sin(2*x)=1 (уравнение)

Найду корень уравнения: sin(2*x)=1

Вы ввели

sin(2*x) = 1

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

Подробное решение

Дано уравнение
$$\sin{\left(2 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$2 x = 2 \pi n + \frac{\pi}{2}$$
$$2 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n + \frac{\pi}{4}$$
$$x_{2} = \pi n + \frac{\pi}{4}$$

Быстрый ответ

     pi
x1 = --
     4 

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

Сумма и произведение корней

сумма

    pi
0 + --
    4 

$$0 + \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

произведение

  pi
1*--
  4 

$$1 \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

Численный ответ

x1 = 3.92699088042162

x2 = -30.6305281172761

x3 = -58.9048620578704

x4 = -55.7632695910029

x5 = -30.6305280514717

x6 = -90.320788607123

x7 = 57.334066070126

x8 = 63.6172514399813

x9 = 60.4756584571505

x10 = 47.9092880421864

x11 = 35.3429176094788

x12 = -52.621676693071

x13 = -80.8960106270747

x14 = 25.9181398404781

x15 = -8.6393795270917

x16 = -40.0553062823371

x17 = 95.0331775275438

x18 = -58.9048624818554

x19 = -68.3296400287794

x20 = 19.6349542839773

x21 = 91.8915852031867

x22 = -46.3384918201522

x23 = -52.6216765719183

x24 = -36.9137134891678

x25 = 69.9004366227711

x26 = 54.192473326822

x27 = 101.316363152916

x28 = 82.4668070362749

x29 = 79.3252147600926

x30 = 79.3252146099091

x31 = -2.35619439286547

x32 = -96.6039738449592

x33 = -43.1968992207295

x34 = 16.4933612990544

x35 = -96.6039736043971

x36 = -14.9225649210104

x37 = 73.0420293451081

x38 = -2.35619429411883

x39 = -27.4889358588398

x40 = -11.7809724257318

x41 = 32.2013247418177

x42 = 22.7765465102862

x43 = 35.3429175338589

x44 = -24.3473430701779

x45 = 73.0420289540461

x46 = -84.0376034464448

x47 = -49.4800844377116

x48 = 51.0508803807674

x49 = 57.3340661848436

x50 = -65.1880480738962

x51 = 10.2101761576945

x52 = -153.15264217109

x53 = -77.754418173028

x54 = -43.1968987801324

x55 = 44.7676950874451

x56 = 88.7499922419838

x57 = 13.3517690013813

x58 = -62.0464548641931

x59 = 7.06858323491875

x60 = -24.3473428722772

x61 = 25.9181394614117

x62 = 41.6261028620108

x63 = -21.2057506438029

x64 = -46.3384914504975

x65 = -18.064157700815

x66 = 13.3517690340018

x67 = -74.6128250890583

x68 = 51.0508807796768

x69 = 38.4845098780771

x70 = -8.63937954158422

x71 = -5.49778727991785

x72 = -14.9225653376224

x73 = 7.06858364655338

x74 = -99.745566754733

x75 = -36.9137139098865

x76 = 0.785397933202895

x77 = -80.8960110535094

x78 = 85.6084000178882

x79 = 98.1747705006042

x80 = -65.1880477975749

x81 = 95.0331779096874

x82 = -87.1791963743373

x83 = -33.7721210085969

x84 = 66.7588436646782

x85 = 29.0597318077204

x86 = -74.6128252689663

x87 = 76.1836219129628

x88 = -62.0464545510179

x89 = -93.4623815953041

x90 = -87.1791967606238

x91 = 29.0597322134693

x92 = -71.471233016533

График