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Resolver desigualdades/ 2*sin2x-7*sin(x)+3>0

2*sin2x-7*sin(x)+3>0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
2*sin(2*x) - 7*sin(x) + 3 > 0
(−7sin⁡(x)+2sin⁡(2x))+3>0\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0 
-7*sin(x) + 2*sin(2*x) + 3 > 0
Solución detallada
Se da la desigualdad:
(−7sin⁡(x)+2sin⁡(2x))+3>0\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0
Para resolver esta desigualdad primero hay que resolver la ecuación correspondiente:
(−7sin⁡(x)+2sin⁡(2x))+3=0\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 = 0
Resolvemos:
x1=−87.1690749807234x_{1} = -87.1690749807234
x2=−36.9035925232867x_{2} = -36.9035925232867
x3=95.0432989274846x_{3} = 95.0432989274846
x4=−66.2537559502919x_{4} = -66.2537559502919
x5=25.9282605485092x_{5} = 25.9282605485092
x6=−74.6027043663642x_{6} = -74.6027043663642
x7=63.6273723915867x_{7} = 63.6273723915867
x8=−49.4699631376459x_{8} = -49.4699631376459
x9=−59.9705706431123x_{9} = -59.9705706431123
x10=57.3441870844071x_{10} = 57.3441870844071
x11=−28.5546441072143x_{11} = -28.5546441072143
x12=−3.421902878496x_{12} = -3.421902878496
x13=13.36188993415x_{13} = 13.36188993415
x14=−99.7354455950826x_{14} = -99.7354455950826
x15=−72.5369412574715x_{15} = -72.5369412574715
x16=−30.6204072161071x_{16} = -30.6204072161071
x17=38.4946311628683x_{17} = 38.4946311628683
x18=−24.3372219089275x_{18} = -24.3372219089275
x19=−9.70508818567559x_{19} = -9.70508818567559
x20=65.6931355004795x_{20} = 65.6931355004795
x21=−11.7708512945684x_{21} = -11.7708512945684
x22=−80.8858896735438x_{22} = -80.8858896735438
x23=88.760113620305x_{23} = 88.760113620305
x24=32.2114458556888x_{24} = 32.2114458556888
x25=90.8258767291978x_{25} = 90.8258767291978
x26=−41.1210147215735x_{26} = -41.1210147215735
x27=−91.3864971790102x_{27} = -91.3864971790102
x28=27.9940236574019x_{28} = 27.9940236574019
x29=−18.0540366017479x_{29} = -18.0540366017479
x30=−62.036333752005x_{30} = -62.036333752005
x31=34.2772089645815x_{31} = 34.2772089645815
x32=84.5426914220182x_{32} = 84.5426914220182
x33=78.2595061148386x_{33} = 78.2595061148386
x34=−78.820126564651x_{34} = -78.820126564651
x35=−47.4042000287531x_{35} = -47.4042000287531
x36=51.0610017772275x_{36} = 51.0610017772275
x37=97.1090620363774x_{37} = 97.1090620363774
x38=76.1937430059459x_{38} = 76.1937430059459
x39=40.5603942717611x_{39} = 40.5603942717611
x40=−43.1867778304663x_{40} = -43.1867778304663
x41=−97.6696824861898x_{41} = -97.6696824861898
x42=53.1267648861203x_{42} = 53.1267648861203
x43=−93.452260287903x_{43} = -93.452260287903
x44=21.7108383502223x_{44} = 21.7108383502223
x45=2.86128242868359x_{45} = 2.86128242868359
x46=−68.3195190591846x_{46} = -68.3195190591846
x47=−22.2714588000348x_{47} = -22.2714588000348
x48=−15.9882734928552x_{48} = -15.9882734928552
x49=9.14446773586317x_{49} = 9.14446773586317
x50=44.7778164700479x_{50} = 44.7778164700479
x51=14194.5111282385x_{51} = 14194.5111282385
x52=69.9105576987663x_{52} = 69.9105576987663
x53=101.326484234664x_{53} = 101.326484234664
x54=46.8435795789407x_{54} = 46.8435795789407
x55=15.4276530430428x_{55} = 15.4276530430428
x56=71.976320807659x_{56} = 71.976320807659
x57=7.07870462697041x_{57} = 7.07870462697041
x58=0.795519319790823x_{58} = 0.795519319790823
x59=−34.8378294143939x_{59} = -34.8378294143939
x60=82.4769283131254x_{60} = 82.4769283131254
x61=−53.6873853359327x_{61} = -53.6873853359327
x62=−5.48766598738876x_{62} = -5.48766598738876
x63=−55.7531484448255x_{63} = -55.7531484448255
x64=59.4099501932999x_{64} = 59.4099501932999
x65=19.6450752413296x_{65} = 19.6450752413296
x1=−87.1690749807234x_{1} = -87.1690749807234
x2=−36.9035925232867x_{2} = -36.9035925232867
x3=95.0432989274846x_{3} = 95.0432989274846
x4=−66.2537559502919x_{4} = -66.2537559502919
x5=25.9282605485092x_{5} = 25.9282605485092
x6=−74.6027043663642x_{6} = -74.6027043663642
x7=63.6273723915867x_{7} = 63.6273723915867
x8=−49.4699631376459x_{8} = -49.4699631376459
x9=−59.9705706431123x_{9} = -59.9705706431123
x10=57.3441870844071x_{10} = 57.3441870844071
x11=−28.5546441072143x_{11} = -28.5546441072143
x12=−3.421902878496x_{12} = -3.421902878496
x13=13.36188993415x_{13} = 13.36188993415
x14=−99.7354455950826x_{14} = -99.7354455950826
x15=−72.5369412574715x_{15} = -72.5369412574715
x16=−30.6204072161071x_{16} = -30.6204072161071
x17=38.4946311628683x_{17} = 38.4946311628683
x18=−24.3372219089275x_{18} = -24.3372219089275
x19=−9.70508818567559x_{19} = -9.70508818567559
x20=65.6931355004795x_{20} = 65.6931355004795
x21=−11.7708512945684x_{21} = -11.7708512945684
x22=−80.8858896735438x_{22} = -80.8858896735438
x23=88.760113620305x_{23} = 88.760113620305
x24=32.2114458556888x_{24} = 32.2114458556888
x25=90.8258767291978x_{25} = 90.8258767291978
x26=−41.1210147215735x_{26} = -41.1210147215735
x27=−91.3864971790102x_{27} = -91.3864971790102
x28=27.9940236574019x_{28} = 27.9940236574019
x29=−18.0540366017479x_{29} = -18.0540366017479
x30=−62.036333752005x_{30} = -62.036333752005
x31=34.2772089645815x_{31} = 34.2772089645815
x32=84.5426914220182x_{32} = 84.5426914220182
x33=78.2595061148386x_{33} = 78.2595061148386
x34=−78.820126564651x_{34} = -78.820126564651
x35=−47.4042000287531x_{35} = -47.4042000287531
x36=51.0610017772275x_{36} = 51.0610017772275
x37=97.1090620363774x_{37} = 97.1090620363774
x38=76.1937430059459x_{38} = 76.1937430059459
x39=40.5603942717611x_{39} = 40.5603942717611
x40=−43.1867778304663x_{40} = -43.1867778304663
x41=−97.6696824861898x_{41} = -97.6696824861898
x42=53.1267648861203x_{42} = 53.1267648861203
x43=−93.452260287903x_{43} = -93.452260287903
x44=21.7108383502223x_{44} = 21.7108383502223
x45=2.86128242868359x_{45} = 2.86128242868359
x46=−68.3195190591846x_{46} = -68.3195190591846
x47=−22.2714588000348x_{47} = -22.2714588000348
x48=−15.9882734928552x_{48} = -15.9882734928552
x49=9.14446773586317x_{49} = 9.14446773586317
x50=44.7778164700479x_{50} = 44.7778164700479
x51=14194.5111282385x_{51} = 14194.5111282385
x52=69.9105576987663x_{52} = 69.9105576987663
x53=101.326484234664x_{53} = 101.326484234664
x54=46.8435795789407x_{54} = 46.8435795789407
x55=15.4276530430428x_{55} = 15.4276530430428
x56=71.976320807659x_{56} = 71.976320807659
x57=7.07870462697041x_{57} = 7.07870462697041
x58=0.795519319790823x_{58} = 0.795519319790823
x59=−34.8378294143939x_{59} = -34.8378294143939
x60=82.4769283131254x_{60} = 82.4769283131254
x61=−53.6873853359327x_{61} = -53.6873853359327
x62=−5.48766598738876x_{62} = -5.48766598738876
x63=−55.7531484448255x_{63} = -55.7531484448255
x64=59.4099501932999x_{64} = 59.4099501932999
x65=19.6450752413296x_{65} = 19.6450752413296
Las raíces dadas
x14=−99.7354455950826x_{14} = -99.7354455950826
x41=−97.6696824861898x_{41} = -97.6696824861898
x43=−93.452260287903x_{43} = -93.452260287903
x27=−91.3864971790102x_{27} = -91.3864971790102
x1=−87.1690749807234x_{1} = -87.1690749807234
x22=−80.8858896735438x_{22} = -80.8858896735438
x34=−78.820126564651x_{34} = -78.820126564651
x6=−74.6027043663642x_{6} = -74.6027043663642
x15=−72.5369412574715x_{15} = -72.5369412574715
x46=−68.3195190591846x_{46} = -68.3195190591846
x4=−66.2537559502919x_{4} = -66.2537559502919
x30=−62.036333752005x_{30} = -62.036333752005
x9=−59.9705706431123x_{9} = -59.9705706431123
x63=−55.7531484448255x_{63} = -55.7531484448255
x61=−53.6873853359327x_{61} = -53.6873853359327
x8=−49.4699631376459x_{8} = -49.4699631376459
x35=−47.4042000287531x_{35} = -47.4042000287531
x40=−43.1867778304663x_{40} = -43.1867778304663
x26=−41.1210147215735x_{26} = -41.1210147215735
x2=−36.9035925232867x_{2} = -36.9035925232867
x59=−34.8378294143939x_{59} = -34.8378294143939
x16=−30.6204072161071x_{16} = -30.6204072161071
x11=−28.5546441072143x_{11} = -28.5546441072143
x18=−24.3372219089275x_{18} = -24.3372219089275
x47=−22.2714588000348x_{47} = -22.2714588000348
x29=−18.0540366017479x_{29} = -18.0540366017479
x48=−15.9882734928552x_{48} = -15.9882734928552
x21=−11.7708512945684x_{21} = -11.7708512945684
x19=−9.70508818567559x_{19} = -9.70508818567559
x62=−5.48766598738876x_{62} = -5.48766598738876
x12=−3.421902878496x_{12} = -3.421902878496
x58=0.795519319790823x_{58} = 0.795519319790823
x45=2.86128242868359x_{45} = 2.86128242868359
x57=7.07870462697041x_{57} = 7.07870462697041
x49=9.14446773586317x_{49} = 9.14446773586317
x13=13.36188993415x_{13} = 13.36188993415
x55=15.4276530430428x_{55} = 15.4276530430428
x65=19.6450752413296x_{65} = 19.6450752413296
x44=21.7108383502223x_{44} = 21.7108383502223
x5=25.9282605485092x_{5} = 25.9282605485092
x28=27.9940236574019x_{28} = 27.9940236574019
x24=32.2114458556888x_{24} = 32.2114458556888
x31=34.2772089645815x_{31} = 34.2772089645815
x17=38.4946311628683x_{17} = 38.4946311628683
x39=40.5603942717611x_{39} = 40.5603942717611
x50=44.7778164700479x_{50} = 44.7778164700479
x54=46.8435795789407x_{54} = 46.8435795789407
x36=51.0610017772275x_{36} = 51.0610017772275
x42=53.1267648861203x_{42} = 53.1267648861203
x10=57.3441870844071x_{10} = 57.3441870844071
x64=59.4099501932999x_{64} = 59.4099501932999
x7=63.6273723915867x_{7} = 63.6273723915867
x20=65.6931355004795x_{20} = 65.6931355004795
x52=69.9105576987663x_{52} = 69.9105576987663
x56=71.976320807659x_{56} = 71.976320807659
x38=76.1937430059459x_{38} = 76.1937430059459
x33=78.2595061148386x_{33} = 78.2595061148386
x60=82.4769283131254x_{60} = 82.4769283131254
x32=84.5426914220182x_{32} = 84.5426914220182
x23=88.760113620305x_{23} = 88.760113620305
x25=90.8258767291978x_{25} = 90.8258767291978
x3=95.0432989274846x_{3} = 95.0432989274846
x37=97.1090620363774x_{37} = 97.1090620363774
x53=101.326484234664x_{53} = 101.326484234664
x51=14194.5111282385x_{51} = 14194.5111282385
son puntos de cambio del signo de desigualdad en las soluciones.
Primero definámonos con el signo hasta el punto extremo izquierdo:
x0<x14x_{0} < x_{14}
Consideremos, por ejemplo, el punto
x0=x14−110x_{0} = x_{14} - \frac{1}{10}
=
−99.7354455950826+−110-99.7354455950826 + - \frac{1}{10}
=
−99.8354455950826-99.8354455950826
lo sustituimos en la expresión
(−7sin⁡(x)+2sin⁡(2x))+3>0\left(- 7 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}\right) + 3 > 0
(−7sin⁡(−99.8354455950826)+2sin⁡((−99.8354455950826)2))+3>0\left(- 7 \sin{\left(-99.8354455950826 \right)} + 2 \sin{\left(\left(-99.8354455950826\right) 2 \right)}\right) + 3 > 0
0.482284559587646 > 0

significa que una de las soluciones de nuestra ecuación será con:
x<−99.7354455950826x < -99.7354455950826
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-------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-------
       x14      x41      x43      x27      x1      x22      x34      x6      x15      x46      x4      x30      x9      x63      x61      x8      x35      x40      x26      x2      x59      x16      x11      x18      x47      x29      x48      x21      x19      x62      x12      x58      x45      x57      x49      x13      x55      x65      x44      x5      x28      x24      x31      x17      x39      x50      x54      x36      x42      x10      x64      x7      x20      x52      x56      x38      x33      x60      x32      x23      x25      x3      x37      x53      x51

Recibiremos otras soluciones de la desigualdad pasando al polo siguiente etc.
etc.
Respuesta:
x<−99.7354455950826x < -99.7354455950826
x>−97.6696824861898∧x<−93.452260287903x > -97.6696824861898 \wedge x < -93.452260287903
x>−91.3864971790102∧x<−87.1690749807234x > -91.3864971790102 \wedge x < -87.1690749807234
x>−80.8858896735438∧x<−78.820126564651x > -80.8858896735438 \wedge x < -78.820126564651
x>−74.6027043663642∧x<−72.5369412574715x > -74.6027043663642 \wedge x < -72.5369412574715
x>−68.3195190591846∧x<−66.2537559502919x > -68.3195190591846 \wedge x < -66.2537559502919
x>−62.036333752005∧x<−59.9705706431123x > -62.036333752005 \wedge x < -59.9705706431123
x>−55.7531484448255∧x<−53.6873853359327x > -55.7531484448255 \wedge x < -53.6873853359327
x>−49.4699631376459∧x<−47.4042000287531x > -49.4699631376459 \wedge x < -47.4042000287531
x>−43.1867778304663∧x<−41.1210147215735x > -43.1867778304663 \wedge x < -41.1210147215735
x>−36.9035925232867∧x<−34.8378294143939x > -36.9035925232867 \wedge x < -34.8378294143939
x>−30.6204072161071∧x<−28.5546441072143x > -30.6204072161071 \wedge x < -28.5546441072143
x>−24.3372219089275∧x<−22.2714588000348x > -24.3372219089275 \wedge x < -22.2714588000348
x>−18.0540366017479∧x<−15.9882734928552x > -18.0540366017479 \wedge x < -15.9882734928552
x>−11.7708512945684∧x<−9.70508818567559x > -11.7708512945684 \wedge x < -9.70508818567559
x>−5.48766598738876∧x<−3.421902878496x > -5.48766598738876 \wedge x < -3.421902878496
x>0.795519319790823∧x<2.86128242868359x > 0.795519319790823 \wedge x < 2.86128242868359
x>7.07870462697041∧x<9.14446773586317x > 7.07870462697041 \wedge x < 9.14446773586317
x>13.36188993415∧x<15.4276530430428x > 13.36188993415 \wedge x < 15.4276530430428
x>19.6450752413296∧x<21.7108383502223x > 19.6450752413296 \wedge x < 21.7108383502223
x>25.9282605485092∧x<27.9940236574019x > 25.9282605485092 \wedge x < 27.9940236574019
x>32.2114458556888∧x<34.2772089645815x > 32.2114458556888 \wedge x < 34.2772089645815
x>38.4946311628683∧x<40.5603942717611x > 38.4946311628683 \wedge x < 40.5603942717611
x>44.7778164700479∧x<46.8435795789407x > 44.7778164700479 \wedge x < 46.8435795789407
x>51.0610017772275∧x<53.1267648861203x > 51.0610017772275 \wedge x < 53.1267648861203
x>57.3441870844071∧x<59.4099501932999x > 57.3441870844071 \wedge x < 59.4099501932999
x>63.6273723915867∧x<65.6931355004795x > 63.6273723915867 \wedge x < 65.6931355004795
x>69.9105576987663∧x<71.976320807659x > 69.9105576987663 \wedge x < 71.976320807659
x>76.1937430059459∧x<78.2595061148386x > 76.1937430059459 \wedge x < 78.2595061148386
x>82.4769283131254∧x<84.5426914220182x > 82.4769283131254 \wedge x < 84.5426914220182
x>88.760113620305∧x<90.8258767291978x > 88.760113620305 \wedge x < 90.8258767291978
x>95.0432989274846∧x<97.1090620363774x > 95.0432989274846 \wedge x < 97.1090620363774
x>101.326484234664∧x<14194.5111282385x > 101.326484234664 \wedge x < 14194.5111282385
Solución de la desigualdad en el gráfico
0-60-50-40-30-20-10102030405060-2020
Respuesta rápida [src] 
  /   /                  /                                                                                            ______________________________________________________________________________________________________________________________________\\     /                 /                                                                                            ______________________________________________________________________________________________________________________________________\    \\
  |   |                  |                                                                                           /              _________________                                                                                                       ||     |                 |                                                                                           /              _________________                                                                                                       |    ||
  |   |                  |                                                                                          /              /          ______                                                                                                        ||     |                 |                                                                                          /              /          ______                                                                                                        |    ||
  |   |                  |                                                                                         /   218        /  73   2*\/ 1418                14                                                2374                                   ||     |                 |                                                                                         /   218        /  73   2*\/ 1418                14                                                2374                                   |    ||
  |   |                  |                                                                                        /    --- - 2*3 /   -- + ----------  + ------------------------ + ------------------------------------------------------------------------ ||     |                 |                                                                                        /    --- - 2*3 /   -- + ----------  + ------------------------ + ------------------------------------------------------------------------ |    ||
  |   |                  |               ___________________________________________________________             /      9      \/    27       27               _________________                ___________________________________________________________ ||     |                 |               ___________________________________________________________             /      9      \/    27       27               _________________                ___________________________________________________________ |    ||
  |   |                  |              /              _________________                                        /                                             /          ______                /              _________________                             ||     |                 |              /              _________________                                        /                                             /          ______                /              _________________                             |    ||
  |   |                  |             /              /          ______                                        /                                             /  73   2*\/ 1418                /              /          ______                              ||     |                 |             /              /          ______                                        /                                             /  73   2*\/ 1418                /              /          ______                              |    ||
  |   |                  |            /   109        /  73   2*\/ 1418                14                      /                                         9*3 /   -- + ----------              /   109        /  73   2*\/ 1418                14             ||     |                 |            /   109        /  73   2*\/ 1418                14                      /                                         9*3 /   -- + ----------              /   109        /  73   2*\/ 1418                14             |    ||
  |   |                  |           /    --- + 2*3 /   -- + ----------  - ------------------------          /                                            \/    27       27        27*      /    --- + 2*3 /   -- + ----------  - ------------------------  ||     |                 |           /    --- + 2*3 /   -- + ----------  - ------------------------          /                                            \/    27       27        27*      /    --- + 2*3 /   -- + ----------  - ------------------------  |    ||
  |   |                  |          /      9      \/    27       27               _________________         /                                                                              /      9      \/    27       27               _________________  ||     |                 |          /      9      \/    27       27               _________________         /                                                                              /      9      \/    27       27               _________________  |    ||
  |   |                  |         /                                             /          ______         /                                                                              /                                             /          ______   ||     |                 |         /                                             /          ______         /                                                                              /                                             /          ______   |    ||
  |   |                  |        /                                             /  73   2*\/ 1418         /                                                                              /                                             /  73   2*\/ 1418    ||     |                 |        /                                             /  73   2*\/ 1418         /                                                                              /                                             /  73   2*\/ 1418    |    ||
  |   |                  |       /                                         9*3 /   -- + ----------       /                                                                              /                                         9*3 /   -- + ----------   ||     |                 |       /                                         9*3 /   -- + ----------       /                                                                              /                                         9*3 /   -- + ----------   |    ||
  |   |                  |11   \/                                            \/    27       27         \/                                                                             \/                                            \/    27       27       ||     |                 |11   \/                                            \/    27       27         \/                                                                             \/                                            \/    27       27       |    ||
Or|And|0 <= x, x < 2*atan|-- + --------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------||, And|x <= 2*pi, 2*atan|-- + --------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------| < x||
  \   \                  \6                                      2                                                                                                               2                                                                          //     \                 \6                                      2                                                                                                               2                                                                          /    //
(0≤x∧x<2atan⁡(−−27327+21418273+1497327+21418273+237427−1497327+21418273+27327+21418273+1099+21892+116+−1497327+21418273+27327+21418273+10992))∨(x≤2π∧2atan⁡(116+−1497327+21418273+27327+21418273+10992+−27327+21418273+1497327+21418273+237427−1497327+21418273+27327+21418273+1099+21892)<x)\left(0 \leq x \wedge x < 2 \operatorname{atan}{\left(- \frac{\sqrt{- 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + \frac{2374}{27 \sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}} + \frac{218}{9}}}{2} + \frac{11}{6} + \frac{\sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}}{2} \right)}\right) \vee \left(x \leq 2 \pi \wedge 2 \operatorname{atan}{\left(\frac{11}{6} + \frac{\sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + \frac{2374}{27 \sqrt{- \frac{14}{9 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}}} + 2 \sqrt[3]{\frac{73}{27} + \frac{2 \sqrt{1418}}{27}} + \frac{109}{9}}} + \frac{218}{9}}}{2} \right)} < x\right) 
((0 <= x)∧(x < 2*atan(11/6 + sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))/2 - sqrt(218/9 - 2*(73/27 + 2*sqrt(1418)/27)^(1/3) + 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)) + 2374/(27*sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))))/2)))∨((x <= 2*pi)∧(2*atan(11/6 + sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))/2 + sqrt(218/9 - 2*(73/27 + 2*sqrt(1418)/27)^(1/3) + 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)) + 2374/(27*sqrt(109/9 + 2*(73/27 + 2*sqrt(1418)/27)^(1/3) - 14/(9*(73/27 + 2*sqrt(1418)/27)^(1/3)))))/2) < x))
    © Sr Examen – Калькулятор