|sin(2x)| = 1 (уравнение)

Найду корень уравнения: |sin(2x)| = 1

Вы ввели

|sin(2*x)| = 1

$$\left|{\sin{\left(2 x \right)}}\right| = 1$$

Подробное решение

Дано уравнение
$$\left|{\sin{\left(2 x \right)}}\right| = 1$$
преобразуем
$$\left|{\sin{\left(2 x \right)}}\right| - 1 = 0$$
$$\left|{\sin{\left(2 x \right)}}\right| - 1 = 0$$
Сделаем замену
$$w = \left|{\sin{\left(2 x \right)}}\right|$$
Переносим свободные слагаемые (без w)
из левой части в правую, получим:
$$w = 1$$
Получим ответ: w = 1
делаем обратную замену
$$\left|{\sin{\left(2 x \right)}}\right| = w$$
подставляем w:

Быстрый ответ

     -pi 
x1 = ----
      4  

$$x_{1} = - \frac{\pi}{4}$$

     pi
x2 = --
     4 

$$x_{2} = \frac{\pi}{4}$$

     3*pi
x3 = ----
      4  

$$x_{3} = \frac{3 \pi}{4}$$

Численный ответ

x1 = 55.7632697511726

x2 = 91.8915854699216

x3 = 98.1747705006042

x4 = -91.8915845717239

x5 = -55.7632695910029

x6 = -5.49778727991785

x7 = -82.4668069282144

x8 = -11.7809724257318

x9 = -41.6261027352652

x10 = -84.0376034464448

x11 = 91.8915852031867

x12 = -62.0464548641931

x13 = -49.4800844377116

x14 = -63.6172513149926

x15 = -93.4623815953041

x16 = -35.3429175479242

x17 = -98.1747703033985

x18 = 8.63937960822746

x19 = 3.92699088042162

x20 = -40.0553062823371

x21 = 66.7588441859847

x22 = -3.92699107594367

x23 = -99.745566754733

x24 = 82.4668070362749

x25 = 25.9181394614117

x26 = -76.1836217239439

x27 = 63.6172514399813

x28 = 30.6305281863893

x29 = 40.0553062099627

x30 = -24.3473428722772

x31 = 71.471233111112

x32 = 38.4845098780771

x33 = -38.4845097737495

x34 = -96.6039742867344

x35 = 74.6128253428807

x36 = 2.35619442440536

x37 = -68.3296400287794

x38 = 5.49778738042301

x39 = -16.4933611966261

x40 = 52.6216767646073

x41 = -2.35619429411883

x42 = -10.2101760980097

x43 = -27.4889358588398

x44 = 68.3296401645238

x45 = 24.3473430043575

x46 = -54.1924731445711

x47 = 772.046394503981

x48 = 77.7544183301131

x49 = 54.192473326822

x50 = 69.9004366227711

x51 = -90.320788607123

x52 = -21.2057506299817

x53 = 85.6084000178882

x54 = 76.1836219129628

x55 = 90.3207887447523

x56 = -87.1791962863867

x57 = -60.4756583509459

x58 = -19.6349541554673

x59 = -13.3517689698773

x60 = 18.0641575837788

x61 = 32.2013247418177

x62 = 46.3384915843947

x63 = -57.3340661259123

x64 = 62.0464548195549

x65 = -79.3252147038408

x66 = 27.4889359573966

x67 = -71.471233016533

x68 = -46.3384914504975

x69 = 10.2101761576945

x70 = 33.7721211721652

x71 = 49.4800845342934

x72 = -33.7721210085969

x73 = -77.754418173028

x74 = -74.6128259730616

x75 = 22.7765465102862

x76 = 96.6039739212089

x77 = 84.0376034199549

x78 = 11.7809725930891

x79 = 41.6261028620108

x80 = -10.2101759860574

x81 = 44.7676950874451

x82 = -43.1968991889715

x83 = 99.7455669089878

x84 = 10.210175998366

x85 = -85.608399894653

x86 = 47.9092880421864

x87 = 66.7588436646782

x88 = -32.2013253166755

x89 = 16.4933612990544

x90 = 93.4623816836307

x91 = 0.785397933202895

x92 = 19.6349542839773

x93 = -32.2013245652766

x94 = 60.4756584571505

x95 = -18.064157700815

x96 = -65.1880477420354

x97 = 88.7499922419838

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