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:
$$x_{1} = \pi n + \frac{\pi}{4}$$
$$x_{2} = \pi n + \frac{\pi}{4}$$

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 = 82.4668070362749

x2 = 7.06858323491875

x3 = 0.785397933202895

x4 = -65.1880477975749

x5 = -80.8960110535094

x6 = -46.3384918201522

x7 = -43.1968987801324

x8 = -62.0464545510179

x9 = -74.6128252689663

x10 = 91.8915852031867

x11 = 16.4933612990544

x12 = 38.4845098780771

x13 = 7.06858364655338

x14 = -52.621676693071

x15 = -14.9225649210104

x16 = -65.1880480738962

x17 = -62.0464548641931

x18 = 35.3429176094788

x19 = 13.3517690013813

x20 = -30.6305281172761

x21 = 88.7499922419838

x22 = 10.2101761576945

x23 = -14.9225653376224

x24 = 57.334066070126

x25 = -27.4889358588398

x26 = 19.6349542839773

x27 = 73.0420289540461

x28 = 66.7588436646782

x29 = -74.6128250890583

x30 = 25.9181398404781

x31 = -90.320788607123

x32 = 47.9092880421864

x33 = -24.3473428722772

x34 = -24.3473430701779

x35 = -77.754418173028

x36 = -2.35619429411883

x37 = -46.3384914504975

x38 = -87.1791967606238

x39 = 57.3340661848436

x40 = -80.8960106270747

x41 = -40.0553062823371

x42 = 85.6084000178882

x43 = 3.92699088042162

x44 = 101.316363152916

x45 = -21.2057506438029

x46 = -33.7721210085969

x47 = -52.6216765719183

x48 = 95.0331775275438

x49 = 95.0331779096874

x50 = 51.0508807796768

x51 = 41.6261028620108

x52 = -55.7632695910029

x53 = 63.6172514399813

x54 = 76.1836219129628

x55 = -2.35619439286547

x56 = -99.745566754733

x57 = -68.3296400287794

x58 = 60.4756584571505

x59 = 98.1747705006042

x60 = -84.0376034464448

x61 = -8.6393795270917

x62 = -96.6039738449592

x63 = -5.49778727991785

x64 = 73.0420293451081

x65 = -58.9048620578704

x66 = -96.6039736043971

x67 = 44.7676950874451

x68 = 35.3429175338589

x69 = -8.63937954158422

x70 = 32.2013247418177

x71 = 29.0597318077204

x72 = 79.3252147600926

x73 = -87.1791963743373

x74 = -49.4800844377116

x75 = -18.064157700815

x76 = 69.9004366227711

x77 = 25.9181394614117

x78 = -71.471233016533

x79 = -93.4623815953041

x80 = -58.9048624818554

x81 = 79.3252146099091

x82 = -43.1968992207295

x83 = -36.9137134891678

x84 = 29.0597322134693

x85 = -153.15264217109

x86 = 51.0508803807674

x87 = -30.6305280514717

x88 = -11.7809724257318

x89 = 13.3517690340018

x90 = -36.9137139098865

x91 = 54.192473326822

x92 = 22.7765465102862

График