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:
-
2^x>-1
- x^2+64<0
-
x^2<=6,5-9*(4-x)^2
-
(x+4)(x-1)>(x-7)(x+10)
- Derivada de:
-
sqrt(2)
- Límite de la función:
-
sqrt(2)
- Integral de d{x}:
- sqrt(2)
-
Expresiones idénticas
- cuatro *sin(x)*cos(dos *x)>sqrt(dos)
- 4 multiplicar por seno de (x) multiplicar por coseno de (2 multiplicar por x) más raíz cuadrada de (2)
- cuatro multiplicar por seno de (x) multiplicar por coseno de (dos multiplicar por x) más raíz cuadrada de (dos)
- 4*sin(x)*cos(2*x)>√(2)
- 4sin(x)cos(2x)>sqrt(2)
- 4sinxcos2x>sqrt2
-
Expresiones semejantes
- sin3x>4sinxcos2x
- x(x+4)^sqrt(25-x^2)>=0
- x^2-(sqrt5-sqrt2)x-sqrt10<=0
- ((x^2-9)*sqrt(2-x))/(2*x+3)>=0
- (x^2-9)*sqrt(2-x)/(2x+3)>=0
- sin3x>4sinx*cos2x
- 4*sinx*cos(2*x)>sqrt(2)
-
Expresiones con funciones
- Seno sin
- sin(3x)>0
- sin((-4)*x+3*pi/2)>=0
- sin(2*x)>1/2
- sin(3*x)<-1/2
- sin^2x-3sinx-4>0
- Coseno cos
- cosπ/3<1/2
- cos(t)<1/7
- cos(3*x)<=sqrt*3/2
- cos2x<=(sqrt)3x/2
- cos(sin1996x)>0
- Raíz cuadrada sqrt
- sqrt(x^2-2x+1)-sqrt(x^2+8x+16)>7
- sqrt(x^2-5)/(3-x)>=0
- sqrt(x^2+6*x)>-4
- sqrt(x+1)<-2
- sqrt(x+2)>4/x
4*sin(x)*cos(2*x)>sqrt(2) desigualdades
Solución
Ha introducido
[src]
___ 4*sin(x)*cos(2*x) > \/ 2
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} > \sqrt{2}$$
(4*sin(x))*cos(2*x) > sqrt(2)
Solución detallada
Se da la desigualdad:
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} > \sqrt{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} = \sqrt{2}$$
Resolvemos:
$$x_{1} = -96.3874479009414$$
$$x_{2} = 80.6794846329925$$
$$x_{3} = -14.7060389076068$$
$$x_{4} = -8.42285360042721$$
$$x_{5} = 41.8426288570095$$
$$x_{6} = 193.776820162225$$
$$x_{7} = 66.9753700857278$$
$$x_{8} = 17.8476315611966$$
$$x_{9} = -1.00192436034217$$
$$x_{10} = -101.532889275216$$
$$x_{11} = 73.2585553929074$$
$$x_{12} = -13.5682949747013$$
$$x_{13} = 68.1131140186333$$
$$x_{14} = -90.1042625937618$$
$$x_{15} = -46.1219654435047$$
$$x_{16} = -39.8387801363251$$
$$x_{17} = -70.1169627393176$$
$$x_{18} = 10.4267023211115$$
$$x_{19} = 4.14351701393196$$
$$x_{20} = -58.6883360578639$$
$$x_{21} = 60.6921847785482$$
$$x_{22} = 48.1258141641891$$
$$x_{23} = 55.5467434042741$$
$$x_{24} = -1980.20529612191$$
$$x_{25} = 22.9930729354707$$
$$x_{26} = -77.5378919794027$$
$$x_{27} = -57.5505921249584$$
$$x_{28} = -32.4178508962401$$
$$x_{29} = -2.13966829324762$$
$$x_{30} = -33.5555948291456$$
$$x_{31} = 98.3912966216258$$
$$x_{32} = -51.2674068177789$$
$$x_{33} = -26.1346655890605$$
$$x_{34} = 92.1081113144462$$
$$x_{35} = 85.8249260072666$$
$$x_{36} = -19.8514802818809$$
$$x_{37} = 495.369714906845$$
$$x_{38} = 54.4089994713687$$
$$x_{39} = -63.833777432138$$
$$x_{40} = 24.1308168683762$$
$$x_{41} = -83.8210772865823$$
$$x_{42} = 74.3962993258129$$
$$x_{43} = 30.4140021755558$$
$$x_{44} = -95.249703968036$$
$$x_{45} = 61.8299287114537$$
$$x_{1} = -96.3874479009414$$
$$x_{2} = 80.6794846329925$$
$$x_{3} = -14.7060389076068$$
$$x_{4} = -8.42285360042721$$
$$x_{5} = 41.8426288570095$$
$$x_{6} = 193.776820162225$$
$$x_{7} = 66.9753700857278$$
$$x_{8} = 17.8476315611966$$
$$x_{9} = -1.00192436034217$$
$$x_{10} = -101.532889275216$$
$$x_{11} = 73.2585553929074$$
$$x_{12} = -13.5682949747013$$
$$x_{13} = 68.1131140186333$$
$$x_{14} = -90.1042625937618$$
$$x_{15} = -46.1219654435047$$
$$x_{16} = -39.8387801363251$$
$$x_{17} = -70.1169627393176$$
$$x_{18} = 10.4267023211115$$
$$x_{19} = 4.14351701393196$$
$$x_{20} = -58.6883360578639$$
$$x_{21} = 60.6921847785482$$
$$x_{22} = 48.1258141641891$$
$$x_{23} = 55.5467434042741$$
$$x_{24} = -1980.20529612191$$
$$x_{25} = 22.9930729354707$$
$$x_{26} = -77.5378919794027$$
$$x_{27} = -57.5505921249584$$
$$x_{28} = -32.4178508962401$$
$$x_{29} = -2.13966829324762$$
$$x_{30} = -33.5555948291456$$
$$x_{31} = 98.3912966216258$$
$$x_{32} = -51.2674068177789$$
$$x_{33} = -26.1346655890605$$
$$x_{34} = 92.1081113144462$$
$$x_{35} = 85.8249260072666$$
$$x_{36} = -19.8514802818809$$
$$x_{37} = 495.369714906845$$
$$x_{38} = 54.4089994713687$$
$$x_{39} = -63.833777432138$$
$$x_{40} = 24.1308168683762$$
$$x_{41} = -83.8210772865823$$
$$x_{42} = 74.3962993258129$$
$$x_{43} = 30.4140021755558$$
$$x_{44} = -95.249703968036$$
$$x_{45} = 61.8299287114537$$
Las raíces dadas
$$x_{24} = -1980.20529612191$$
$$x_{10} = -101.532889275216$$
$$x_{1} = -96.3874479009414$$
$$x_{44} = -95.249703968036$$
$$x_{14} = -90.1042625937618$$
$$x_{41} = -83.8210772865823$$
$$x_{26} = -77.5378919794027$$
$$x_{17} = -70.1169627393176$$
$$x_{39} = -63.833777432138$$
$$x_{20} = -58.6883360578639$$
$$x_{27} = -57.5505921249584$$
$$x_{32} = -51.2674068177789$$
$$x_{15} = -46.1219654435047$$
$$x_{16} = -39.8387801363251$$
$$x_{30} = -33.5555948291456$$
$$x_{28} = -32.4178508962401$$
$$x_{33} = -26.1346655890605$$
$$x_{36} = -19.8514802818809$$
$$x_{3} = -14.7060389076068$$
$$x_{12} = -13.5682949747013$$
$$x_{4} = -8.42285360042721$$
$$x_{29} = -2.13966829324762$$
$$x_{9} = -1.00192436034217$$
$$x_{19} = 4.14351701393196$$
$$x_{18} = 10.4267023211115$$
$$x_{8} = 17.8476315611966$$
$$x_{25} = 22.9930729354707$$
$$x_{40} = 24.1308168683762$$
$$x_{43} = 30.4140021755558$$
$$x_{5} = 41.8426288570095$$
$$x_{22} = 48.1258141641891$$
$$x_{38} = 54.4089994713687$$
$$x_{23} = 55.5467434042741$$
$$x_{21} = 60.6921847785482$$
$$x_{45} = 61.8299287114537$$
$$x_{7} = 66.9753700857278$$
$$x_{13} = 68.1131140186333$$
$$x_{11} = 73.2585553929074$$
$$x_{42} = 74.3962993258129$$
$$x_{2} = 80.6794846329925$$
$$x_{35} = 85.8249260072666$$
$$x_{34} = 92.1081113144462$$
$$x_{31} = 98.3912966216258$$
$$x_{6} = 193.776820162225$$
$$x_{37} = 495.369714906845$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{24}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{24} - \frac{1}{10}$$
=
$$-1980.20529612191 + - \frac{1}{10}$$
=
$$-1980.30529612191$$
lo sustituimos en la expresión
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} > \sqrt{2}$$
$$4 \sin{\left(-1980.30529612191 \right)} \cos{\left(\left(-1980.30529612191\right) 2 \right)} > \sqrt{2}$$
significa que una de las soluciones de nuestra ecuación será con:
$$x < -1980.20529612191$$
Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -1980.20529612191$$
$$x > -101.532889275216 \wedge x < -96.3874479009414$$
$$x > -95.249703968036 \wedge x < -90.1042625937618$$
$$x > -83.8210772865823 \wedge x < -77.5378919794027$$
$$x > -70.1169627393176 \wedge x < -63.833777432138$$
$$x > -58.6883360578639 \wedge x < -57.5505921249584$$
$$x > -51.2674068177789 \wedge x < -46.1219654435047$$
$$x > -39.8387801363251 \wedge x < -33.5555948291456$$
$$x > -32.4178508962401 \wedge x < -26.1346655890605$$
$$x > -19.8514802818809 \wedge x < -14.7060389076068$$
$$x > -13.5682949747013 \wedge x < -8.42285360042721$$
$$x > -2.13966829324762 \wedge x < -1.00192436034217$$
$$x > 4.14351701393196 \wedge x < 10.4267023211115$$
$$x > 17.8476315611966 \wedge x < 22.9930729354707$$
$$x > 24.1308168683762 \wedge x < 30.4140021755558$$
$$x > 41.8426288570095 \wedge x < 48.1258141641891$$
$$x > 54.4089994713687 \wedge x < 55.5467434042741$$
$$x > 60.6921847785482 \wedge x < 61.8299287114537$$
$$x > 66.9753700857278 \wedge x < 68.1131140186333$$
$$x > 73.2585553929074 \wedge x < 74.3962993258129$$
$$x > 80.6794846329925 \wedge x < 85.8249260072666$$
$$x > 92.1081113144462 \wedge x < 98.3912966216258$$
$$x > 193.776820162225 \wedge x < 495.369714906845$$
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} > \sqrt{2}$$
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} = \sqrt{2}$$
Resolvemos:
$$x_{1} = -96.3874479009414$$
$$x_{2} = 80.6794846329925$$
$$x_{3} = -14.7060389076068$$
$$x_{4} = -8.42285360042721$$
$$x_{5} = 41.8426288570095$$
$$x_{6} = 193.776820162225$$
$$x_{7} = 66.9753700857278$$
$$x_{8} = 17.8476315611966$$
$$x_{9} = -1.00192436034217$$
$$x_{10} = -101.532889275216$$
$$x_{11} = 73.2585553929074$$
$$x_{12} = -13.5682949747013$$
$$x_{13} = 68.1131140186333$$
$$x_{14} = -90.1042625937618$$
$$x_{15} = -46.1219654435047$$
$$x_{16} = -39.8387801363251$$
$$x_{17} = -70.1169627393176$$
$$x_{18} = 10.4267023211115$$
$$x_{19} = 4.14351701393196$$
$$x_{20} = -58.6883360578639$$
$$x_{21} = 60.6921847785482$$
$$x_{22} = 48.1258141641891$$
$$x_{23} = 55.5467434042741$$
$$x_{24} = -1980.20529612191$$
$$x_{25} = 22.9930729354707$$
$$x_{26} = -77.5378919794027$$
$$x_{27} = -57.5505921249584$$
$$x_{28} = -32.4178508962401$$
$$x_{29} = -2.13966829324762$$
$$x_{30} = -33.5555948291456$$
$$x_{31} = 98.3912966216258$$
$$x_{32} = -51.2674068177789$$
$$x_{33} = -26.1346655890605$$
$$x_{34} = 92.1081113144462$$
$$x_{35} = 85.8249260072666$$
$$x_{36} = -19.8514802818809$$
$$x_{37} = 495.369714906845$$
$$x_{38} = 54.4089994713687$$
$$x_{39} = -63.833777432138$$
$$x_{40} = 24.1308168683762$$
$$x_{41} = -83.8210772865823$$
$$x_{42} = 74.3962993258129$$
$$x_{43} = 30.4140021755558$$
$$x_{44} = -95.249703968036$$
$$x_{45} = 61.8299287114537$$
$$x_{1} = -96.3874479009414$$
$$x_{2} = 80.6794846329925$$
$$x_{3} = -14.7060389076068$$
$$x_{4} = -8.42285360042721$$
$$x_{5} = 41.8426288570095$$
$$x_{6} = 193.776820162225$$
$$x_{7} = 66.9753700857278$$
$$x_{8} = 17.8476315611966$$
$$x_{9} = -1.00192436034217$$
$$x_{10} = -101.532889275216$$
$$x_{11} = 73.2585553929074$$
$$x_{12} = -13.5682949747013$$
$$x_{13} = 68.1131140186333$$
$$x_{14} = -90.1042625937618$$
$$x_{15} = -46.1219654435047$$
$$x_{16} = -39.8387801363251$$
$$x_{17} = -70.1169627393176$$
$$x_{18} = 10.4267023211115$$
$$x_{19} = 4.14351701393196$$
$$x_{20} = -58.6883360578639$$
$$x_{21} = 60.6921847785482$$
$$x_{22} = 48.1258141641891$$
$$x_{23} = 55.5467434042741$$
$$x_{24} = -1980.20529612191$$
$$x_{25} = 22.9930729354707$$
$$x_{26} = -77.5378919794027$$
$$x_{27} = -57.5505921249584$$
$$x_{28} = -32.4178508962401$$
$$x_{29} = -2.13966829324762$$
$$x_{30} = -33.5555948291456$$
$$x_{31} = 98.3912966216258$$
$$x_{32} = -51.2674068177789$$
$$x_{33} = -26.1346655890605$$
$$x_{34} = 92.1081113144462$$
$$x_{35} = 85.8249260072666$$
$$x_{36} = -19.8514802818809$$
$$x_{37} = 495.369714906845$$
$$x_{38} = 54.4089994713687$$
$$x_{39} = -63.833777432138$$
$$x_{40} = 24.1308168683762$$
$$x_{41} = -83.8210772865823$$
$$x_{42} = 74.3962993258129$$
$$x_{43} = 30.4140021755558$$
$$x_{44} = -95.249703968036$$
$$x_{45} = 61.8299287114537$$
Las raíces dadas
$$x_{24} = -1980.20529612191$$
$$x_{10} = -101.532889275216$$
$$x_{1} = -96.3874479009414$$
$$x_{44} = -95.249703968036$$
$$x_{14} = -90.1042625937618$$
$$x_{41} = -83.8210772865823$$
$$x_{26} = -77.5378919794027$$
$$x_{17} = -70.1169627393176$$
$$x_{39} = -63.833777432138$$
$$x_{20} = -58.6883360578639$$
$$x_{27} = -57.5505921249584$$
$$x_{32} = -51.2674068177789$$
$$x_{15} = -46.1219654435047$$
$$x_{16} = -39.8387801363251$$
$$x_{30} = -33.5555948291456$$
$$x_{28} = -32.4178508962401$$
$$x_{33} = -26.1346655890605$$
$$x_{36} = -19.8514802818809$$
$$x_{3} = -14.7060389076068$$
$$x_{12} = -13.5682949747013$$
$$x_{4} = -8.42285360042721$$
$$x_{29} = -2.13966829324762$$
$$x_{9} = -1.00192436034217$$
$$x_{19} = 4.14351701393196$$
$$x_{18} = 10.4267023211115$$
$$x_{8} = 17.8476315611966$$
$$x_{25} = 22.9930729354707$$
$$x_{40} = 24.1308168683762$$
$$x_{43} = 30.4140021755558$$
$$x_{5} = 41.8426288570095$$
$$x_{22} = 48.1258141641891$$
$$x_{38} = 54.4089994713687$$
$$x_{23} = 55.5467434042741$$
$$x_{21} = 60.6921847785482$$
$$x_{45} = 61.8299287114537$$
$$x_{7} = 66.9753700857278$$
$$x_{13} = 68.1131140186333$$
$$x_{11} = 73.2585553929074$$
$$x_{42} = 74.3962993258129$$
$$x_{2} = 80.6794846329925$$
$$x_{35} = 85.8249260072666$$
$$x_{34} = 92.1081113144462$$
$$x_{31} = 98.3912966216258$$
$$x_{6} = 193.776820162225$$
$$x_{37} = 495.369714906845$$
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
$$x_{0} < x_{24}$$
Consideremos, por ejemplo, el punto
$$x_{0} = x_{24} - \frac{1}{10}$$
=
$$-1980.20529612191 + - \frac{1}{10}$$
=
$$-1980.30529612191$$
lo sustituimos en la expresión
$$4 \sin{\left(x \right)} \cos{\left(2 x \right)} > \sqrt{2}$$
$$4 \sin{\left(-1980.30529612191 \right)} \cos{\left(\left(-1980.30529612191\right) 2 \right)} > \sqrt{2}$$
___
2.11104485252890 > \/ 2
significa que una de las soluciones de nuestra ecuación será con:
$$x < -1980.20529612191$$
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
\ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \
-------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-------
x24 x10 x1 x44 x14 x41 x26 x17 x39 x20 x27 x32 x15 x16 x30 x28 x33 x36 x3 x12 x4 x29 x9 x19 x18 x8 x25 x40 x43 x5 x22 x38 x23 x21 x45 x7 x13 x11 x42 x2 x35 x34 x31 x6 x37Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
$$x < -1980.20529612191$$
$$x > -101.532889275216 \wedge x < -96.3874479009414$$
$$x > -95.249703968036 \wedge x < -90.1042625937618$$
$$x > -83.8210772865823 \wedge x < -77.5378919794027$$
$$x > -70.1169627393176 \wedge x < -63.833777432138$$
$$x > -58.6883360578639 \wedge x < -57.5505921249584$$
$$x > -51.2674068177789 \wedge x < -46.1219654435047$$
$$x > -39.8387801363251 \wedge x < -33.5555948291456$$
$$x > -32.4178508962401 \wedge x < -26.1346655890605$$
$$x > -19.8514802818809 \wedge x < -14.7060389076068$$
$$x > -13.5682949747013 \wedge x < -8.42285360042721$$
$$x > -2.13966829324762 \wedge x < -1.00192436034217$$
$$x > 4.14351701393196 \wedge x < 10.4267023211115$$
$$x > 17.8476315611966 \wedge x < 22.9930729354707$$
$$x > 24.1308168683762 \wedge x < 30.4140021755558$$
$$x > 41.8426288570095 \wedge x < 48.1258141641891$$
$$x > 54.4089994713687 \wedge x < 55.5467434042741$$
$$x > 60.6921847785482 \wedge x < 61.8299287114537$$
$$x > 66.9753700857278 \wedge x < 68.1131140186333$$
$$x > 73.2585553929074 \wedge x < 74.3962993258129$$
$$x > 80.6794846329925 \wedge x < 85.8249260072666$$
$$x > 92.1081113144462 \wedge x < 98.3912966216258$$
$$x > 193.776820162225 \wedge x < 495.369714906845$$
Solución de la desigualdad en el gráfico