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- Sistemas de desigualdades paso a paso
- Ecuaciones básicas paso a paso
- Sistemas de ecuaciones paso a paso
- Solución de desigualdades trigonométricas en línea
- Resolución de desigualdades exponenciales en línea
- Resolución de desigualdades con un módulo en línea
-
¿Cómo usar?
- Desigualdades:
-
7x-x^2>=0
-
x^2+x-12<0
-
x^2<9
-
x^2-6x+9<0
-
Expresiones idénticas
- cuatro ^x-sqrt(tres)*cos(x)-2sin(x)*cos(x)> cero
- 4 en el grado x menos raíz cuadrada de (3) multiplicar por coseno de (x) menos 2 seno de (x) multiplicar por coseno de (x) más 0
- cuatro en el grado x menos raíz cuadrada de (tres) multiplicar por coseno de (x) menos 2 seno de (x) multiplicar por coseno de (x) más cero
- 4^x-√(3)*cos(x)-2sin(x)*cos(x)>0
- 4x-sqrt(3)*cos(x)-2sin(x)*cos(x)>0
- 4x-sqrt3*cosx-2sinx*cosx>0
- 4^x-sqrt(3)cos(x)-2sin(x)cos(x)>0
- 4x-sqrt(3)cos(x)-2sin(x)cos(x)>0
- 4x-sqrt3cosx-2sinxcosx>0
- 4^x-sqrt3cosx-2sinxcosx>0
-
Expresiones semejantes
- 4^x-sqrt(3)*cos(x)+2sin(x)*cos(x)>0
- 4^x+sqrt(3)*cos(x)-2sin(x)*cos(x)>0
- 4^x-sqrt(3)*cosx-2sinx*cosx>0
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(6-6x)>6
- sqrt(1+x)<=3
- sqrt(2x^2-6x-8)>=x+1
- sqrt(x+2)-sqrt(2*x-1)>sqrt(x-2)
- sqrt(x^2-2x)>1-x
- Coseno cos
- cos(x)>0,5
- cos(x)-sin(x)>0
- cos(x)>-0,5
- cos(x)+sin(x)>0
- cos(x)>=x^2+1
- Coseno cos
- cos(x)>0,5
- cos(x)-sin(x)>0
- cos(x)>-0,5
- cos(x)+sin(x)>0
- cos(x)>=x^2+1
4^x-sqrt(3)*cos(x)-2sin(x)*cos(x)>0 desigualdades
Solución
Ha introducido
[src]
x ___ 4 - \/ 3 *cos(x) - 2*sin(x)*cos(x) > 0
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} > 0$$
4^x - sqrt(3)*cos(x) - 2*sin(x)*cos(x) > 0
Solución detallada
Se da la desigualdad:
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} = 0$$
Resolvemos:
$$x_{1} = -64.9262481741891$$
$$x_{2} = -82.7286065445312$$
$$x_{3} = -29.845130209103$$
$$x_{4} = -39.7935069454707$$
$$x_{5} = -67.5442420521806$$
$$x_{6} = -38.7463093942741$$
$$x_{7} = -36.1283155162826$$
$$x_{8} = -45.0294947014537$$
$$x_{9} = -92.6769832808989$$
$$x_{10} = -61.261056745001$$
$$x_{11} = -83.7758040957278$$
$$x_{12} = -95.8185759344887$$
$$x_{13} = -52.3598775598299$$
$$x_{14} = -89.0117918517108$$
$$x_{15} = -20.9439510239315$$
$$x_{16} = -76.4454212373516$$
$$x_{17} = -7.85405135077815$$
$$x_{18} = -58.6430628670095$$
$$x_{19} = -63.8790506229925$$
$$x_{20} = -48.6946861306418$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = -17.2787595947545$$
$$x_{23} = -27.2271363311115$$
$$x_{24} = -80.1106126665397$$
$$x_{25} = -8.37756232720506$$
$$x_{26} = -14.6607657137713$$
$$x_{27} = -19.8967534727333$$
$$x_{28} = -0.659060267770608$$
$$x_{29} = -45.553093477052$$
$$x_{30} = -26.1799387799149$$
$$x_{31} = -32.4631240870945$$
$$x_{32} = -90.0589894029074$$
$$x_{33} = -58.1194640914112$$
$$x_{34} = -96.342174710087$$
$$x_{35} = -51.8362787842316$$
$$x_{36} = -42.4115008234622$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = 0.618199421804696$$
$$x_{39} = -33.5103216382911$$
$$x_{40} = -77.4926187885482$$
$$x_{41} = -23.5619449019235$$
$$x_{42} = -70.162235930172$$
$$x_{43} = -73.8274273593601$$
$$x_{1} = -64.9262481741891$$
$$x_{2} = -82.7286065445312$$
$$x_{3} = -29.845130209103$$
$$x_{4} = -39.7935069454707$$
$$x_{5} = -67.5442420521806$$
$$x_{6} = -38.7463093942741$$
$$x_{7} = -36.1283155162826$$
$$x_{8} = -45.0294947014537$$
$$x_{9} = -92.6769832808989$$
$$x_{10} = -61.261056745001$$
$$x_{11} = -83.7758040957278$$
$$x_{12} = -95.8185759344887$$
$$x_{13} = -52.3598775598299$$
$$x_{14} = -89.0117918517108$$
$$x_{15} = -20.9439510239315$$
$$x_{16} = -76.4454212373516$$
$$x_{17} = -7.85405135077815$$
$$x_{18} = -58.6430628670095$$
$$x_{19} = -63.8790506229925$$
$$x_{20} = -48.6946861306418$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = -17.2787595947545$$
$$x_{23} = -27.2271363311115$$
$$x_{24} = -80.1106126665397$$
$$x_{25} = -8.37756232720506$$
$$x_{26} = -14.6607657137713$$
$$x_{27} = -19.8967534727333$$
$$x_{28} = -0.659060267770608$$
$$x_{29} = -45.553093477052$$
$$x_{30} = -26.1799387799149$$
$$x_{31} = -32.4631240870945$$
$$x_{32} = -90.0589894029074$$
$$x_{33} = -58.1194640914112$$
$$x_{34} = -96.342174710087$$
$$x_{35} = -51.8362787842316$$
$$x_{36} = -42.4115008234622$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = 0.618199421804696$$
$$x_{39} = -33.5103216382911$$
$$x_{40} = -77.4926187885482$$
$$x_{41} = -23.5619449019235$$
$$x_{42} = -70.162235930172$$
$$x_{43} = -73.8274273593601$$
Las raíces dadas
$$x_{34} = -96.342174710087$$
$$x_{12} = -95.8185759344887$$
$$x_{9} = -92.6769832808989$$
$$x_{32} = -90.0589894029074$$
$$x_{14} = -89.0117918517108$$
$$x_{21} = -86.3937979737193$$
$$x_{11} = -83.7758040957278$$
$$x_{2} = -82.7286065445312$$
$$x_{24} = -80.1106126665397$$
$$x_{40} = -77.4926187885482$$
$$x_{16} = -76.4454212373516$$
$$x_{43} = -73.8274273593601$$
$$x_{37} = -71.2094334813686$$
$$x_{42} = -70.162235930172$$
$$x_{5} = -67.5442420521806$$
$$x_{1} = -64.9262481741891$$
$$x_{19} = -63.8790506229925$$
$$x_{10} = -61.261056745001$$
$$x_{18} = -58.6430628670095$$
$$x_{33} = -58.1194640914112$$
$$x_{13} = -52.3598775598299$$
$$x_{35} = -51.8362787842316$$
$$x_{20} = -48.6946861306418$$
$$x_{29} = -45.553093477052$$
$$x_{8} = -45.0294947014537$$
$$x_{36} = -42.4115008234622$$
$$x_{4} = -39.7935069454707$$
$$x_{6} = -38.7463093942741$$
$$x_{7} = -36.1283155162826$$
$$x_{39} = -33.5103216382911$$
$$x_{31} = -32.4631240870945$$
$$x_{3} = -29.845130209103$$
$$x_{23} = -27.2271363311115$$
$$x_{30} = -26.1799387799149$$
$$x_{41} = -23.5619449019235$$
$$x_{15} = -20.9439510239315$$
$$x_{27} = -19.8967534727333$$
$$x_{22} = -17.2787595947545$$
$$x_{26} = -14.6607657137713$$
$$x_{25} = -8.37756232720506$$
$$x_{17} = -7.85405135077815$$
$$x_{28} = -0.659060267770608$$
$$x_{38} = 0.618199421804696$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{34}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{34} - \frac{1}{10}$$
=
$$-96.342174710087 + - \frac{1}{10}$$
=
$$-96.442174710087$$
lo sustituimos en la expresión
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} > 0$$
$$- 2 \sin{\left(-96.442174710087 \right)} \cos{\left(-96.442174710087 \right)} + \left(4^{-96.442174710087} - \sqrt{3} \cos{\left(-96.442174710087 \right)}\right) > 0$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -96.342174710087$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -96.342174710087$$
$$x > -95.8185759344887 \wedge x < -92.6769832808989$$
$$x > -90.0589894029074 \wedge x < -89.0117918517108$$
$$x > -86.3937979737193 \wedge x < -83.7758040957278$$
$$x > -82.7286065445312 \wedge x < -80.1106126665397$$
$$x > -77.4926187885482 \wedge x < -76.4454212373516$$
$$x > -73.8274273593601 \wedge x < -71.2094334813686$$
$$x > -70.162235930172 \wedge x < -67.5442420521806$$
$$x > -64.9262481741891 \wedge x < -63.8790506229925$$
$$x > -61.261056745001 \wedge x < -58.6430628670095$$
$$x > -58.1194640914112 \wedge x < -52.3598775598299$$
$$x > -51.8362787842316 \wedge x < -48.6946861306418$$
$$x > -45.553093477052 \wedge x < -45.0294947014537$$
$$x > -42.4115008234622 \wedge x < -39.7935069454707$$
$$x > -38.7463093942741 \wedge x < -36.1283155162826$$
$$x > -33.5103216382911 \wedge x < -32.4631240870945$$
$$x > -29.845130209103 \wedge x < -27.2271363311115$$
$$x > -26.1799387799149 \wedge x < -23.5619449019235$$
$$x > -20.9439510239315 \wedge x < -19.8967534727333$$
$$x > -17.2787595947545 \wedge x < -14.6607657137713$$
$$x > -8.37756232720506 \wedge x < -7.85405135077815$$
$$x > -0.659060267770608 \wedge x < 0.618199421804696$$
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} > 0$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} = 0$$
Resolvemos:
$$x_{1} = -64.9262481741891$$
$$x_{2} = -82.7286065445312$$
$$x_{3} = -29.845130209103$$
$$x_{4} = -39.7935069454707$$
$$x_{5} = -67.5442420521806$$
$$x_{6} = -38.7463093942741$$
$$x_{7} = -36.1283155162826$$
$$x_{8} = -45.0294947014537$$
$$x_{9} = -92.6769832808989$$
$$x_{10} = -61.261056745001$$
$$x_{11} = -83.7758040957278$$
$$x_{12} = -95.8185759344887$$
$$x_{13} = -52.3598775598299$$
$$x_{14} = -89.0117918517108$$
$$x_{15} = -20.9439510239315$$
$$x_{16} = -76.4454212373516$$
$$x_{17} = -7.85405135077815$$
$$x_{18} = -58.6430628670095$$
$$x_{19} = -63.8790506229925$$
$$x_{20} = -48.6946861306418$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = -17.2787595947545$$
$$x_{23} = -27.2271363311115$$
$$x_{24} = -80.1106126665397$$
$$x_{25} = -8.37756232720506$$
$$x_{26} = -14.6607657137713$$
$$x_{27} = -19.8967534727333$$
$$x_{28} = -0.659060267770608$$
$$x_{29} = -45.553093477052$$
$$x_{30} = -26.1799387799149$$
$$x_{31} = -32.4631240870945$$
$$x_{32} = -90.0589894029074$$
$$x_{33} = -58.1194640914112$$
$$x_{34} = -96.342174710087$$
$$x_{35} = -51.8362787842316$$
$$x_{36} = -42.4115008234622$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = 0.618199421804696$$
$$x_{39} = -33.5103216382911$$
$$x_{40} = -77.4926187885482$$
$$x_{41} = -23.5619449019235$$
$$x_{42} = -70.162235930172$$
$$x_{43} = -73.8274273593601$$
$$x_{1} = -64.9262481741891$$
$$x_{2} = -82.7286065445312$$
$$x_{3} = -29.845130209103$$
$$x_{4} = -39.7935069454707$$
$$x_{5} = -67.5442420521806$$
$$x_{6} = -38.7463093942741$$
$$x_{7} = -36.1283155162826$$
$$x_{8} = -45.0294947014537$$
$$x_{9} = -92.6769832808989$$
$$x_{10} = -61.261056745001$$
$$x_{11} = -83.7758040957278$$
$$x_{12} = -95.8185759344887$$
$$x_{13} = -52.3598775598299$$
$$x_{14} = -89.0117918517108$$
$$x_{15} = -20.9439510239315$$
$$x_{16} = -76.4454212373516$$
$$x_{17} = -7.85405135077815$$
$$x_{18} = -58.6430628670095$$
$$x_{19} = -63.8790506229925$$
$$x_{20} = -48.6946861306418$$
$$x_{21} = -86.3937979737193$$
$$x_{22} = -17.2787595947545$$
$$x_{23} = -27.2271363311115$$
$$x_{24} = -80.1106126665397$$
$$x_{25} = -8.37756232720506$$
$$x_{26} = -14.6607657137713$$
$$x_{27} = -19.8967534727333$$
$$x_{28} = -0.659060267770608$$
$$x_{29} = -45.553093477052$$
$$x_{30} = -26.1799387799149$$
$$x_{31} = -32.4631240870945$$
$$x_{32} = -90.0589894029074$$
$$x_{33} = -58.1194640914112$$
$$x_{34} = -96.342174710087$$
$$x_{35} = -51.8362787842316$$
$$x_{36} = -42.4115008234622$$
$$x_{37} = -71.2094334813686$$
$$x_{38} = 0.618199421804696$$
$$x_{39} = -33.5103216382911$$
$$x_{40} = -77.4926187885482$$
$$x_{41} = -23.5619449019235$$
$$x_{42} = -70.162235930172$$
$$x_{43} = -73.8274273593601$$
Las raíces dadas
$$x_{34} = -96.342174710087$$
$$x_{12} = -95.8185759344887$$
$$x_{9} = -92.6769832808989$$
$$x_{32} = -90.0589894029074$$
$$x_{14} = -89.0117918517108$$
$$x_{21} = -86.3937979737193$$
$$x_{11} = -83.7758040957278$$
$$x_{2} = -82.7286065445312$$
$$x_{24} = -80.1106126665397$$
$$x_{40} = -77.4926187885482$$
$$x_{16} = -76.4454212373516$$
$$x_{43} = -73.8274273593601$$
$$x_{37} = -71.2094334813686$$
$$x_{42} = -70.162235930172$$
$$x_{5} = -67.5442420521806$$
$$x_{1} = -64.9262481741891$$
$$x_{19} = -63.8790506229925$$
$$x_{10} = -61.261056745001$$
$$x_{18} = -58.6430628670095$$
$$x_{33} = -58.1194640914112$$
$$x_{13} = -52.3598775598299$$
$$x_{35} = -51.8362787842316$$
$$x_{20} = -48.6946861306418$$
$$x_{29} = -45.553093477052$$
$$x_{8} = -45.0294947014537$$
$$x_{36} = -42.4115008234622$$
$$x_{4} = -39.7935069454707$$
$$x_{6} = -38.7463093942741$$
$$x_{7} = -36.1283155162826$$
$$x_{39} = -33.5103216382911$$
$$x_{31} = -32.4631240870945$$
$$x_{3} = -29.845130209103$$
$$x_{23} = -27.2271363311115$$
$$x_{30} = -26.1799387799149$$
$$x_{41} = -23.5619449019235$$
$$x_{15} = -20.9439510239315$$
$$x_{27} = -19.8967534727333$$
$$x_{22} = -17.2787595947545$$
$$x_{26} = -14.6607657137713$$
$$x_{25} = -8.37756232720506$$
$$x_{17} = -7.85405135077815$$
$$x_{28} = -0.659060267770608$$
$$x_{38} = 0.618199421804696$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{34}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{34} - \frac{1}{10}$$
=
$$-96.342174710087 + - \frac{1}{10}$$
=
$$-96.442174710087$$
lo sustituimos en la expresión
$$\left(4^{x} - \sqrt{3} \cos{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)} > 0$$
$$- 2 \sin{\left(-96.442174710087 \right)} \cos{\left(-96.442174710087 \right)} + \left(4^{-96.442174710087} - \sqrt{3} \cos{\left(-96.442174710087 \right)}\right) > 0$$
___
-0.948097219208122 + 0.583960357601758*\/ 3 > 0
significa que una de las soluciones de nuestra ecuación será con:
$$x < -96.342174710087$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x34 x12 x9 x32 x14 x21 x11 x2 x24 x40 x16 x43 x37 x42 x5 x1 x19 x10 x18 x33 x13 x35 x20 x29 x8 x36 x4 x6 x7 x39 x31 x3 x23 x30 x41 x15 x27 x22 x26 x25 x17 x28 x38Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -96.342174710087$$
$$x > -95.8185759344887 \wedge x < -92.6769832808989$$
$$x > -90.0589894029074 \wedge x < -89.0117918517108$$
$$x > -86.3937979737193 \wedge x < -83.7758040957278$$
$$x > -82.7286065445312 \wedge x < -80.1106126665397$$
$$x > -77.4926187885482 \wedge x < -76.4454212373516$$
$$x > -73.8274273593601 \wedge x < -71.2094334813686$$
$$x > -70.162235930172 \wedge x < -67.5442420521806$$
$$x > -64.9262481741891 \wedge x < -63.8790506229925$$
$$x > -61.261056745001 \wedge x < -58.6430628670095$$
$$x > -58.1194640914112 \wedge x < -52.3598775598299$$
$$x > -51.8362787842316 \wedge x < -48.6946861306418$$
$$x > -45.553093477052 \wedge x < -45.0294947014537$$
$$x > -42.4115008234622 \wedge x < -39.7935069454707$$
$$x > -38.7463093942741 \wedge x < -36.1283155162826$$
$$x > -33.5103216382911 \wedge x < -32.4631240870945$$
$$x > -29.845130209103 \wedge x < -27.2271363311115$$
$$x > -26.1799387799149 \wedge x < -23.5619449019235$$
$$x > -20.9439510239315 \wedge x < -19.8967534727333$$
$$x > -17.2787595947545 \wedge x < -14.6607657137713$$
$$x > -8.37756232720506 \wedge x < -7.85405135077815$$
$$x > -0.659060267770608 \wedge x < 0.618199421804696$$
Solución de la desigualdad en el gráfico