sin2x=1 (уравнение)

Найду корень уравнения: sin2x=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:
$$x_{1} = \pi n + \frac{\pi}{4}$$
$$x_{2} = \pi n + \frac{\pi}{4}$$

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 

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

Быстрый ответ

     pi
x1 = --
     4 

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

Численный ответ

x1 = -5.49778727991785

x2 = 69.9004366227711

x3 = -80.8960110535094

x4 = 57.334066070126

x5 = -30.6305280514717

x6 = -27.4889358588398

x7 = -93.4623815953041

x8 = 95.0331775275438

x9 = 73.0420293451081

x10 = -8.63937954158422

x11 = -58.9048624818554

x12 = 101.316363152916

x13 = 76.1836219129628

x14 = 54.192473326822

x15 = -52.621676693071

x16 = 32.2013247418177

x17 = 88.7499922419838

x18 = -90.320788607123

x19 = -2.35619439286547

x20 = -33.7721210085969

x21 = -84.0376034464448

x22 = 91.8915852031867

x23 = 98.1747705006042

x24 = 95.0331779096874

x25 = -2.35619429411883

x26 = 85.6084000178882

x27 = -87.1791963743373

x28 = -62.0464548641931

x29 = 16.4933612990544

x30 = -43.1968987801324

x31 = -74.6128252689663

x32 = 44.7676950874451

x33 = -18.064157700815

x34 = 47.9092880421864

x35 = -77.754418173028

x36 = -36.9137134891678

x37 = -62.0464545510179

x38 = 79.3252146099091

x39 = 35.3429175338589

x40 = -24.3473430701779

x41 = -46.3384914504975

x42 = -80.8960106270747

x43 = -71.471233016533

x44 = 51.0508807796768

x45 = -36.9137139098865

x46 = -43.1968992207295

x47 = -30.6305281172761

x48 = -8.6393795270917

x49 = -52.6216765719183

x50 = 66.7588436646782

x51 = -14.9225649210104

x52 = 79.3252147600926

x53 = -153.15264217109

x54 = -46.3384918201522

x55 = 29.0597318077204

x56 = -55.7632695910029

x57 = -40.0553062823371

x58 = -11.7809724257318

x59 = 41.6261028620108

x60 = -74.6128250890583

x61 = 35.3429176094788

x62 = 19.6349542839773

x63 = 51.0508803807674

x64 = -24.3473428722772

x65 = -65.1880477975749

x66 = -99.745566754733

x67 = -87.1791967606238

x68 = 7.06858364655338

x69 = -14.9225653376224

x70 = -21.2057506438029

x71 = -96.6039736043971

x72 = 38.4845098780771

x73 = 13.3517690340018

x74 = 25.9181394614117

x75 = 29.0597322134693

x76 = 82.4668070362749

x77 = 13.3517690013813

x78 = 10.2101761576945

x79 = 57.3340661848436

x80 = 3.92699088042162

x81 = -68.3296400287794

x82 = -96.6039738449592

x83 = 25.9181398404781

x84 = -65.1880480738962

x85 = 63.6172514399813

x86 = 0.785397933202895

x87 = -49.4800844377116

x88 = -58.9048620578704

x89 = 73.0420289540461

x90 = 7.06858323491875

x91 = 22.7765465102862

x92 = 60.4756584571505

График