103216382911$$
$$x_{13} = -76.4454212373516$$
$$x_{14} = -32.4631240870945$$
$$x_{15} = 30.3687289847013$$
$$x_{16} = -63.8790506229925$$
$$x_{17} = 39.7935069454707$$
$$x_{18} = -70.162235930172$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 269.129770657526$$
$$x_{21} = 38.7463093942741$$
$$x_{22} = 76.4454212373516$$
$$x_{23} = -39.7935069454707$$
$$x_{24} = -77.4926187885482$$
$$x_{25} = -96.342174710087$$
$$x_{26} = 85.870199198121$$
$$x_{27} = 98.4365698124802$$
$$x_{28} = -24.0855436775217$$
$$x_{29} = -90.0589894029074$$
$$x_{30} = -41.8879020478639$$
$$x_{31} = -673.348025419412$$
$$x_{32} = 60.7374579694027$$
$$x_{33} = 90.0589894029074$$
$$x_{34} = 275.412955964705$$
$$x_{35} = -2.0943951023932$$
$$x_{36} = 41.8879020478639$$
$$x_{37} = -74.3510261349584$$
$$x_{38} = 26.1799387799149$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -61.7846555205993$$
$$x_{41} = 68.0678408277789$$
$$x_{42} = -13.6135681655558$$
$$x_{43} = -55.5014702134197$$
$$x_{44} = -30.3687289847013$$
$$x_{45} = 77.4926187885482$$
$$x_{46} = -26.1799387799149$$
$$x_{47} = 8.37758040957278$$
$$x_{48} = 52.3598775598299$$
$$x_{49} = -46.0766922526503$$
$$x_{50} = -33.5103216382911$$
$$x_{51} = 16.7551608191456$$
$$x_{52} = -60.7374579694027$$
$$x_{53} = -99.4837673636768$$
$$x_{54} = -27.2271363311115$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 96.342174710087$$
$$x_{57} = -11.5191730631626$$
$$x_{58} = -83.7758040957278$$
$$x_{59} = -54.4542726622231$$
$$x_{60} = 3803.42150594604$$
$$x_{61} = 19.8967534727354$$
$$x_{62} = 48.1710873550435$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = -10.471975511966$$
$$x_{65} = 4.18879020478639$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = 11.5191730631626$$
$$x_{68} = 83.7758040957278$$
$$x_{69} = -42.9350995990605$$
$$x_{70} = -71.2094334813686$$
$$x_{71} = -19.8967534727354$$
$$x_{72} = 54.4542726622231$$
$$x_{73} = 99.4837673636768$$
$$x_{74} = 92.1533845053006$$
$$x_{75} = -48.1710873550435$$
$$x_{76} = 46.0766922526503$$
$$x_{77} = 24.0855436775217$$
$$x_{78} = 10.471975511966$$
$$x_{79} = 17.8023583703422$$
$$x_{80} = -17.8023583703422$$
$$x_{81} = -57.5958653158129$$
$$x_{82} = -92.1533845053006$$
$$x_{83} = -52.3598775598299$$
$$x_{84} = -98.4365698124802$$
$$x_{1} = -93.2005820564972$$
$$x_{2} = -68.0678408277789$$
$$x_{3} = -79.5870138909414$$
$$x_{4} = 63.8790506229925$$
$$x_{5} = 82.7286065445312$$
$$x_{6} = -85.870199198121$$
$$x_{7} = -4.18879020478639$$
$$x_{8} = 74.3510261349584$$
$$x_{9} = 61.7846555205993$$
$$x_{10} = -35.6047167406843$$
$$x_{11} = 2.0943951023932$$
$$x_{12} = 33.5103216382911$$
$$x_{13} = -76.4454212373516$$
$$x_{14} = -32.4631240870945$$
$$x_{15} = 30.3687289847013$$
$$x_{16} = -63.8790506229925$$
$$x_{17} = 39.7935069454707$$
$$x_{18} = -70.162235930172$$
$$x_{19} = 70.162235930172$$
$$x_{20} = 269.129770657526$$
$$x_{21} = 38.7463093942741$$
$$x_{22} = 76.4454212373516$$
$$x_{23} = -39.7935069454707$$
$$x_{24} = -77.4926187885482$$
$$x_{25} = -96.342174710087$$
$$x_{26} = 85.870199198121$$
$$x_{27} = 98.4365698124802$$
$$x_{28} = -24.0855436775217$$
$$x_{29} = -90.0589894029074$$
$$x_{30} = -41.8879020478639$$
$$x_{31} = -673.348025419412$$
$$x_{32} = 60.7374579694027$$
$$x_{33} = 90.0589894029074$$
$$x_{34} = 275.412955964705$$
$$x_{35} = -2.0943951023932$$
$$x_{36} = 41.8879020478639$$
$$x_{37} = -74.3510261349584$$
$$x_{38} = 26.1799387799149$$
$$x_{39} = 55.5014702134197$$
$$x_{40} = -61.7846555205993$$
$$x_{41} = 68.0678408277789$$
$$x_{42} = -13.6135681655558$$
$$x_{43} = -55.5014702134197$$
$$x_{44} = -30.3687289847013$$
$$x_{45} = 77.4926187885482$$
$$x_{46} = -26.1799387799149$$
$$x_{47} = 8.37758040957278$$
$$x_{48} = 52.3598775598299$$
$$x_{49} = -46.0766922526503$$
$$x_{50} = -33.5103216382911$$
$$x_{51} = 16.7551608191456$$
$$x_{52} = -60.7374579694027$$
$$x_{53} = -99.4837673636768$$
$$x_{54} = -27.2271363311115$$
$$x_{55} = -5.23598775598299$$
$$x_{56} = 96.342174710087$$
$$x_{57} = -11.5191730631626$$
$$x_{58} = -83.7758040957278$$
$$x_{59} = -54.4542726622231$$
$$x_{60} = 3803.42150594604$$
$$x_{61} = 19.8967534727354$$
$$x_{62} = 48.1710873550435$$
$$x_{63} = -49.2182849062401$$
$$x_{64} = -10.471975511966$$
$$x_{65} = 4.18879020478639$$
$$x_{66} = 32.4631240870945$$
$$x_{67} = 11.5191730631626$$
$$x_{68} = 83.7758040957278$$
$$x_{69} = -42.9350995990605$$
$$x_{70} = -71.2094334813686$$
$$x_{71} = -19.8967534727354$$
$$x_{72} = 54.4542726622231$$
$$x_{73} = 99.4837673636768$$
$$x_{74} = 92.1533845053006$$
$$x_{75} = -48.1710873550435$$
$$x_{76} = 46.0766922526503$$
$$x_{77} = 24.0855436775217$$
$$x_{78} = 10.471975511966$$
$$x_{79} = 17.8023583703422$$
$$x_{80} = -17.8023583703422$$
$$x_{81} = -57.5958653158129$$
$$x_{82} = -92.1533845053006$$
$$x_{83} = -52.3598775598299$$
$$x_{84} = -98.4365698124802$$
Las raíces dadas
$$x_{31} = -673.348025419412$$
$$x_{53} = -99.4837673636768$$
$$x_{84} = -98.4365698124802$$
$$x_{25} = -96.342174710087$$
$$x_{1} = -93.2005820564972$$
$$x_{82} = -92.1533845053006$$
$$x_{29} = -90.0589894029074$$
$$x_{6} = -85.870199198121$$
$$x_{58} = -83.7758040957278$$
$$x_{3} = -79.5870138909414$$
$$x_{24} = -77.4926187885482$$
$$x_{13} = -76.4454212373516$$
$$x_{37} = -74.3510261349584$$
$$x_{70} = -71.2094334813686$$
$$x_{18} = -70.162235930172$$
$$x_{2} = -68.0678408277789$$
$$x_{16} = -63.8790506229925$$
$$x_{40} = -61.7846555205993$$
$$x_{52} = -60.7374579694027$$
$$x_{81} = -57.5958653158129$$
$$x_{43} = -55.5014702134197$$
$$x_{59} = -54.4542726622231$$
$$x_{83} = -52.3598775598299$$
$$x_{63} = -49.2182849062401$$
$$x_{75} = -48.1710873550435$$
$$x_{49} = -46.0766922526503$$
$$x_{69} = -42.9350995990605$$
$$x_{30} = -41.8879020478639$$
$$x_{23} = -39.7935069454707$$
$$x_{10} = -35.6047167406843$$
$$x_{50} = -33.5103216382911$$
$$x_{14} = -32.4631240870945$$
$$x_{44} = -30.3687289847013$$
$$x_{54} = -27.2271363311115$$
$$x_{46} = -26.1799387799149$$
$$x_{28} = -24.0855436775217$$
$$x_{71} = -19.8967534727354$$
$$x_{80} = -17.8023583703422$$
$$x_{42} = -13.6135681655558$$
$$x_{57} = -11.5191730631626$$
$$x_{64} = -10.471975511966$$
$$x_{55} = -5.23598775598299$$
$$x_{7} = -4.18879020478639$$
$$x_{35} = -2.0943951023932$$
$$x_{11} = 2.0943951023932$$
$$x_{65} = 4.18879020478639$$
$$x_{47} = 8.37758040957278$$
$$x_{78} = 10.471975511966$$
$$x_{67} = 11.5191730631626$$
$$x_{51} = 16.7551608191456$$
$$x_{79} = 17.8023583703422$$
$$x_{61} = 19.8967534727354$$
$$x_{77} = 24.0855436775217$$
$$x_{38} = 26.1799387799149$$
$$x_{15} = 30.3687289847013$$
$$x_{66} = 32.4631240870945$$
$$x_{12} = 33.5103216382911$$
$$x_{21} = 38.7463093942741$$
$$x_{17} = 39.7935069454707$$
$$x_{36} = 41.8879020478639$$
$$x_{76} = 46.0766922526503$$
$$x_{62} = 48.1710873550435$$
$$x_{48} = 52.3598775598299$$
$$x_{72} = 54.4542726622231$$
$$x_{39} = 55.5014702134197$$
$$x_{32} = 60.7374579694027$$
$$x_{9} = 61.7846555205993$$
$$x_{4} = 63.8790506229925$$
$$x_{41} = 68.0678408277789$$
$$x_{19} = 70.162235930172$$
$$x_{8} = 74.3510261349584$$
$$x_{22} = 76.4454212373516$$
$$x_{45} = 77.4926187885482$$
$$x_{5} = 82.7286065445312$$
$$x_{68} = 83.7758040957278$$
$$x_{26} = 85.870199198121$$
$$x_{33} = 90.0589894029074$$
$$x_{74} = 92.1533845053006$$
$$x_{56} = 96.342174710087$$
$$x_{27} = 98.4365698124802$$
$$x_{73} = 99.4837673636768$$
$$x_{20} = 269.129770657526$$
$$x_{34} = 275.412955964705$$
$$x_{60} = 3803.42150594604$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{31}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{31} - \frac{1}{10}$$
=
$$-673.348025419412 + - \frac{1}{10}$$
=
$$-673.448025419412$$
lo sustituimos en la expresión
$$\left|{\cos{\left(x \right)}}\right| < \frac{1}{2}$$
$$\left|{\cos{\left(-673.448025419412 \right)}}\right| < \frac{1}{2}$$
0.411043807676242 < 1/2
significa que una de las soluciones de nuestra ecuación será con:
$$x < -673.348025419412$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------ο-------
x31 x53 x84 x25 x1 x82 x29 x6 x58 x3 x24 x13 x37 x70 x18 x2 x16 x40 x52 x81 x43 x59 x83 x63 x75 x49 x69 x30 x23 x10 x50 x14 x44 x54 x46 x28 x71 x80 x42 x57 x64 x55 x7 x35 x11 x65 x47 x78 x67 x51 x79 x61 x77 x38 x15 x66 x12 x21 x17 x36 x76 x62 x48 x72 x39 x32 x9 x4 x41 x19 x8 x22 x45 x5 x68 x26 x33 x74 x56 x27 x73 x20 x34 x60Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -673.348025419412$$
$$x > -99.4837673636768 \wedge x < -98.4365698124802$$
$$x > -96.342174710087 \wedge x < -93.2005820564972$$
$$x > -92.1533845053006 \wedge x < -90.0589894029074$$
$$x > -85.870199198121 \wedge x < -83.7758040957278$$
$$x > -79.5870138909414 \wedge x < -77.4926187885482$$
$$x > -76.4454212373516 \wedge x < -74.3510261349584$$
$$x > -71.2094334813686 \wedge x < -70.162235930172$$
$$x > -68.0678408277789 \wedge x < -63.8790506229925$$
$$x > -61.7846555205993 \wedge x < -60.7374579694027$$
$$x > -57.5958653158129 \wedge x < -55.5014702134197$$
$$x > -54.4542726622231 \wedge x < -52.3598775598299$$
$$x > -49.2182849062401 \wedge x < -48.1710873550435$$
$$x > -46.0766922526503 \wedge x < -42.9350995990605$$
$$x > -41.8879020478639 \wedge x < -39.7935069454707$$
$$x > -35.6047167406843 \wedge x < -33.5103216382911$$
$$x > -32.4631240870945 \wedge x < -30.3687289847013$$
$$x > -27.2271363311115 \wedge x < -26.1799387799149$$
$$x > -24.0855436775217 \wedge x < -19.8967534727354$$
$$x > -17.8023583703422 \wedge x < -13.6135681655558$$
$$x > -11.5191730631626 \wedge x < -10.471975511966$$
$$x > -5.23598775598299 \wedge x < -4.18879020478639$$
$$x > -2.0943951023932 \wedge x < 2.0943951023932$$
$$x > 4.18879020478639 \wedge x < 8.37758040957278$$
$$x > 10.471975511966 \wedge x < 11.5191730631626$$
$$x > 16.7551608191456 \wedge x < 17.8023583703422$$
$$x > 19.8967534727354 \wedge x < 24.0855436775217$$
$$x > 26.1799387799149 \wedge x < 30.3687289847013$$
$$x > 32.4631240870945 \wedge x < 33.5103216382911$$
$$x > 38.7463093942741 \wedge x < 39.7935069454707$$
$$x > 41.8879020478639 \wedge x < 46.0766922526503$$
$$x > 48.1710873550435 \wedge x < 52.3598775598299$$
$$x > 54.4542726622231 \wedge x < 55.5014702134197$$
$$x > 60.7374579694027 \wedge x < 61.7846555205993$$
$$x > 63.8790506229925 \wedge x < 68.0678408277789$$
$$x > 70.162235930172 \wedge x < 74.3510261349584$$
$$x > 76.4454212373516 \wedge x < 77.4926187885482$$
$$x > 82.7286065445312 \wedge x < 83.7758040957278$$
$$x > 85.870199198121 \wedge x < 90.0589894029074$$
$$x > 92.1533845053006 \wedge x < 96.342174710087$$
$$x > 98.4365698124802 \wedge x < 99.4837673636768$$
$$x > 269.129770657526 \wedge x < 275.412955964705$$
$$x > 3803.42150594604$$
Solución de la desigualdad en el gráfico