Решение неравенств/ Abs(sin(x))<1

Abs(sin(x))<1 (неравенство)

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    Укажите решение неравенства: Abs(sin(x))<1 (множество решений неравенства)

    Решение

    Вы ввели [src]
    |sin(x)| < 1
    ∣sin⁡(x)∣<1\left|{\sin{\left (x \right )}}\right| < 1
    Подробное решение
    Дано неравенство:
    ∣sin⁡(x)∣<1\left|{\sin{\left (x \right )}}\right| < 1
    Чтобы решить это нер-во - надо сначала решить соотвествующее ур-ние:
    ∣sin⁡(x)∣=1\left|{\sin{\left (x \right )}}\right| = 1
    Решаем:
    Дано уравнение
    ∣sin⁡(x)∣=1\left|{\sin{\left (x \right )}}\right| = 1
    преобразуем
    ∣sin⁡(x)∣−1=0\left|{\sin{\left (x \right )}}\right| - 1 = 0
    ∣sin⁡(x)∣−1=0\left|{\sin{\left (x \right )}}\right| - 1 = 0
    Сделаем замену
    w=∣sin⁡(x)∣w = \left|{\sin{\left (x \right )}}\right|
    Переносим свободные слагаемые (без w)
    из левой части в правую, получим:
    w=1w = 1
    Получим ответ: w = 1
    делаем обратную замену
    ∣sin⁡(x)∣=w\left|{\sin{\left (x \right )}}\right| = w
    подставляем w:
    x1=26.7035380604x_{1} = 26.7035380604
    x2=39.2699085343x_{2} = 39.2699085343
    x3=20.4203521478x_{3} = 20.4203521478
    x4=−86.3937982346x_{4} = -86.3937982346
    x5=−29.8451300955x_{5} = -29.8451300955
    x6=−58.1194639977x_{6} = -58.1194639977
    x7=32.9867233135x_{7} = 32.9867233135
    x8=76.9690204681x_{8} = 76.9690204681
    x9=−51.8362786893x_{9} = -51.8362786893
    x10=48.6946866366x_{10} = 48.6946866366
    x11=−48.6946857788x_{11} = -48.6946857788
    x12=45.5530937308x_{12} = 45.5530937308
    x13=45.5530929823x_{13} = 45.5530929823
    x14=83.2522048888x_{14} = 83.2522048888
    x15=23.5619451519x_{15} = 23.5619451519
    x16=51.8362789032x_{16} = 51.8362789032
    x17=17.2787599561x_{17} = 17.2787599561
    x18=−64.4026497466x_{18} = -64.4026497466
    x19=−83.2522048211x_{19} = -83.2522048211
    x20=−76.9690203749x_{20} = -76.9690203749
    x21=−26.7035372005x_{21} = -26.7035372005
    x22=−70.6858343571x_{22} = -70.6858343571
    x23=−86.3937977431x_{23} = -86.3937977431
    x24=10.9955739382x_{24} = 10.9955739382
    x25=−17.2787590921x_{25} = -17.2787590921
    x26=−80.1106125782x_{26} = -80.1106125782
    x27=−39.2699084146x_{27} = -39.2699084146
    x28=29.8451303232x_{28} = 29.8451303232
    x29=80.1106131369x_{29} = 80.1106131369
    x30=−95.8185758681x_{30} = -95.8185758681
    x31=92.6769837789x_{31} = 92.6769837789
    x32=−10.9955738414x_{32} = -10.9955738414
    x33=−26.7035379987x_{33} = -26.7035379987
    x34=14.13716711x_{34} = 14.13716711
    x35=70.6858352127x_{35} = 70.6858352127
    x36=17.2787591562x_{36} = 17.2787591562
    x37=−61.2610569934x_{37} = -61.2610569934
    x38=−7.85398149665x_{38} = -7.85398149665
    x39=32.9867225165x_{39} = 32.9867225165
    x40=7.85398174307x_{40} = 7.85398174307
    x41=61.2610563112x_{41} = 61.2610563112
    x42=−98.9601681513x_{42} = -98.9601681513
    x43=−4.71238862219x_{43} = -4.71238862219
    x44=−10.9955746401x_{44} = -10.9955746401
    x45=92.6769830592x_{45} = 92.6769830592
    x46=−70.6858351534x_{46} = -70.6858351534
    x47=23.561944406x_{47} = 23.561944406
    x48=54.9778710948x_{48} = 54.9778710948
    x49=−32.9867224188x_{49} = -32.9867224188
    x50=−61.2610562447x_{50} = -61.2610562447
    x51=98.9601690454x_{51} = 98.9601690454
    x52=−48.6946865761x_{52} = -48.6946865761
    x53=86.393797887x_{53} = 86.393797887
    x54=−36.1283154173x_{54} = -36.1283154173
    x55=95.818576063x_{55} = 95.818576063
    x56=−17.2787598356x_{56} = -17.2787598356
    x57=89.5353901351x_{57} = 89.5353901351
    x58=67.5442423097x_{58} = 67.5442423097
    x59=−42.4115005851x_{59} = -42.4115005851
    x60=−32.9867232184x_{60} = -32.9867232184
    x61=−20.4203520061x_{61} = -20.4203520061
    x62=10.9955747361x_{62} = 10.9955747361
    x63=−98.9601689531x_{63} = -98.9601689531
    x64=−23.5619450115x_{64} = -23.5619450115
    x65=−64.4026491641x_{65} = -64.4026491641
    x66=73.8274274831x_{66} = 73.8274274831
    x67=70.6858344802x_{67} = 70.6858344802
    x68=89.5353908886x_{68} = 89.5353908886
    x69=−4.71238942125x_{69} = -4.71238942125
    x70=36.1283156186x_{70} = 36.1283156186
    x71=1.5707965729x_{71} = 1.5707965729
    x72=48.6946859012x_{72} = 48.6946859012
    x73=−92.6769829355x_{73} = -92.6769829355
    x74=−83.2522055723x_{74} = -83.2522055723
    x75=−89.5353907502x_{75} = -89.5353907502
    x76=−92.6769837308x_{76} = -92.6769837308
    x77=−1.57079643189x_{77} = -1.57079643189
    x78=26.7035373222x_{78} = 26.7035373222
    x79=58.119464398x_{79} = 58.119464398
    x80=98.9601682516x_{80} = 98.9601682516
    x81=67.5442415587x_{81} = 67.5442415587
    x82=1.57079582972x_{82} = 1.57079582972
    x83=−67.5442421707x_{83} = -67.5442421707
    x84=−20.4203527083x_{84} = -20.4203527083
    x85=−42.4115012353x_{85} = -42.4115012353
    x86=42.4115007275x_{86} = 42.4115007275
    x87=76.9690196732x_{87} = 76.9690196732
    x88=83.2522056908x_{88} = 83.2522056908
    x89=−45.5530935911x_{89} = -45.5530935911
    x90=61.2610571126x_{90} = 61.2610571126
    x91=4.7123894842x_{91} = 4.7123894842
    x92=−73.8274272798x_{92} = -73.8274272798
    x93=−54.9778717967x_{93} = -54.9778717967
    x94=64.4026493072x_{94} = 64.4026493072
    x95=−76.9690195738x_{95} = -76.9690195738
    x96=4.7123887433x_{96} = 4.7123887433
    x97=−54.9778709963x_{97} = -54.9778709963
    x98=39.2699077337x_{98} = 39.2699077337
    x99=−14.1371668371x_{99} = -14.1371668371
    x100=54.9778718908x_{100} = 54.9778718908
    x101=−39.2699076684x_{101} = -39.2699076684
    x1=26.7035380604x_{1} = 26.7035380604
    x2=39.2699085343x_{2} = 39.2699085343
    x3=20.4203521478x_{3} = 20.4203521478
    x4=−86.3937982346x_{4} = -86.3937982346
    x5=−29.8451300955x_{5} = -29.8451300955
    x6=−58.1194639977x_{6} = -58.1194639977
    x7=32.9867233135x_{7} = 32.9867233135
    x8=76.9690204681x_{8} = 76.9690204681
    x9=−51.8362786893x_{9} = -51.8362786893
    x10=48.6946866366x_{10} = 48.6946866366
    x11=−48.6946857788x_{11} = -48.6946857788
    x12=45.5530937308x_{12} = 45.5530937308
    x13=45.5530929823x_{13} = 45.5530929823
    x14=83.2522048888x_{14} = 83.2522048888
    x15=23.5619451519x_{15} = 23.5619451519
    x16=51.8362789032x_{16} = 51.8362789032
    x17=17.2787599561x_{17} = 17.2787599561
    x18=−64.4026497466x_{18} = -64.4026497466
    x19=−83.2522048211x_{19} = -83.2522048211
    x20=−76.9690203749x_{20} = -76.9690203749
    x21=−26.7035372005x_{21} = -26.7035372005
    x22=−70.6858343571x_{22} = -70.6858343571
    x23=−86.3937977431x_{23} = -86.3937977431
    x24=10.9955739382x_{24} = 10.9955739382
    x25=−17.2787590921x_{25} = -17.2787590921
    x26=−80.1106125782x_{26} = -80.1106125782
    x27=−39.2699084146x_{27} = -39.2699084146
    x28=29.8451303232x_{28} = 29.8451303232
    x29=80.1106131369x_{29} = 80.1106131369
    x30=−95.8185758681x_{30} = -95.8185758681
    x31=92.6769837789x_{31} = 92.6769837789
    x32=−10.9955738414x_{32} = -10.9955738414
    x33=−26.7035379987x_{33} = -26.7035379987
    x34=14.13716711x_{34} = 14.13716711
    x35=70.6858352127x_{35} = 70.6858352127
    x36=17.2787591562x_{36} = 17.2787591562
    x37=−61.2610569934x_{37} = -61.2610569934
    x38=−7.85398149665x_{38} = -7.85398149665
    x39=32.9867225165x_{39} = 32.9867225165
    x40=7.85398174307x_{40} = 7.85398174307
    x41=61.2610563112x_{41} = 61.2610563112
    x42=−98.9601681513x_{42} = -98.9601681513
    x43=−4.71238862219x_{43} = -4.71238862219
    x44=−10.9955746401x_{44} = -10.9955746401
    x45=92.6769830592x_{45} = 92.6769830592
    x46=−70.6858351534x_{46} = -70.6858351534
    x47=23.561944406x_{47} = 23.561944406
    x48=54.9778710948x_{48} = 54.9778710948
    x49=−32.9867224188x_{49} = -32.9867224188
    x50=−61.2610562447x_{50} = -61.2610562447
    x51=98.9601690454x_{51} = 98.9601690454
    x52=−48.6946865761x_{52} = -48.6946865761
    x53=86.393797887x_{53} = 86.393797887
    x54=−36.1283154173x_{54} = -36.1283154173
    x55=95.818576063x_{55} = 95.818576063
    x56=−17.2787598356x_{56} = -17.2787598356
    x57=89.5353901351x_{57} = 89.5353901351
    x58=67.5442423097x_{58} = 67.5442423097
    x59=−42.4115005851x_{59} = -42.4115005851
    x60=−32.9867232184x_{60} = -32.9867232184
    x61=−20.4203520061x_{61} = -20.4203520061
    x62=10.9955747361x_{62} = 10.9955747361
    x63=−98.9601689531x_{63} = -98.9601689531
    x64=−23.5619450115x_{64} = -23.5619450115
    x65=−64.4026491641x_{65} = -64.4026491641
    x66=73.8274274831x_{66} = 73.8274274831
    x67=70.6858344802x_{67} = 70.6858344802
    x68=89.5353908886x_{68} = 89.5353908886
    x69=−4.71238942125x_{69} = -4.71238942125
    x70=36.1283156186x_{70} = 36.1283156186
    x71=1.5707965729x_{71} = 1.5707965729
    x72=48.6946859012x_{72} = 48.6946859012
    x73=−92.6769829355x_{73} = -92.6769829355
    x74=−83.2522055723x_{74} = -83.2522055723
    x75=−89.5353907502x_{75} = -89.5353907502
    x76=−92.6769837308x_{76} = -92.6769837308
    x77=−1.57079643189x_{77} = -1.57079643189
    x78=26.7035373222x_{78} = 26.7035373222
    x79=58.119464398x_{79} = 58.119464398
    x80=98.9601682516x_{80} = 98.9601682516
    x81=67.5442415587x_{81} = 67.5442415587
    x82=1.57079582972x_{82} = 1.57079582972
    x83=−67.5442421707x_{83} = -67.5442421707
    x84=−20.4203527083x_{84} = -20.4203527083
    x85=−42.4115012353x_{85} = -42.4115012353
    x86=42.4115007275x_{86} = 42.4115007275
    x87=76.9690196732x_{87} = 76.9690196732
    x88=83.2522056908x_{88} = 83.2522056908
    x89=−45.5530935911x_{89} = -45.5530935911
    x90=61.2610571126x_{90} = 61.2610571126
    x91=4.7123894842x_{91} = 4.7123894842
    x92=−73.8274272798x_{92} = -73.8274272798
    x93=−54.9778717967x_{93} = -54.9778717967
    x94=64.4026493072x_{94} = 64.4026493072
    x95=−76.9690195738x_{95} = -76.9690195738
    x96=4.7123887433x_{96} = 4.7123887433
    x97=−54.9778709963x_{97} = -54.9778709963
    x98=39.2699077337x_{98} = 39.2699077337
    x99=−14.1371668371x_{99} = -14.1371668371
    x100=54.9778718908x_{100} = 54.9778718908
    x101=−39.2699076684x_{101} = -39.2699076684
    Данные корни
    x63=−98.9601689531x_{63} = -98.9601689531
    x42=−98.9601681513x_{42} = -98.9601681513
    x30=−95.8185758681x_{30} = -95.8185758681
    x76=−92.6769837308x_{76} = -92.6769837308
    x73=−92.6769829355x_{73} = -92.6769829355
    x75=−89.5353907502x_{75} = -89.5353907502
    x4=−86.3937982346x_{4} = -86.3937982346
    x23=−86.3937977431x_{23} = -86.3937977431
    x74=−83.2522055723x_{74} = -83.2522055723
    x19=−83.2522048211x_{19} = -83.2522048211
    x26=−80.1106125782x_{26} = -80.1106125782
    x20=−76.9690203749x_{20} = -76.9690203749
    x95=−76.9690195738x_{95} = -76.9690195738
    x92=−73.8274272798x_{92} = -73.8274272798
    x46=−70.6858351534x_{46} = -70.6858351534
    x22=−70.6858343571x_{22} = -70.6858343571
    x83=−67.5442421707x_{83} = -67.5442421707
    x18=−64.4026497466x_{18} = -64.4026497466
    x65=−64.4026491641x_{65} = -64.4026491641
    x37=−61.2610569934x_{37} = -61.2610569934
    x50=−61.2610562447x_{50} = -61.2610562447
    x6=−58.1194639977x_{6} = -58.1194639977
    x93=−54.9778717967x_{93} = -54.9778717967
    x97=−54.9778709963x_{97} = -54.9778709963
    x9=−51.8362786893x_{9} = -51.8362786893
    x52=−48.6946865761x_{52} = -48.6946865761
    x11=−48.6946857788x_{11} = -48.6946857788
    x89=−45.5530935911x_{89} = -45.5530935911
    x85=−42.4115012353x_{85} = -42.4115012353
    x59=−42.4115005851x_{59} = -42.4115005851
    x27=−39.2699084146x_{27} = -39.2699084146
    x101=−39.2699076684x_{101} = -39.2699076684
    x54=−36.1283154173x_{54} = -36.1283154173
    x60=−32.9867232184x_{60} = -32.9867232184
    x49=−32.9867224188x_{49} = -32.9867224188
    x5=−29.8451300955x_{5} = -29.8451300955
    x33=−26.7035379987x_{33} = -26.7035379987
    x21=−26.7035372005x_{21} = -26.7035372005
    x64=−23.5619450115x_{64} = -23.5619450115
    x84=−20.4203527083x_{84} = -20.4203527083
    x61=−20.4203520061x_{61} = -20.4203520061
    x56=−17.2787598356x_{56} = -17.2787598356
    x25=−17.2787590921x_{25} = -17.2787590921
    x99=−14.1371668371x_{99} = -14.1371668371
    x44=−10.9955746401x_{44} = -10.9955746401
    x32=−10.9955738414x_{32} = -10.9955738414
    x38=−7.85398149665x_{38} = -7.85398149665
    x69=−4.71238942125x_{69} = -4.71238942125
    x43=−4.71238862219x_{43} = -4.71238862219
    x77=−1.57079643189x_{77} = -1.57079643189
    x82=1.57079582972x_{82} = 1.57079582972
    x71=1.5707965729x_{71} = 1.5707965729
    x96=4.7123887433x_{96} = 4.7123887433
    x91=4.7123894842x_{91} = 4.7123894842
    x40=7.85398174307x_{40} = 7.85398174307
    x24=10.9955739382x_{24} = 10.9955739382
    x62=10.9955747361x_{62} = 10.9955747361
    x34=14.13716711x_{34} = 14.13716711
    x36=17.2787591562x_{36} = 17.2787591562
    x17=17.2787599561x_{17} = 17.2787599561
    x3=20.4203521478x_{3} = 20.4203521478
    x47=23.561944406x_{47} = 23.561944406
    x15=23.5619451519x_{15} = 23.5619451519
    x78=26.7035373222x_{78} = 26.7035373222
    x1=26.7035380604x_{1} = 26.7035380604
    x28=29.8451303232x_{28} = 29.8451303232
    x39=32.9867225165x_{39} = 32.9867225165
    x7=32.9867233135x_{7} = 32.9867233135
    x70=36.1283156186x_{70} = 36.1283156186
    x98=39.2699077337x_{98} = 39.2699077337
    x2=39.2699085343x_{2} = 39.2699085343
    x86=42.4115007275x_{86} = 42.4115007275
    x13=45.5530929823x_{13} = 45.5530929823
    x12=45.5530937308x_{12} = 45.5530937308
    x72=48.6946859012x_{72} = 48.6946859012
    x10=48.6946866366x_{10} = 48.6946866366
    x16=51.8362789032x_{16} = 51.8362789032
    x48=54.9778710948x_{48} = 54.9778710948
    x100=54.9778718908x_{100} = 54.9778718908
    x79=58.119464398x_{79} = 58.119464398
    x41=61.2610563112x_{41} = 61.2610563112
    x90=61.2610571126x_{90} = 61.2610571126
    x94=64.4026493072x_{94} = 64.4026493072
    x81=67.5442415587x_{81} = 67.5442415587
    x58=67.5442423097x_{58} = 67.5442423097
    x67=70.6858344802x_{67} = 70.6858344802
    x35=70.6858352127x_{35} = 70.6858352127
    x66=73.8274274831x_{66} = 73.8274274831
    x87=76.9690196732x_{87} = 76.9690196732
    x8=76.9690204681x_{8} = 76.9690204681
    x29=80.1106131369x_{29} = 80.1106131369
    x14=83.2522048888x_{14} = 83.2522048888
    x88=83.2522056908x_{88} = 83.2522056908
    x53=86.393797887x_{53} = 86.393797887
    x57=89.5353901351x_{57} = 89.5353901351
    x68=89.5353908886x_{68} = 89.5353908886
    x45=92.6769830592x_{45} = 92.6769830592
    x31=92.6769837789x_{31} = 92.6769837789
    x55=95.818576063x_{55} = 95.818576063
    x80=98.9601682516x_{80} = 98.9601682516
    x51=98.9601690454x_{51} = 98.9601690454
    являются точками смены знака неравенства в решениях.
    Сначала определимся со знаком до крайней левой точки:
    x0<x63x_{0} < x_{63}
    Возьмём например точку
    x0=x63−110x_{0} = x_{63} - \frac{1}{10}
    =
    −99.0601689531-99.0601689531
    =
    −99.0601689531-99.0601689531
    подставляем в выражение
    ∣sin⁡(x)∣<1\left|{\sin{\left (x \right )}}\right| < 1
    ∣sin⁡(−99.0601689531)∣<1\left|{\sin{\left (-99.0601689531 \right )}}\right| < 1
    0.995004128836616 < 1

    значит одно из решений нашего неравенства будет при:
    x<−98.9601689531x < -98.9601689531
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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-------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-------
       x63      x42      x30      x76      x73      x75      x4      x23      x74      x19      x26      x20      x95      x92      x46      x22      x83      x18      x65      x37      x50      x6      x93      x97      x9      x52      x11      x89      x85      x59      x27      x101      x54      x60      x49      x5      x33      x21      x64      x84      x61      x56      x25      x99      x44      x32      x38      x69      x43      x77      x82      x71      x96      x91      x40      x24      x62      x34      x36      x17      x3      x47      x15      x78      x1      x28      x39      x7      x70      x98      x2      x86      x13      x12      x72      x10      x16      x48      x100      x79      x41      x90      x94      x81      x58      x67      x35      x66      x87      x8      x29      x14      x88      x53      x57      x68      x45      x31      x55      x80      x51

    Другие решения неравенства будем получать переходом на следующий полюс
    и т.д.
    Ответ:
    x<−98.9601689531x < -98.9601689531
    x>−98.9601681513∧x<−95.8185758681x > -98.9601681513 \wedge x < -95.8185758681
    x>−92.6769837308∧x<−92.6769829355x > -92.6769837308 \wedge x < -92.6769829355
    x>−89.5353907502∧x<−86.3937982346x > -89.5353907502 \wedge x < -86.3937982346
    x>−86.3937977431∧x<−83.2522055723x > -86.3937977431 \wedge x < -83.2522055723
    x>−83.2522048211∧x<−80.1106125782x > -83.2522048211 \wedge x < -80.1106125782
    x>−76.9690203749∧x<−76.9690195738x > -76.9690203749 \wedge x < -76.9690195738
    x>−73.8274272798∧x<−70.6858351534x > -73.8274272798 \wedge x < -70.6858351534
    x>−70.6858343571∧x<−67.5442421707x > -70.6858343571 \wedge x < -67.5442421707
    x>−64.4026497466∧x<−64.4026491641x > -64.4026497466 \wedge x < -64.4026491641
    x>−61.2610569934∧x<−61.2610562447x > -61.2610569934 \wedge x < -61.2610562447
    x>−58.1194639977∧x<−54.9778717967x > -58.1194639977 \wedge x < -54.9778717967
    x>−54.9778709963∧x<−51.8362786893x > -54.9778709963 \wedge x < -51.8362786893
    x>−48.6946865761∧x<−48.6946857788x > -48.6946865761 \wedge x < -48.6946857788
    x>−45.5530935911∧x<−42.4115012353x > -45.5530935911 \wedge x < -42.4115012353
    x>−42.4115005851∧x<−39.2699084146x > -42.4115005851 \wedge x < -39.2699084146
    x>−39.2699076684∧x<−36.1283154173x > -39.2699076684 \wedge x < -36.1283154173
    x>−32.9867232184∧x<−32.9867224188x > -32.9867232184 \wedge x < -32.9867224188
    x>−29.8451300955∧x<−26.7035379987x > -29.8451300955 \wedge x < -26.7035379987
    x>−26.7035372005∧x<−23.5619450115x > -26.7035372005 \wedge x < -23.5619450115
    x>−20.4203527083∧x<−20.4203520061x > -20.4203527083 \wedge x < -20.4203520061
    x>−17.2787598356∧x<−17.2787590921x > -17.2787598356 \wedge x < -17.2787590921
    x>−14.1371668371∧x<−10.9955746401x > -14.1371668371 \wedge x < -10.9955746401
    x>−10.9955738414∧x<−7.85398149665x > -10.9955738414 \wedge x < -7.85398149665
    x>−4.71238942125∧x<−4.71238862219x > -4.71238942125 \wedge x < -4.71238862219
    x>−1.57079643189∧x<1.57079582972x > -1.57079643189 \wedge x < 1.57079582972
    x>1.5707965729∧x<4.7123887433x > 1.5707965729 \wedge x < 4.7123887433
    x>4.7123894842∧x<7.85398174307x > 4.7123894842 \wedge x < 7.85398174307
    x>10.9955739382∧x<10.9955747361x > 10.9955739382 \wedge x < 10.9955747361
    x>14.13716711∧x<17.2787591562x > 14.13716711 \wedge x < 17.2787591562
    x>17.2787599561∧x<20.4203521478x > 17.2787599561 \wedge x < 20.4203521478
    x>23.561944406∧x<23.5619451519x > 23.561944406 \wedge x < 23.5619451519
    x>26.7035373222∧x<26.7035380604x > 26.7035373222 \wedge x < 26.7035380604
    x>29.8451303232∧x<32.9867225165x > 29.8451303232 \wedge x < 32.9867225165
    x>32.9867233135∧x<36.1283156186x > 32.9867233135 \wedge x < 36.1283156186
    x>39.2699077337∧x<39.2699085343x > 39.2699077337 \wedge x < 39.2699085343
    x>42.4115007275∧x<45.5530929823x > 42.4115007275 \wedge x < 45.5530929823
    x>45.5530937308∧x<48.6946859012x > 45.5530937308 \wedge x < 48.6946859012
    x>48.6946866366∧x<51.8362789032x > 48.6946866366 \wedge x < 51.8362789032
    x>54.9778710948∧x<54.9778718908x > 54.9778710948 \wedge x < 54.9778718908
    x>58.119464398∧x<61.2610563112x > 58.119464398 \wedge x < 61.2610563112
    x>61.2610571126∧x<64.4026493072x > 61.2610571126 \wedge x < 64.4026493072
    x>67.5442415587∧x<67.5442423097x > 67.5442415587 \wedge x < 67.5442423097
    x>70.6858344802∧x<70.6858352127x > 70.6858344802 \wedge x < 70.6858352127
    x>73.8274274831∧x<76.9690196732x > 73.8274274831 \wedge x < 76.9690196732
    x>76.9690204681∧x<80.1106131369x > 76.9690204681 \wedge x < 80.1106131369
    x>83.2522048888∧x<83.2522056908x > 83.2522048888 \wedge x < 83.2522056908
    x>86.393797887∧x<89.5353901351x > 86.393797887 \wedge x < 89.5353901351
    x>89.5353908886∧x<92.6769830592x > 89.5353908886 \wedge x < 92.6769830592
    x>92.6769837789∧x<95.818576063x > 92.6769837789 \wedge x < 95.818576063
    x>98.9601682516∧x<98.9601690454x > 98.9601682516 \wedge x < 98.9601690454
    Решение неравенства на графике
    02468-8-6-4-2-101002
    Быстрый ответ [src]
      /   /             -pi \     /-pi           pi\     /pi          3*pi\     /3*pi            \\
Or|And|-oo < x, x < ----|, And|---- < x, x < --|, And|-- < x, x < ----|, And|---- < x, x < oo||
  \   \              2  /     \ 2            2 /     \2            2  /     \ 2              //
    (−∞<x∧x<−π2)∨(−π2<x∧x<π2)∨(π2<x∧x<3π2)∨(3π2<x∧x<∞)\left(-\infty < x \wedge x < - \frac{\pi}{2}\right) \vee \left(- \frac{\pi}{2} < x \wedge x < \frac{\pi}{2}\right) \vee \left(\frac{\pi}{2} < x \wedge x < \frac{3 \pi}{2}\right) \vee \left(\frac{3 \pi}{2} < x \wedge x < \infty\right)
    Быстрый ответ 2 [src]
          -pi      -pi   pi     pi  3*pi     3*pi     
(-oo, ----) U (----, --) U (--, ----) U (----, oo)
       2        2    2      2    2        2
    x∈(−∞,−π2)∪(−π2,π2)∪(π2,3π2)∪(3π2,∞)x \in \left(-\infty, - \frac{\pi}{2}\right) \cup \left(- \frac{\pi}{2}, \frac{\pi}{2}\right) \cup \left(\frac{\pi}{2}, \frac{3 \pi}{2}\right) \cup \left(\frac{3 \pi}{2}, \infty\right)