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>1
-
(x-2)/(x-4)>0
-
x+1>0
- (x-7)(x+8)>0
- Gráfico de la función y =:
-
|sinx|
- Integral de d{x}:
- |sinx|
-
Expresiones idénticas
- |sinx|>=√ tres / dos
- módulo de seno de x| más o igual a √3 dividir por 2
- módulo de seno de x| más o igual a √ tres dividir por dos
- |sinx|>=√3 dividir por 2
-
Expresiones semejantes
- |sin(x)|<=2/sqrt2
- |sin(x)|<1
- |sin(x)|<=sqrt(3)/2
-
Expresiones con funciones
- sinx
- sinxcos2x+cosxsin2x>1/2
- sinx>=-√2/2
- sinx≥√22
- sinx<_1:2
- sinx/2>=sqrt2/2
- Módulo |
- |x^2-5|x|+4|<=|2x^2-3|x|+1|
- |x^2-4x|<5
- |x+2/2x-3|<3
- |x-2|>=10
- |x^2-1|<x^2-|x|+1
|sinx|>=√3/2 desigualdades
Solución
Ha introducido
[src]
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|sin(x)| >= -----
2
$$\left|{\sin{\left(x \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
Abs(sin(x)) >= sqrt(3)/2
Solución detallada
Se da la desigualdad:
$$\left|{\sin{\left(x \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(x \right)}}\right| = \frac{\sqrt{3}}{2}$$
Resolvemos:
Tenemos la ecuación
$$\left|{\sin{\left(x \right)}}\right| = \frac{\sqrt{3}}{2}$$
cambiamos
$$\left|{\sin{\left(x \right)}}\right| - 1 - \frac{\sqrt{3}}{2} = 0$$
$$\left|{\sin{\left(x \right)}}\right| - 1 - \frac{\sqrt{3}}{2} = 0$$
Sustituimos
$$w = \left|{\sin{\left(x \right)}}\right|$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w - \frac{\sqrt{3}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (w - sqrt(3)/2)/w
Obtenemos la respuesta: w = 1 + sqrt(3)/2
hacemos cambio inverso
$$\left|{\sin{\left(x \right)}}\right| = w$$
sustituimos w:
$$x_{1} = -39.7935069454707$$
$$x_{2} = 45.0294947014537$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -26.1799387799149$$
$$x_{5} = 48.1710873550435$$
$$x_{6} = -5.23598775598299$$
$$x_{7} = 32.4631240870945$$
$$x_{8} = 93.2005820564972$$
$$x_{9} = -93.2005820564972$$
$$x_{10} = 49.2182849062401$$
$$x_{11} = -41.8879020478639$$
$$x_{12} = 90.0589894029074$$
$$x_{13} = 4.18879020478639$$
$$x_{14} = -20.943951023932$$
$$x_{15} = 89.0117918517108$$
$$x_{16} = 26.1799387799149$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = -42.9350995990605$$
$$x_{19} = -16.7551608191456$$
$$x_{20} = -10.471975511966$$
$$x_{21} = 19.8967534727354$$
$$x_{22} = 8.37758040957278$$
$$x_{23} = 86.9173967493176$$
$$x_{24} = 33.5103216382911$$
$$x_{25} = -2.0943951023932$$
$$x_{26} = -86.9173967493176$$
$$x_{27} = 24.0855436775217$$
$$x_{28} = -64.9262481741891$$
$$x_{29} = -11.5191730631626$$
$$x_{30} = -90.0589894029074$$
$$x_{31} = -33.5103216382911$$
$$x_{32} = -82.7286065445312$$
$$x_{33} = -27.2271363311115$$
$$x_{34} = 68.0678408277789$$
$$x_{35} = 55.5014702134197$$
$$x_{36} = 99.4837673636768$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = -76.4454212373516$$
$$x_{39} = -24.0855436775217$$
$$x_{40} = -68.0678408277789$$
$$x_{41} = 98.4365698124802$$
$$x_{42} = -70.162235930172$$
$$x_{43} = 61.7846555205993$$
$$x_{44} = 17.8023583703422$$
$$x_{45} = -85.870199198121$$
$$x_{46} = -38.7463093942741$$
$$x_{47} = -79.5870138909414$$
$$x_{48} = 27.2271363311115$$
$$x_{49} = 38.7463093942741$$
$$x_{50} = -46.0766922526503$$
$$x_{51} = -13.6135681655558$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -54.4542726622231$$
$$x_{54} = -98.4365698124802$$
$$x_{55} = 60.7374579694027$$
$$x_{56} = -32.4631240870945$$
$$x_{57} = -77.4926187885482$$
$$x_{58} = 67.0206432765823$$
$$x_{59} = 41.8879020478639$$
$$x_{60} = -99.4837673636768$$
$$x_{61} = 1.0471975511966$$
$$x_{62} = 77.4926187885482$$
$$x_{63} = -80.634211442138$$
$$x_{64} = 30.3687289847013$$
$$x_{65} = 39.7935069454707$$
$$x_{66} = -83.7758040957278$$
$$x_{67} = -60.7374579694027$$
$$x_{68} = 16.7551608191456$$
$$x_{69} = -17.8023583703422$$
$$x_{70} = 71.2094334813686$$
$$x_{71} = -48.1710873550435$$
$$x_{72} = 46.0766922526503$$
$$x_{73} = 11.5191730631626$$
$$x_{74} = -63.8790506229925$$
$$x_{75} = -61.7846555205993$$
$$x_{76} = 63.8790506229925$$
$$x_{77} = 23.0383461263252$$
$$x_{78} = -92.1533845053006$$
$$x_{79} = 2.0943951023932$$
$$x_{80} = 74.3510261349584$$
$$x_{81} = 83.7758040957278$$
$$x_{82} = 96.342174710087$$
$$x_{83} = 54.4542726622231$$
$$x_{84} = -57.5958653158129$$
$$x_{85} = -19.8967534727354$$
$$x_{86} = 85.870199198121$$
$$x_{87} = 5.23598775598299$$
$$x_{88} = -55.5014702134197$$
$$x_{89} = 76.4454212373516$$
$$x_{90} = -49.2182849062401$$
$$x_{91} = 92.1533845053006$$
$$x_{92} = 70.162235930172$$
$$x_{93} = -35.6047167406843$$
$$x_{94} = -36.6519142918809$$
$$x_{95} = 10.471975511966$$
$$x_{1} = -39.7935069454707$$
$$x_{2} = 45.0294947014537$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -26.1799387799149$$
$$x_{5} = 48.1710873550435$$
$$x_{6} = -5.23598775598299$$
$$x_{7} = 32.4631240870945$$
$$x_{8} = 93.2005820564972$$
$$x_{9} = -93.2005820564972$$
$$x_{10} = 49.2182849062401$$
$$x_{11} = -41.8879020478639$$
$$x_{12} = 90.0589894029074$$
$$x_{13} = 4.18879020478639$$
$$x_{14} = -20.943951023932$$
$$x_{15} = 89.0117918517108$$
$$x_{16} = 26.1799387799149$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = -42.9350995990605$$
$$x_{19} = -16.7551608191456$$
$$x_{20} = -10.471975511966$$
$$x_{21} = 19.8967534727354$$
$$x_{22} = 8.37758040957278$$
$$x_{23} = 86.9173967493176$$
$$x_{24} = 33.5103216382911$$
$$x_{25} = -2.0943951023932$$
$$x_{26} = -86.9173967493176$$
$$x_{27} = 24.0855436775217$$
$$x_{28} = -64.9262481741891$$
$$x_{29} = -11.5191730631626$$
$$x_{30} = -90.0589894029074$$
$$x_{31} = -33.5103216382911$$
$$x_{32} = -82.7286065445312$$
$$x_{33} = -27.2271363311115$$
$$x_{34} = 68.0678408277789$$
$$x_{35} = 55.5014702134197$$
$$x_{36} = 99.4837673636768$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = -76.4454212373516$$
$$x_{39} = -24.0855436775217$$
$$x_{40} = -68.0678408277789$$
$$x_{41} = 98.4365698124802$$
$$x_{42} = -70.162235930172$$
$$x_{43} = 61.7846555205993$$
$$x_{44} = 17.8023583703422$$
$$x_{45} = -85.870199198121$$
$$x_{46} = -38.7463093942741$$
$$x_{47} = -79.5870138909414$$
$$x_{48} = 27.2271363311115$$
$$x_{49} = 38.7463093942741$$
$$x_{50} = -46.0766922526503$$
$$x_{51} = -13.6135681655558$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -54.4542726622231$$
$$x_{54} = -98.4365698124802$$
$$x_{55} = 60.7374579694027$$
$$x_{56} = -32.4631240870945$$
$$x_{57} = -77.4926187885482$$
$$x_{58} = 67.0206432765823$$
$$x_{59} = 41.8879020478639$$
$$x_{60} = -99.4837673636768$$
$$x_{61} = 1.0471975511966$$
$$x_{62} = 77.4926187885482$$
$$x_{63} = -80.634211442138$$
$$x_{64} = 30.3687289847013$$
$$x_{65} = 39.7935069454707$$
$$x_{66} = -83.7758040957278$$
$$x_{67} = -60.7374579694027$$
$$x_{68} = 16.7551608191456$$
$$x_{69} = -17.8023583703422$$
$$x_{70} = 71.2094334813686$$
$$x_{71} = -48.1710873550435$$
$$x_{72} = 46.0766922526503$$
$$x_{73} = 11.5191730631626$$
$$x_{74} = -63.8790506229925$$
$$x_{75} = -61.7846555205993$$
$$x_{76} = 63.8790506229925$$
$$x_{77} = 23.0383461263252$$
$$x_{78} = -92.1533845053006$$
$$x_{79} = 2.0943951023932$$
$$x_{80} = 74.3510261349584$$
$$x_{81} = 83.7758040957278$$
$$x_{82} = 96.342174710087$$
$$x_{83} = 54.4542726622231$$
$$x_{84} = -57.5958653158129$$
$$x_{85} = -19.8967534727354$$
$$x_{86} = 85.870199198121$$
$$x_{87} = 5.23598775598299$$
$$x_{88} = -55.5014702134197$$
$$x_{89} = 76.4454212373516$$
$$x_{90} = -49.2182849062401$$
$$x_{91} = 92.1533845053006$$
$$x_{92} = 70.162235930172$$
$$x_{93} = -35.6047167406843$$
$$x_{94} = -36.6519142918809$$
$$x_{95} = 10.471975511966$$
Las raíces dadas
$$x_{60} = -99.4837673636768$$
$$x_{54} = -98.4365698124802$$
$$x_{9} = -93.2005820564972$$
$$x_{78} = -92.1533845053006$$
$$x_{30} = -90.0589894029074$$
$$x_{26} = -86.9173967493176$$
$$x_{45} = -85.870199198121$$
$$x_{66} = -83.7758040957278$$
$$x_{32} = -82.7286065445312$$
$$x_{63} = -80.634211442138$$
$$x_{47} = -79.5870138909414$$
$$x_{57} = -77.4926187885482$$
$$x_{38} = -76.4454212373516$$
$$x_{37} = -71.2094334813686$$
$$x_{42} = -70.162235930172$$
$$x_{40} = -68.0678408277789$$
$$x_{28} = -64.9262481741891$$
$$x_{74} = -63.8790506229925$$
$$x_{75} = -61.7846555205993$$
$$x_{67} = -60.7374579694027$$
$$x_{84} = -57.5958653158129$$
$$x_{88} = -55.5014702134197$$
$$x_{53} = -54.4542726622231$$
$$x_{90} = -49.2182849062401$$
$$x_{71} = -48.1710873550435$$
$$x_{50} = -46.0766922526503$$
$$x_{18} = -42.9350995990605$$
$$x_{11} = -41.8879020478639$$
$$x_{1} = -39.7935069454707$$
$$x_{46} = -38.7463093942741$$
$$x_{94} = -36.6519142918809$$
$$x_{93} = -35.6047167406843$$
$$x_{31} = -33.5103216382911$$
$$x_{56} = -32.4631240870945$$
$$x_{33} = -27.2271363311115$$
$$x_{4} = -26.1799387799149$$
$$x_{39} = -24.0855436775217$$
$$x_{14} = -20.943951023932$$
$$x_{85} = -19.8967534727354$$
$$x_{69} = -17.8023583703422$$
$$x_{19} = -16.7551608191456$$
$$x_{51} = -13.6135681655558$$
$$x_{29} = -11.5191730631626$$
$$x_{20} = -10.471975511966$$
$$x_{6} = -5.23598775598299$$
$$x_{52} = -4.18879020478639$$
$$x_{25} = -2.0943951023932$$
$$x_{61} = 1.0471975511966$$
$$x_{79} = 2.0943951023932$$
$$x_{13} = 4.18879020478639$$
$$x_{87} = 5.23598775598299$$
$$x_{22} = 8.37758040957278$$
$$x_{95} = 10.471975511966$$
$$x_{73} = 11.5191730631626$$
$$x_{68} = 16.7551608191456$$
$$x_{44} = 17.8023583703422$$
$$x_{21} = 19.8967534727354$$
$$x_{77} = 23.0383461263252$$
$$x_{27} = 24.0855436775217$$
$$x_{16} = 26.1799387799149$$
$$x_{48} = 27.2271363311115$$
$$x_{64} = 30.3687289847013$$
$$x_{7} = 32.4631240870945$$
$$x_{24} = 33.5103216382911$$
$$x_{49} = 38.7463093942741$$
$$x_{65} = 39.7935069454707$$
$$x_{59} = 41.8879020478639$$
$$x_{2} = 45.0294947014537$$
$$x_{72} = 46.0766922526503$$
$$x_{5} = 48.1710873550435$$
$$x_{10} = 49.2182849062401$$
$$x_{17} = 52.3598775598299$$
$$x_{83} = 54.4542726622231$$
$$x_{35} = 55.5014702134197$$
$$x_{55} = 60.7374579694027$$
$$x_{43} = 61.7846555205993$$
$$x_{76} = 63.8790506229925$$
$$x_{58} = 67.0206432765823$$
$$x_{34} = 68.0678408277789$$
$$x_{92} = 70.162235930172$$
$$x_{70} = 71.2094334813686$$
$$x_{80} = 74.3510261349584$$
$$x_{89} = 76.4454212373516$$
$$x_{62} = 77.4926187885482$$
$$x_{3} = 82.7286065445312$$
$$x_{81} = 83.7758040957278$$
$$x_{86} = 85.870199198121$$
$$x_{23} = 86.9173967493176$$
$$x_{15} = 89.0117918517108$$
$$x_{12} = 90.0589894029074$$
$$x_{91} = 92.1533845053006$$
$$x_{8} = 93.2005820564972$$
$$x_{82} = 96.342174710087$$
$$x_{41} = 98.4365698124802$$
$$x_{36} = 99.4837673636768$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{60}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{60} - \frac{1}{10}$$
=
$$-99.4837673636768 + - \frac{1}{10}$$
=
$$-99.5837673636768$$
lo sustituimos en la expresión
$$\left|{\sin{\left(x \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
$$\left|{\sin{\left(-99.5837673636768 \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
pero
Entonces
$$x \leq -99.4837673636768$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
$$x \geq -93.2005820564972 \wedge x \leq -92.1533845053006$$
$$x \geq -90.0589894029074 \wedge x \leq -86.9173967493176$$
$$x \geq -85.870199198121 \wedge x \leq -83.7758040957278$$
$$x \geq -82.7286065445312 \wedge x \leq -80.634211442138$$
$$x \geq -79.5870138909414 \wedge x \leq -77.4926187885482$$
$$x \geq -76.4454212373516 \wedge x \leq -71.2094334813686$$
$$x \geq -70.162235930172 \wedge x \leq -68.0678408277789$$
$$x \geq -64.9262481741891 \wedge x \leq -63.8790506229925$$
$$x \geq -61.7846555205993 \wedge x \leq -60.7374579694027$$
$$x \geq -57.5958653158129 \wedge x \leq -55.5014702134197$$
$$x \geq -54.4542726622231 \wedge x \leq -49.2182849062401$$
$$x \geq -48.1710873550435 \wedge x \leq -46.0766922526503$$
$$x \geq -42.9350995990605 \wedge x \leq -41.8879020478639$$
$$x \geq -39.7935069454707 \wedge x \leq -38.7463093942741$$
$$x \geq -36.6519142918809 \wedge x \leq -35.6047167406843$$
$$x \geq -33.5103216382911 \wedge x \leq -32.4631240870945$$
$$x \geq -27.2271363311115 \wedge x \leq -26.1799387799149$$
$$x \geq -24.0855436775217 \wedge x \leq -20.943951023932$$
$$x \geq -19.8967534727354 \wedge x \leq -17.8023583703422$$
$$x \geq -16.7551608191456 \wedge x \leq -13.6135681655558$$
$$x \geq -11.5191730631626 \wedge x \leq -10.471975511966$$
$$x \geq -5.23598775598299 \wedge x \leq -4.18879020478639$$
$$x \geq -2.0943951023932 \wedge x \leq 1.0471975511966$$
$$x \geq 2.0943951023932 \wedge x \leq 4.18879020478639$$
$$x \geq 5.23598775598299 \wedge x \leq 8.37758040957278$$
$$x \geq 10.471975511966 \wedge x \leq 11.5191730631626$$
$$x \geq 16.7551608191456 \wedge x \leq 17.8023583703422$$
$$x \geq 19.8967534727354 \wedge x \leq 23.0383461263252$$
$$x \geq 24.0855436775217 \wedge x \leq 26.1799387799149$$
$$x \geq 27.2271363311115 \wedge x \leq 30.3687289847013$$
$$x \geq 32.4631240870945 \wedge x \leq 33.5103216382911$$
$$x \geq 38.7463093942741 \wedge x \leq 39.7935069454707$$
$$x \geq 41.8879020478639 \wedge x \leq 45.0294947014537$$
$$x \geq 46.0766922526503 \wedge x \leq 48.1710873550435$$
$$x \geq 49.2182849062401 \wedge x \leq 52.3598775598299$$
$$x \geq 54.4542726622231 \wedge x \leq 55.5014702134197$$
$$x \geq 60.7374579694027 \wedge x \leq 61.7846555205993$$
$$x \geq 63.8790506229925 \wedge x \leq 67.0206432765823$$
$$x \geq 68.0678408277789 \wedge x \leq 70.162235930172$$
$$x \geq 71.2094334813686 \wedge x \leq 74.3510261349584$$
$$x \geq 76.4454212373516 \wedge x \leq 77.4926187885482$$
$$x \geq 82.7286065445312 \wedge x \leq 83.7758040957278$$
$$x \geq 85.870199198121 \wedge x \leq 86.9173967493176$$
$$x \geq 89.0117918517108 \wedge x \leq 90.0589894029074$$
$$x \geq 92.1533845053006 \wedge x \leq 93.2005820564972$$
$$x \geq 96.342174710087 \wedge x \leq 98.4365698124802$$
$$x \geq 99.4837673636768$$
$$\left|{\sin{\left(x \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left|{\sin{\left(x \right)}}\right| = \frac{\sqrt{3}}{2}$$
Resolvemos:
Tenemos la ecuación
$$\left|{\sin{\left(x \right)}}\right| = \frac{\sqrt{3}}{2}$$
cambiamos
$$\left|{\sin{\left(x \right)}}\right| - 1 - \frac{\sqrt{3}}{2} = 0$$
$$\left|{\sin{\left(x \right)}}\right| - 1 - \frac{\sqrt{3}}{2} = 0$$
Sustituimos
$$w = \left|{\sin{\left(x \right)}}\right|$$
Abrimos los paréntesis en el miembro izquierdo de la ecuación
-1 + w - sqrt3/2 = 0
Transportamos los términos libres (sin w)
del miembro izquierdo al derecho, obtenemos:
$$w - \frac{\sqrt{3}}{2} = 1$$
Dividamos ambos miembros de la ecuación en (w - sqrt(3)/2)/w
w = 1 / ((w - sqrt(3)/2)/w)
Obtenemos la respuesta: w = 1 + sqrt(3)/2
hacemos cambio inverso
$$\left|{\sin{\left(x \right)}}\right| = w$$
sustituimos w:
$$x_{1} = -39.7935069454707$$
$$x_{2} = 45.0294947014537$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -26.1799387799149$$
$$x_{5} = 48.1710873550435$$
$$x_{6} = -5.23598775598299$$
$$x_{7} = 32.4631240870945$$
$$x_{8} = 93.2005820564972$$
$$x_{9} = -93.2005820564972$$
$$x_{10} = 49.2182849062401$$
$$x_{11} = -41.8879020478639$$
$$x_{12} = 90.0589894029074$$
$$x_{13} = 4.18879020478639$$
$$x_{14} = -20.943951023932$$
$$x_{15} = 89.0117918517108$$
$$x_{16} = 26.1799387799149$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = -42.9350995990605$$
$$x_{19} = -16.7551608191456$$
$$x_{20} = -10.471975511966$$
$$x_{21} = 19.8967534727354$$
$$x_{22} = 8.37758040957278$$
$$x_{23} = 86.9173967493176$$
$$x_{24} = 33.5103216382911$$
$$x_{25} = -2.0943951023932$$
$$x_{26} = -86.9173967493176$$
$$x_{27} = 24.0855436775217$$
$$x_{28} = -64.9262481741891$$
$$x_{29} = -11.5191730631626$$
$$x_{30} = -90.0589894029074$$
$$x_{31} = -33.5103216382911$$
$$x_{32} = -82.7286065445312$$
$$x_{33} = -27.2271363311115$$
$$x_{34} = 68.0678408277789$$
$$x_{35} = 55.5014702134197$$
$$x_{36} = 99.4837673636768$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = -76.4454212373516$$
$$x_{39} = -24.0855436775217$$
$$x_{40} = -68.0678408277789$$
$$x_{41} = 98.4365698124802$$
$$x_{42} = -70.162235930172$$
$$x_{43} = 61.7846555205993$$
$$x_{44} = 17.8023583703422$$
$$x_{45} = -85.870199198121$$
$$x_{46} = -38.7463093942741$$
$$x_{47} = -79.5870138909414$$
$$x_{48} = 27.2271363311115$$
$$x_{49} = 38.7463093942741$$
$$x_{50} = -46.0766922526503$$
$$x_{51} = -13.6135681655558$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -54.4542726622231$$
$$x_{54} = -98.4365698124802$$
$$x_{55} = 60.7374579694027$$
$$x_{56} = -32.4631240870945$$
$$x_{57} = -77.4926187885482$$
$$x_{58} = 67.0206432765823$$
$$x_{59} = 41.8879020478639$$
$$x_{60} = -99.4837673636768$$
$$x_{61} = 1.0471975511966$$
$$x_{62} = 77.4926187885482$$
$$x_{63} = -80.634211442138$$
$$x_{64} = 30.3687289847013$$
$$x_{65} = 39.7935069454707$$
$$x_{66} = -83.7758040957278$$
$$x_{67} = -60.7374579694027$$
$$x_{68} = 16.7551608191456$$
$$x_{69} = -17.8023583703422$$
$$x_{70} = 71.2094334813686$$
$$x_{71} = -48.1710873550435$$
$$x_{72} = 46.0766922526503$$
$$x_{73} = 11.5191730631626$$
$$x_{74} = -63.8790506229925$$
$$x_{75} = -61.7846555205993$$
$$x_{76} = 63.8790506229925$$
$$x_{77} = 23.0383461263252$$
$$x_{78} = -92.1533845053006$$
$$x_{79} = 2.0943951023932$$
$$x_{80} = 74.3510261349584$$
$$x_{81} = 83.7758040957278$$
$$x_{82} = 96.342174710087$$
$$x_{83} = 54.4542726622231$$
$$x_{84} = -57.5958653158129$$
$$x_{85} = -19.8967534727354$$
$$x_{86} = 85.870199198121$$
$$x_{87} = 5.23598775598299$$
$$x_{88} = -55.5014702134197$$
$$x_{89} = 76.4454212373516$$
$$x_{90} = -49.2182849062401$$
$$x_{91} = 92.1533845053006$$
$$x_{92} = 70.162235930172$$
$$x_{93} = -35.6047167406843$$
$$x_{94} = -36.6519142918809$$
$$x_{95} = 10.471975511966$$
$$x_{1} = -39.7935069454707$$
$$x_{2} = 45.0294947014537$$
$$x_{3} = 82.7286065445312$$
$$x_{4} = -26.1799387799149$$
$$x_{5} = 48.1710873550435$$
$$x_{6} = -5.23598775598299$$
$$x_{7} = 32.4631240870945$$
$$x_{8} = 93.2005820564972$$
$$x_{9} = -93.2005820564972$$
$$x_{10} = 49.2182849062401$$
$$x_{11} = -41.8879020478639$$
$$x_{12} = 90.0589894029074$$
$$x_{13} = 4.18879020478639$$
$$x_{14} = -20.943951023932$$
$$x_{15} = 89.0117918517108$$
$$x_{16} = 26.1799387799149$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = -42.9350995990605$$
$$x_{19} = -16.7551608191456$$
$$x_{20} = -10.471975511966$$
$$x_{21} = 19.8967534727354$$
$$x_{22} = 8.37758040957278$$
$$x_{23} = 86.9173967493176$$
$$x_{24} = 33.5103216382911$$
$$x_{25} = -2.0943951023932$$
$$x_{26} = -86.9173967493176$$
$$x_{27} = 24.0855436775217$$
$$x_{28} = -64.9262481741891$$
$$x_{29} = -11.5191730631626$$
$$x_{30} = -90.0589894029074$$
$$x_{31} = -33.5103216382911$$
$$x_{32} = -82.7286065445312$$
$$x_{33} = -27.2271363311115$$
$$x_{34} = 68.0678408277789$$
$$x_{35} = 55.5014702134197$$
$$x_{36} = 99.4837673636768$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = -76.4454212373516$$
$$x_{39} = -24.0855436775217$$
$$x_{40} = -68.0678408277789$$
$$x_{41} = 98.4365698124802$$
$$x_{42} = -70.162235930172$$
$$x_{43} = 61.7846555205993$$
$$x_{44} = 17.8023583703422$$
$$x_{45} = -85.870199198121$$
$$x_{46} = -38.7463093942741$$
$$x_{47} = -79.5870138909414$$
$$x_{48} = 27.2271363311115$$
$$x_{49} = 38.7463093942741$$
$$x_{50} = -46.0766922526503$$
$$x_{51} = -13.6135681655558$$
$$x_{52} = -4.18879020478639$$
$$x_{53} = -54.4542726622231$$
$$x_{54} = -98.4365698124802$$
$$x_{55} = 60.7374579694027$$
$$x_{56} = -32.4631240870945$$
$$x_{57} = -77.4926187885482$$
$$x_{58} = 67.0206432765823$$
$$x_{59} = 41.8879020478639$$
$$x_{60} = -99.4837673636768$$
$$x_{61} = 1.0471975511966$$
$$x_{62} = 77.4926187885482$$
$$x_{63} = -80.634211442138$$
$$x_{64} = 30.3687289847013$$
$$x_{65} = 39.7935069454707$$
$$x_{66} = -83.7758040957278$$
$$x_{67} = -60.7374579694027$$
$$x_{68} = 16.7551608191456$$
$$x_{69} = -17.8023583703422$$
$$x_{70} = 71.2094334813686$$
$$x_{71} = -48.1710873550435$$
$$x_{72} = 46.0766922526503$$
$$x_{73} = 11.5191730631626$$
$$x_{74} = -63.8790506229925$$
$$x_{75} = -61.7846555205993$$
$$x_{76} = 63.8790506229925$$
$$x_{77} = 23.0383461263252$$
$$x_{78} = -92.1533845053006$$
$$x_{79} = 2.0943951023932$$
$$x_{80} = 74.3510261349584$$
$$x_{81} = 83.7758040957278$$
$$x_{82} = 96.342174710087$$
$$x_{83} = 54.4542726622231$$
$$x_{84} = -57.5958653158129$$
$$x_{85} = -19.8967534727354$$
$$x_{86} = 85.870199198121$$
$$x_{87} = 5.23598775598299$$
$$x_{88} = -55.5014702134197$$
$$x_{89} = 76.4454212373516$$
$$x_{90} = -49.2182849062401$$
$$x_{91} = 92.1533845053006$$
$$x_{92} = 70.162235930172$$
$$x_{93} = -35.6047167406843$$
$$x_{94} = -36.6519142918809$$
$$x_{95} = 10.471975511966$$
Las raíces dadas
$$x_{60} = -99.4837673636768$$
$$x_{54} = -98.4365698124802$$
$$x_{9} = -93.2005820564972$$
$$x_{78} = -92.1533845053006$$
$$x_{30} = -90.0589894029074$$
$$x_{26} = -86.9173967493176$$
$$x_{45} = -85.870199198121$$
$$x_{66} = -83.7758040957278$$
$$x_{32} = -82.7286065445312$$
$$x_{63} = -80.634211442138$$
$$x_{47} = -79.5870138909414$$
$$x_{57} = -77.4926187885482$$
$$x_{38} = -76.4454212373516$$
$$x_{37} = -71.2094334813686$$
$$x_{42} = -70.162235930172$$
$$x_{40} = -68.0678408277789$$
$$x_{28} = -64.9262481741891$$
$$x_{74} = -63.8790506229925$$
$$x_{75} = -61.7846555205993$$
$$x_{67} = -60.7374579694027$$
$$x_{84} = -57.5958653158129$$
$$x_{88} = -55.5014702134197$$
$$x_{53} = -54.4542726622231$$
$$x_{90} = -49.2182849062401$$
$$x_{71} = -48.1710873550435$$
$$x_{50} = -46.0766922526503$$
$$x_{18} = -42.9350995990605$$
$$x_{11} = -41.8879020478639$$
$$x_{1} = -39.7935069454707$$
$$x_{46} = -38.7463093942741$$
$$x_{94} = -36.6519142918809$$
$$x_{93} = -35.6047167406843$$
$$x_{31} = -33.5103216382911$$
$$x_{56} = -32.4631240870945$$
$$x_{33} = -27.2271363311115$$
$$x_{4} = -26.1799387799149$$
$$x_{39} = -24.0855436775217$$
$$x_{14} = -20.943951023932$$
$$x_{85} = -19.8967534727354$$
$$x_{69} = -17.8023583703422$$
$$x_{19} = -16.7551608191456$$
$$x_{51} = -13.6135681655558$$
$$x_{29} = -11.5191730631626$$
$$x_{20} = -10.471975511966$$
$$x_{6} = -5.23598775598299$$
$$x_{52} = -4.18879020478639$$
$$x_{25} = -2.0943951023932$$
$$x_{61} = 1.0471975511966$$
$$x_{79} = 2.0943951023932$$
$$x_{13} = 4.18879020478639$$
$$x_{87} = 5.23598775598299$$
$$x_{22} = 8.37758040957278$$
$$x_{95} = 10.471975511966$$
$$x_{73} = 11.5191730631626$$
$$x_{68} = 16.7551608191456$$
$$x_{44} = 17.8023583703422$$
$$x_{21} = 19.8967534727354$$
$$x_{77} = 23.0383461263252$$
$$x_{27} = 24.0855436775217$$
$$x_{16} = 26.1799387799149$$
$$x_{48} = 27.2271363311115$$
$$x_{64} = 30.3687289847013$$
$$x_{7} = 32.4631240870945$$
$$x_{24} = 33.5103216382911$$
$$x_{49} = 38.7463093942741$$
$$x_{65} = 39.7935069454707$$
$$x_{59} = 41.8879020478639$$
$$x_{2} = 45.0294947014537$$
$$x_{72} = 46.0766922526503$$
$$x_{5} = 48.1710873550435$$
$$x_{10} = 49.2182849062401$$
$$x_{17} = 52.3598775598299$$
$$x_{83} = 54.4542726622231$$
$$x_{35} = 55.5014702134197$$
$$x_{55} = 60.7374579694027$$
$$x_{43} = 61.7846555205993$$
$$x_{76} = 63.8790506229925$$
$$x_{58} = 67.0206432765823$$
$$x_{34} = 68.0678408277789$$
$$x_{92} = 70.162235930172$$
$$x_{70} = 71.2094334813686$$
$$x_{80} = 74.3510261349584$$
$$x_{89} = 76.4454212373516$$
$$x_{62} = 77.4926187885482$$
$$x_{3} = 82.7286065445312$$
$$x_{81} = 83.7758040957278$$
$$x_{86} = 85.870199198121$$
$$x_{23} = 86.9173967493176$$
$$x_{15} = 89.0117918517108$$
$$x_{12} = 90.0589894029074$$
$$x_{91} = 92.1533845053006$$
$$x_{8} = 93.2005820564972$$
$$x_{82} = 96.342174710087$$
$$x_{41} = 98.4365698124802$$
$$x_{36} = 99.4837673636768$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{60}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{60} - \frac{1}{10}$$
=
$$-99.4837673636768 + - \frac{1}{10}$$
=
$$-99.5837673636768$$
lo sustituimos en la expresión
$$\left|{\sin{\left(x \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
$$\left|{\sin{\left(-99.5837673636768 \right)}}\right| \geq \frac{\sqrt{3}}{2}$$
___
\/ 3
0.811782175678687 >= -----
2
pero
___
\/ 3
0.811782175678687 < -----
2
Entonces
$$x \leq -99.4837673636768$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
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x60 x54 x9 x78 x30 x26 x45 x66 x32 x63 x47 x57 x38 x37 x42 x40 x28 x74 x75 x67 x84 x88 x53 x90 x71 x50 x18 x11 x1 x46 x94 x93 x31 x56 x33 x4 x39 x14 x85 x69 x19 x51 x29 x20 x6 x52 x25 x61 x79 x13 x87 x22 x95 x73 x68 x44 x21 x77 x27 x16 x48 x64 x7 x24 x49 x65 x59 x2 x72 x5 x10 x17 x83 x35 x55 x43 x76 x58 x34 x92 x70 x80 x89 x62 x3 x81 x86 x23 x15 x12 x91 x8 x82 x41 x36Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -99.4837673636768 \wedge x \leq -98.4365698124802$$
$$x \geq -93.2005820564972 \wedge x \leq -92.1533845053006$$
$$x \geq -90.0589894029074 \wedge x \leq -86.9173967493176$$
$$x \geq -85.870199198121 \wedge x \leq -83.7758040957278$$
$$x \geq -82.7286065445312 \wedge x \leq -80.634211442138$$
$$x \geq -79.5870138909414 \wedge x \leq -77.4926187885482$$
$$x \geq -76.4454212373516 \wedge x \leq -71.2094334813686$$
$$x \geq -70.162235930172 \wedge x \leq -68.0678408277789$$
$$x \geq -64.9262481741891 \wedge x \leq -63.8790506229925$$
$$x \geq -61.7846555205993 \wedge x \leq -60.7374579694027$$
$$x \geq -57.5958653158129 \wedge x \leq -55.5014702134197$$
$$x \geq -54.4542726622231 \wedge x \leq -49.2182849062401$$
$$x \geq -48.1710873550435 \wedge x \leq -46.0766922526503$$
$$x \geq -42.9350995990605 \wedge x \leq -41.8879020478639$$
$$x \geq -39.7935069454707 \wedge x \leq -38.7463093942741$$
$$x \geq -36.6519142918809 \wedge x \leq -35.6047167406843$$
$$x \geq -33.5103216382911 \wedge x \leq -32.4631240870945$$
$$x \geq -27.2271363311115 \wedge x \leq -26.1799387799149$$
$$x \geq -24.0855436775217 \wedge x \leq -20.943951023932$$
$$x \geq -19.8967534727354 \wedge x \leq -17.8023583703422$$
$$x \geq -16.7551608191456 \wedge x \leq -13.6135681655558$$
$$x \geq -11.5191730631626 \wedge x \leq -10.471975511966$$
$$x \geq -5.23598775598299 \wedge x \leq -4.18879020478639$$
$$x \geq -2.0943951023932 \wedge x \leq 1.0471975511966$$
$$x \geq 2.0943951023932 \wedge x \leq 4.18879020478639$$
$$x \geq 5.23598775598299 \wedge x \leq 8.37758040957278$$
$$x \geq 10.471975511966 \wedge x \leq 11.5191730631626$$
$$x \geq 16.7551608191456 \wedge x \leq 17.8023583703422$$
$$x \geq 19.8967534727354 \wedge x \leq 23.0383461263252$$
$$x \geq 24.0855436775217 \wedge x \leq 26.1799387799149$$
$$x \geq 27.2271363311115 \wedge x \leq 30.3687289847013$$
$$x \geq 32.4631240870945 \wedge x \leq 33.5103216382911$$
$$x \geq 38.7463093942741 \wedge x \leq 39.7935069454707$$
$$x \geq 41.8879020478639 \wedge x \leq 45.0294947014537$$
$$x \geq 46.0766922526503 \wedge x \leq 48.1710873550435$$
$$x \geq 49.2182849062401 \wedge x \leq 52.3598775598299$$
$$x \geq 54.4542726622231 \wedge x \leq 55.5014702134197$$
$$x \geq 60.7374579694027 \wedge x \leq 61.7846555205993$$
$$x \geq 63.8790506229925 \wedge x \leq 67.0206432765823$$
$$x \geq 68.0678408277789 \wedge x \leq 70.162235930172$$
$$x \geq 71.2094334813686 \wedge x \leq 74.3510261349584$$
$$x \geq 76.4454212373516 \wedge x \leq 77.4926187885482$$
$$x \geq 82.7286065445312 \wedge x \leq 83.7758040957278$$
$$x \geq 85.870199198121 \wedge x \leq 86.9173967493176$$
$$x \geq 89.0117918517108 \wedge x \leq 90.0589894029074$$
$$x \geq 92.1533845053006 \wedge x \leq 93.2005820564972$$
$$x \geq 96.342174710087 \wedge x \leq 98.4365698124802$$
$$x \geq 99.4837673636768$$
Solución de la desigualdad en el gráfico
Gráfico