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^2-3x+11>0
-
x^2-36<=0
-
x-1<=6x+15
-
x^2-4>0
- Integral de d{x}:
- cos(t)
- Límite de la función:
- cos(t)
- Derivada de:
-
cos(t)
-
Expresiones idénticas
- cos(t)<=- uno / dos
- coseno de (t) menos o igual a menos 1 dividir por 2
- coseno de (t) menos o igual a menos uno dividir por dos
- cost<=-1/2
- cos(t)<=-1 dividir por 2
-
Expresiones semejantes
- cost>√3/2
- cost≤-√2/2
- cost<=-3/2
- cos(t)<=+1/2
-
Expresiones con funciones
- Coseno cos
- cos(x)>=-1/2
- cos2x>1/2
- cos(x)<√3/2
- cos(x)<0
- cos(x)<=-√3/2
cos(t)<=-1/2 desigualdades
Solución
Solución detallada
Se da la desigualdad:
$$\cos{\left(t \right)} \leq - \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = - \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = - \frac{1}{2}$$
cambiamos
$$\cos{\left(t \right)} + \frac{1}{2} = 0$$
$$\cos{\left(t \right)} + \frac{1}{2} = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
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
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = -73.3038285837618$$
$$x_{2} = -10.471975511966$$
$$x_{3} = 4.18879020478639$$
$$x_{4} = 83.7758040957278$$
$$x_{5} = 58.6430628670095$$
$$x_{6} = -79.5870138909414$$
$$x_{7} = 117.286125734019$$
$$x_{8} = -96.342174710087$$
$$x_{9} = -14.6607657167524$$
$$x_{10} = 85.870199198121$$
$$x_{11} = 77.4926187885482$$
$$x_{12} = 8.37758040957278$$
$$x_{13} = -85.870199198121$$
$$x_{14} = -71.2094334813686$$
$$x_{15} = -4.18879020478639$$
$$x_{16} = 98.4365698124802$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = 27.2271363311115$$
$$x_{19} = -46.0766922526503$$
$$x_{20} = -64.9262481741891$$
$$x_{21} = -33.5103216382911$$
$$x_{22} = -58.6430628670095$$
$$x_{23} = 54.4542726622231$$
$$x_{24} = -67.0206432765823$$
$$x_{25} = 20.943951023932$$
$$x_{26} = -20.943951023932$$
$$x_{27} = 16.7551608191456$$
$$x_{28} = -90.0589894029074$$
$$x_{29} = 73.3038285837618$$
$$x_{30} = -16.7551608191456$$
$$x_{31} = -41.8879020478639$$
$$x_{32} = -60.7374579694027$$
$$x_{33} = 35.6047167406843$$
$$x_{34} = 92.1533845053006$$
$$x_{35} = -27.2271363311115$$
$$x_{36} = -23.0383461263252$$
$$x_{37} = -48.1710873550435$$
$$x_{38} = 46.0766922526503$$
$$x_{39} = 64.9262481741891$$
$$x_{40} = 67.0206432765823$$
$$x_{41} = -35.6047167406843$$
$$x_{42} = -29.3215314335047$$
$$x_{43} = 23.0383461263252$$
$$x_{44} = 60.7374579694027$$
$$x_{45} = -1623.15620435473$$
$$x_{46} = 90.0589894029074$$
$$x_{47} = 10.471975511966$$
$$x_{48} = 96.342174710087$$
$$x_{49} = 630.412925820352$$
$$x_{50} = -2.0943951023932$$
$$x_{51} = 41.8879020478639$$
$$x_{52} = 2.0943951023932$$
$$x_{53} = 33.5103216382911$$
$$x_{54} = -83.7758040957278$$
$$x_{55} = 39.7935069454707$$
$$x_{56} = 14.6607657167524$$
$$x_{57} = -54.4542726622231$$
$$x_{58} = 79.5870138909414$$
$$x_{59} = -92.1533845053006$$
$$x_{60} = -8.37758040957278$$
$$x_{61} = 71.2094334813686$$
$$x_{62} = -52.3598775598299$$
$$x_{63} = -39.7935069454707$$
$$x_{64} = -77.4926187885482$$
$$x_{65} = 29.3215314335047$$
$$x_{66} = 416.784625376246$$
$$x_{67} = 48.1710873550435$$
$$x_{68} = -98.4365698124802$$
$$x_{1} = -73.3038285837618$$
$$x_{2} = -10.471975511966$$
$$x_{3} = 4.18879020478639$$
$$x_{4} = 83.7758040957278$$
$$x_{5} = 58.6430628670095$$
$$x_{6} = -79.5870138909414$$
$$x_{7} = 117.286125734019$$
$$x_{8} = -96.342174710087$$
$$x_{9} = -14.6607657167524$$
$$x_{10} = 85.870199198121$$
$$x_{11} = 77.4926187885482$$
$$x_{12} = 8.37758040957278$$
$$x_{13} = -85.870199198121$$
$$x_{14} = -71.2094334813686$$
$$x_{15} = -4.18879020478639$$
$$x_{16} = 98.4365698124802$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = 27.2271363311115$$
$$x_{19} = -46.0766922526503$$
$$x_{20} = -64.9262481741891$$
$$x_{21} = -33.5103216382911$$
$$x_{22} = -58.6430628670095$$
$$x_{23} = 54.4542726622231$$
$$x_{24} = -67.0206432765823$$
$$x_{25} = 20.943951023932$$
$$x_{26} = -20.943951023932$$
$$x_{27} = 16.7551608191456$$
$$x_{28} = -90.0589894029074$$
$$x_{29} = 73.3038285837618$$
$$x_{30} = -16.7551608191456$$
$$x_{31} = -41.8879020478639$$
$$x_{32} = -60.7374579694027$$
$$x_{33} = 35.6047167406843$$
$$x_{34} = 92.1533845053006$$
$$x_{35} = -27.2271363311115$$
$$x_{36} = -23.0383461263252$$
$$x_{37} = -48.1710873550435$$
$$x_{38} = 46.0766922526503$$
$$x_{39} = 64.9262481741891$$
$$x_{40} = 67.0206432765823$$
$$x_{41} = -35.6047167406843$$
$$x_{42} = -29.3215314335047$$
$$x_{43} = 23.0383461263252$$
$$x_{44} = 60.7374579694027$$
$$x_{45} = -1623.15620435473$$
$$x_{46} = 90.0589894029074$$
$$x_{47} = 10.471975511966$$
$$x_{48} = 96.342174710087$$
$$x_{49} = 630.412925820352$$
$$x_{50} = -2.0943951023932$$
$$x_{51} = 41.8879020478639$$
$$x_{52} = 2.0943951023932$$
$$x_{53} = 33.5103216382911$$
$$x_{54} = -83.7758040957278$$
$$x_{55} = 39.7935069454707$$
$$x_{56} = 14.6607657167524$$
$$x_{57} = -54.4542726622231$$
$$x_{58} = 79.5870138909414$$
$$x_{59} = -92.1533845053006$$
$$x_{60} = -8.37758040957278$$
$$x_{61} = 71.2094334813686$$
$$x_{62} = -52.3598775598299$$
$$x_{63} = -39.7935069454707$$
$$x_{64} = -77.4926187885482$$
$$x_{65} = 29.3215314335047$$
$$x_{66} = 416.784625376246$$
$$x_{67} = 48.1710873550435$$
$$x_{68} = -98.4365698124802$$
Las raíces dadas
$$x_{45} = -1623.15620435473$$
$$x_{68} = -98.4365698124802$$
$$x_{8} = -96.342174710087$$
$$x_{59} = -92.1533845053006$$
$$x_{28} = -90.0589894029074$$
$$x_{13} = -85.870199198121$$
$$x_{54} = -83.7758040957278$$
$$x_{6} = -79.5870138909414$$
$$x_{64} = -77.4926187885482$$
$$x_{1} = -73.3038285837618$$
$$x_{14} = -71.2094334813686$$
$$x_{24} = -67.0206432765823$$
$$x_{20} = -64.9262481741891$$
$$x_{32} = -60.7374579694027$$
$$x_{22} = -58.6430628670095$$
$$x_{57} = -54.4542726622231$$
$$x_{62} = -52.3598775598299$$
$$x_{37} = -48.1710873550435$$
$$x_{19} = -46.0766922526503$$
$$x_{31} = -41.8879020478639$$
$$x_{63} = -39.7935069454707$$
$$x_{41} = -35.6047167406843$$
$$x_{21} = -33.5103216382911$$
$$x_{42} = -29.3215314335047$$
$$x_{35} = -27.2271363311115$$
$$x_{36} = -23.0383461263252$$
$$x_{26} = -20.943951023932$$
$$x_{30} = -16.7551608191456$$
$$x_{9} = -14.6607657167524$$
$$x_{2} = -10.471975511966$$
$$x_{60} = -8.37758040957278$$
$$x_{15} = -4.18879020478639$$
$$x_{50} = -2.0943951023932$$
$$x_{52} = 2.0943951023932$$
$$x_{3} = 4.18879020478639$$
$$x_{12} = 8.37758040957278$$
$$x_{47} = 10.471975511966$$
$$x_{56} = 14.6607657167524$$
$$x_{27} = 16.7551608191456$$
$$x_{25} = 20.943951023932$$
$$x_{43} = 23.0383461263252$$
$$x_{18} = 27.2271363311115$$
$$x_{65} = 29.3215314335047$$
$$x_{53} = 33.5103216382911$$
$$x_{33} = 35.6047167406843$$
$$x_{55} = 39.7935069454707$$
$$x_{51} = 41.8879020478639$$
$$x_{38} = 46.0766922526503$$
$$x_{67} = 48.1710873550435$$
$$x_{17} = 52.3598775598299$$
$$x_{23} = 54.4542726622231$$
$$x_{5} = 58.6430628670095$$
$$x_{44} = 60.7374579694027$$
$$x_{39} = 64.9262481741891$$
$$x_{40} = 67.0206432765823$$
$$x_{61} = 71.2094334813686$$
$$x_{29} = 73.3038285837618$$
$$x_{11} = 77.4926187885482$$
$$x_{58} = 79.5870138909414$$
$$x_{4} = 83.7758040957278$$
$$x_{10} = 85.870199198121$$
$$x_{46} = 90.0589894029074$$
$$x_{34} = 92.1533845053006$$
$$x_{48} = 96.342174710087$$
$$x_{16} = 98.4365698124802$$
$$x_{7} = 117.286125734019$$
$$x_{66} = 416.784625376246$$
$$x_{49} = 630.412925820352$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{45}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{45} - \frac{1}{10}$$
=
$$-1623.15620435473 + - \frac{1}{10}$$
=
$$-1623.25620435473$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \leq - \frac{1}{2}$$
$$\cos{\left(t \right)} \leq - \frac{1}{2}$$
Entonces
$$x \leq -1623.15620435473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -1623.15620435473 \wedge x \leq -98.4365698124802$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -1623.15620435473 \wedge x \leq -98.4365698124802$$
$$x \geq -96.342174710087 \wedge x \leq -92.1533845053006$$
$$x \geq -90.0589894029074 \wedge x \leq -85.870199198121$$
$$x \geq -83.7758040957278 \wedge x \leq -79.5870138909414$$
$$x \geq -77.4926187885482 \wedge x \leq -73.3038285837618$$
$$x \geq -71.2094334813686 \wedge x \leq -67.0206432765823$$
$$x \geq -64.9262481741891 \wedge x \leq -60.7374579694027$$
$$x \geq -58.6430628670095 \wedge x \leq -54.4542726622231$$
$$x \geq -52.3598775598299 \wedge x \leq -48.1710873550435$$
$$x \geq -46.0766922526503 \wedge x \leq -41.8879020478639$$
$$x \geq -39.7935069454707 \wedge x \leq -35.6047167406843$$
$$x \geq -33.5103216382911 \wedge x \leq -29.3215314335047$$
$$x \geq -27.2271363311115 \wedge x \leq -23.0383461263252$$
$$x \geq -20.943951023932 \wedge x \leq -16.7551608191456$$
$$x \geq -14.6607657167524 \wedge x \leq -10.471975511966$$
$$x \geq -8.37758040957278 \wedge x \leq -4.18879020478639$$
$$x \geq -2.0943951023932 \wedge x \leq 2.0943951023932$$
$$x \geq 4.18879020478639 \wedge x \leq 8.37758040957278$$
$$x \geq 10.471975511966 \wedge x \leq 14.6607657167524$$
$$x \geq 16.7551608191456 \wedge x \leq 20.943951023932$$
$$x \geq 23.0383461263252 \wedge x \leq 27.2271363311115$$
$$x \geq 29.3215314335047 \wedge x \leq 33.5103216382911$$
$$x \geq 35.6047167406843 \wedge x \leq 39.7935069454707$$
$$x \geq 41.8879020478639 \wedge x \leq 46.0766922526503$$
$$x \geq 48.1710873550435 \wedge x \leq 52.3598775598299$$
$$x \geq 54.4542726622231 \wedge x \leq 58.6430628670095$$
$$x \geq 60.7374579694027 \wedge x \leq 64.9262481741891$$
$$x \geq 67.0206432765823 \wedge x \leq 71.2094334813686$$
$$x \geq 73.3038285837618 \wedge x \leq 77.4926187885482$$
$$x \geq 79.5870138909414 \wedge x \leq 83.7758040957278$$
$$x \geq 85.870199198121 \wedge x \leq 90.0589894029074$$
$$x \geq 92.1533845053006 \wedge x \leq 96.342174710087$$
$$x \geq 98.4365698124802 \wedge x \leq 117.286125734019$$
$$x \geq 416.784625376246 \wedge x \leq 630.412925820352$$
$$\cos{\left(t \right)} \leq - \frac{1}{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\cos{\left(t \right)} = - \frac{1}{2}$$
Resolvemos:
Tenemos la ecuación
$$\cos{\left(t \right)} = - \frac{1}{2}$$
cambiamos
$$\cos{\left(t \right)} + \frac{1}{2} = 0$$
$$\cos{\left(t \right)} + \frac{1}{2} = 0$$
Sustituimos
$$w = \cos{\left(t \right)}$$
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
$$\cos{\left(t \right)} = w$$
sustituimos w:
$$x_{1} = -73.3038285837618$$
$$x_{2} = -10.471975511966$$
$$x_{3} = 4.18879020478639$$
$$x_{4} = 83.7758040957278$$
$$x_{5} = 58.6430628670095$$
$$x_{6} = -79.5870138909414$$
$$x_{7} = 117.286125734019$$
$$x_{8} = -96.342174710087$$
$$x_{9} = -14.6607657167524$$
$$x_{10} = 85.870199198121$$
$$x_{11} = 77.4926187885482$$
$$x_{12} = 8.37758040957278$$
$$x_{13} = -85.870199198121$$
$$x_{14} = -71.2094334813686$$
$$x_{15} = -4.18879020478639$$
$$x_{16} = 98.4365698124802$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = 27.2271363311115$$
$$x_{19} = -46.0766922526503$$
$$x_{20} = -64.9262481741891$$
$$x_{21} = -33.5103216382911$$
$$x_{22} = -58.6430628670095$$
$$x_{23} = 54.4542726622231$$
$$x_{24} = -67.0206432765823$$
$$x_{25} = 20.943951023932$$
$$x_{26} = -20.943951023932$$
$$x_{27} = 16.7551608191456$$
$$x_{28} = -90.0589894029074$$
$$x_{29} = 73.3038285837618$$
$$x_{30} = -16.7551608191456$$
$$x_{31} = -41.8879020478639$$
$$x_{32} = -60.7374579694027$$
$$x_{33} = 35.6047167406843$$
$$x_{34} = 92.1533845053006$$
$$x_{35} = -27.2271363311115$$
$$x_{36} = -23.0383461263252$$
$$x_{37} = -48.1710873550435$$
$$x_{38} = 46.0766922526503$$
$$x_{39} = 64.9262481741891$$
$$x_{40} = 67.0206432765823$$
$$x_{41} = -35.6047167406843$$
$$x_{42} = -29.3215314335047$$
$$x_{43} = 23.0383461263252$$
$$x_{44} = 60.7374579694027$$
$$x_{45} = -1623.15620435473$$
$$x_{46} = 90.0589894029074$$
$$x_{47} = 10.471975511966$$
$$x_{48} = 96.342174710087$$
$$x_{49} = 630.412925820352$$
$$x_{50} = -2.0943951023932$$
$$x_{51} = 41.8879020478639$$
$$x_{52} = 2.0943951023932$$
$$x_{53} = 33.5103216382911$$
$$x_{54} = -83.7758040957278$$
$$x_{55} = 39.7935069454707$$
$$x_{56} = 14.6607657167524$$
$$x_{57} = -54.4542726622231$$
$$x_{58} = 79.5870138909414$$
$$x_{59} = -92.1533845053006$$
$$x_{60} = -8.37758040957278$$
$$x_{61} = 71.2094334813686$$
$$x_{62} = -52.3598775598299$$
$$x_{63} = -39.7935069454707$$
$$x_{64} = -77.4926187885482$$
$$x_{65} = 29.3215314335047$$
$$x_{66} = 416.784625376246$$
$$x_{67} = 48.1710873550435$$
$$x_{68} = -98.4365698124802$$
$$x_{1} = -73.3038285837618$$
$$x_{2} = -10.471975511966$$
$$x_{3} = 4.18879020478639$$
$$x_{4} = 83.7758040957278$$
$$x_{5} = 58.6430628670095$$
$$x_{6} = -79.5870138909414$$
$$x_{7} = 117.286125734019$$
$$x_{8} = -96.342174710087$$
$$x_{9} = -14.6607657167524$$
$$x_{10} = 85.870199198121$$
$$x_{11} = 77.4926187885482$$
$$x_{12} = 8.37758040957278$$
$$x_{13} = -85.870199198121$$
$$x_{14} = -71.2094334813686$$
$$x_{15} = -4.18879020478639$$
$$x_{16} = 98.4365698124802$$
$$x_{17} = 52.3598775598299$$
$$x_{18} = 27.2271363311115$$
$$x_{19} = -46.0766922526503$$
$$x_{20} = -64.9262481741891$$
$$x_{21} = -33.5103216382911$$
$$x_{22} = -58.6430628670095$$
$$x_{23} = 54.4542726622231$$
$$x_{24} = -67.0206432765823$$
$$x_{25} = 20.943951023932$$
$$x_{26} = -20.943951023932$$
$$x_{27} = 16.7551608191456$$
$$x_{28} = -90.0589894029074$$
$$x_{29} = 73.3038285837618$$
$$x_{30} = -16.7551608191456$$
$$x_{31} = -41.8879020478639$$
$$x_{32} = -60.7374579694027$$
$$x_{33} = 35.6047167406843$$
$$x_{34} = 92.1533845053006$$
$$x_{35} = -27.2271363311115$$
$$x_{36} = -23.0383461263252$$
$$x_{37} = -48.1710873550435$$
$$x_{38} = 46.0766922526503$$
$$x_{39} = 64.9262481741891$$
$$x_{40} = 67.0206432765823$$
$$x_{41} = -35.6047167406843$$
$$x_{42} = -29.3215314335047$$
$$x_{43} = 23.0383461263252$$
$$x_{44} = 60.7374579694027$$
$$x_{45} = -1623.15620435473$$
$$x_{46} = 90.0589894029074$$
$$x_{47} = 10.471975511966$$
$$x_{48} = 96.342174710087$$
$$x_{49} = 630.412925820352$$
$$x_{50} = -2.0943951023932$$
$$x_{51} = 41.8879020478639$$
$$x_{52} = 2.0943951023932$$
$$x_{53} = 33.5103216382911$$
$$x_{54} = -83.7758040957278$$
$$x_{55} = 39.7935069454707$$
$$x_{56} = 14.6607657167524$$
$$x_{57} = -54.4542726622231$$
$$x_{58} = 79.5870138909414$$
$$x_{59} = -92.1533845053006$$
$$x_{60} = -8.37758040957278$$
$$x_{61} = 71.2094334813686$$
$$x_{62} = -52.3598775598299$$
$$x_{63} = -39.7935069454707$$
$$x_{64} = -77.4926187885482$$
$$x_{65} = 29.3215314335047$$
$$x_{66} = 416.784625376246$$
$$x_{67} = 48.1710873550435$$
$$x_{68} = -98.4365698124802$$
Las raíces dadas
$$x_{45} = -1623.15620435473$$
$$x_{68} = -98.4365698124802$$
$$x_{8} = -96.342174710087$$
$$x_{59} = -92.1533845053006$$
$$x_{28} = -90.0589894029074$$
$$x_{13} = -85.870199198121$$
$$x_{54} = -83.7758040957278$$
$$x_{6} = -79.5870138909414$$
$$x_{64} = -77.4926187885482$$
$$x_{1} = -73.3038285837618$$
$$x_{14} = -71.2094334813686$$
$$x_{24} = -67.0206432765823$$
$$x_{20} = -64.9262481741891$$
$$x_{32} = -60.7374579694027$$
$$x_{22} = -58.6430628670095$$
$$x_{57} = -54.4542726622231$$
$$x_{62} = -52.3598775598299$$
$$x_{37} = -48.1710873550435$$
$$x_{19} = -46.0766922526503$$
$$x_{31} = -41.8879020478639$$
$$x_{63} = -39.7935069454707$$
$$x_{41} = -35.6047167406843$$
$$x_{21} = -33.5103216382911$$
$$x_{42} = -29.3215314335047$$
$$x_{35} = -27.2271363311115$$
$$x_{36} = -23.0383461263252$$
$$x_{26} = -20.943951023932$$
$$x_{30} = -16.7551608191456$$
$$x_{9} = -14.6607657167524$$
$$x_{2} = -10.471975511966$$
$$x_{60} = -8.37758040957278$$
$$x_{15} = -4.18879020478639$$
$$x_{50} = -2.0943951023932$$
$$x_{52} = 2.0943951023932$$
$$x_{3} = 4.18879020478639$$
$$x_{12} = 8.37758040957278$$
$$x_{47} = 10.471975511966$$
$$x_{56} = 14.6607657167524$$
$$x_{27} = 16.7551608191456$$
$$x_{25} = 20.943951023932$$
$$x_{43} = 23.0383461263252$$
$$x_{18} = 27.2271363311115$$
$$x_{65} = 29.3215314335047$$
$$x_{53} = 33.5103216382911$$
$$x_{33} = 35.6047167406843$$
$$x_{55} = 39.7935069454707$$
$$x_{51} = 41.8879020478639$$
$$x_{38} = 46.0766922526503$$
$$x_{67} = 48.1710873550435$$
$$x_{17} = 52.3598775598299$$
$$x_{23} = 54.4542726622231$$
$$x_{5} = 58.6430628670095$$
$$x_{44} = 60.7374579694027$$
$$x_{39} = 64.9262481741891$$
$$x_{40} = 67.0206432765823$$
$$x_{61} = 71.2094334813686$$
$$x_{29} = 73.3038285837618$$
$$x_{11} = 77.4926187885482$$
$$x_{58} = 79.5870138909414$$
$$x_{4} = 83.7758040957278$$
$$x_{10} = 85.870199198121$$
$$x_{46} = 90.0589894029074$$
$$x_{34} = 92.1533845053006$$
$$x_{48} = 96.342174710087$$
$$x_{16} = 98.4365698124802$$
$$x_{7} = 117.286125734019$$
$$x_{66} = 416.784625376246$$
$$x_{49} = 630.412925820352$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} \leq x_{45}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{45} - \frac{1}{10}$$
=
$$-1623.15620435473 + - \frac{1}{10}$$
=
$$-1623.25620435473$$
lo sustituimos en la expresión
$$\cos{\left(t \right)} \leq - \frac{1}{2}$$
$$\cos{\left(t \right)} \leq - \frac{1}{2}$$
cos(t) <= -1/2
Entonces
$$x \leq -1623.15620435473$$
no se cumple
significa que una de las soluciones de nuestra ecuación será con:
$$x \geq -1623.15620435473 \wedge x \leq -98.4365698124802$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------•-------
x45 x68 x8 x59 x28 x13 x54 x6 x64 x1 x14 x24 x20 x32 x22 x57 x62 x37 x19 x31 x63 x41 x21 x42 x35 x36 x26 x30 x9 x2 x60 x15 x50 x52 x3 x12 x47 x56 x27 x25 x43 x18 x65 x53 x33 x55 x51 x38 x67 x17 x23 x5 x44 x39 x40 x61 x29 x11 x58 x4 x10 x46 x34 x48 x16 x7 x66 x49Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x \geq -1623.15620435473 \wedge x \leq -98.4365698124802$$
$$x \geq -96.342174710087 \wedge x \leq -92.1533845053006$$
$$x \geq -90.0589894029074 \wedge x \leq -85.870199198121$$
$$x \geq -83.7758040957278 \wedge x \leq -79.5870138909414$$
$$x \geq -77.4926187885482 \wedge x \leq -73.3038285837618$$
$$x \geq -71.2094334813686 \wedge x \leq -67.0206432765823$$
$$x \geq -64.9262481741891 \wedge x \leq -60.7374579694027$$
$$x \geq -58.6430628670095 \wedge x \leq -54.4542726622231$$
$$x \geq -52.3598775598299 \wedge x \leq -48.1710873550435$$
$$x \geq -46.0766922526503 \wedge x \leq -41.8879020478639$$
$$x \geq -39.7935069454707 \wedge x \leq -35.6047167406843$$
$$x \geq -33.5103216382911 \wedge x \leq -29.3215314335047$$
$$x \geq -27.2271363311115 \wedge x \leq -23.0383461263252$$
$$x \geq -20.943951023932 \wedge x \leq -16.7551608191456$$
$$x \geq -14.6607657167524 \wedge x \leq -10.471975511966$$
$$x \geq -8.37758040957278 \wedge x \leq -4.18879020478639$$
$$x \geq -2.0943951023932 \wedge x \leq 2.0943951023932$$
$$x \geq 4.18879020478639 \wedge x \leq 8.37758040957278$$
$$x \geq 10.471975511966 \wedge x \leq 14.6607657167524$$
$$x \geq 16.7551608191456 \wedge x \leq 20.943951023932$$
$$x \geq 23.0383461263252 \wedge x \leq 27.2271363311115$$
$$x \geq 29.3215314335047 \wedge x \leq 33.5103216382911$$
$$x \geq 35.6047167406843 \wedge x \leq 39.7935069454707$$
$$x \geq 41.8879020478639 \wedge x \leq 46.0766922526503$$
$$x \geq 48.1710873550435 \wedge x \leq 52.3598775598299$$
$$x \geq 54.4542726622231 \wedge x \leq 58.6430628670095$$
$$x \geq 60.7374579694027 \wedge x \leq 64.9262481741891$$
$$x \geq 67.0206432765823 \wedge x \leq 71.2094334813686$$
$$x \geq 73.3038285837618 \wedge x \leq 77.4926187885482$$
$$x \geq 79.5870138909414 \wedge x \leq 83.7758040957278$$
$$x \geq 85.870199198121 \wedge x \leq 90.0589894029074$$
$$x \geq 92.1533845053006 \wedge x \leq 96.342174710087$$
$$x \geq 98.4365698124802 \wedge x \leq 117.286125734019$$
$$x \geq 416.784625376246 \wedge x \leq 630.412925820352$$
Respuesta rápida
[src]
/2*pi 4*pi\ And|---- <= t, t <= ----| \ 3 3 /
$$\frac{2 \pi}{3} \leq t \wedge t \leq \frac{4 \pi}{3}$$
(2*pi/3 <= t)∧(t <= 4*pi/3)
Respuesta rápida 2
[src]
2*pi 4*pi [----, ----] 3 3
$$x\ in\ \left[\frac{2 \pi}{3}, \frac{4 \pi}{3}\right]$$
x in Interval(2*pi/3, 4*pi/3)