sin(x)=-√2/2 (уравнение)

Найду корень уравнения: sin(x)=-√2/2

Вы ввели

            ___ 
         -\/ 2  
sin(x) = -------
            2   

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{2}}{2} \right)} + \pi$$
Или
$$x = 2 \pi n - \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{5 \pi}{4}$$
, где n - любое целое число

Быстрый ответ

     -pi 
x1 = ----
      4  

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

     5*pi
x2 = ----
      4  

$$x_{2} = \frac{5 \pi}{4}$$

Численный ответ

x1 = -7.06858347057703

x2 = 99.7455667514759

x3 = 29.0597320457056

x4 = -8.63937979737193

x5 = -215482.625507887

x6 = 54.1924732744239

x7 = -52.621676947629

x8 = 66.7588438887831

x9 = -19.6349540849362

x10 = -46.3384916404494

x11 = 60.4756585816035

x12 = 10.2101761241668

x13 = -96.6039740978861

x14 = 47.9092879672443

x15 = -0.785398163397448

x16 = 16.4933614313464

x17 = 85.6083998103219

x18 = 3.92699081698724

x19 = 18.0641577581413

x20 = 652.665873783279

x21 = -21.2057504117311

x22 = 22.776546738526

x23 = -84.037603483527

x24 = 98.174770424681

x25 = -128.019900633784

x26 = -90.3207887907066

x27 = -704.502152567511

x28 = -371.493331286993

x29 = -44.7676953136546

x30 = -2.35619449019234

x31 = 30.6305283725005

x32 = -830.165858711103

x33 = 68.329640215578

x34 = 62.0464549083984

x35 = -25.9181393921158

x36 = -95.0331777710912

x37 = 5.49778714378214

x38 = 87.1791961371168

x39 = 24.3473430653209

x40 = 73.0420291959627

x41 = 91.8915851175014

x42 = -101.316363078271

x43 = -14.9225651045515

x44 = -76.1836218495525

x45 = 80.8960108299372

x46 = -51.0508806208341

x47 = -88.7499924639117

x48 = -58.9048622548086

x49 = 41.6261026600648

x50 = 79.3252145031423

x51 = -71.4712328691678

x52 = 49.4800842940392

x53 = -82.4668071567321

x54 = -32.2013246992954

x55 = 36.9137136796801

x56 = -38.484510006475

x57 = 55.7632696012188

x58 = -2865.91789823729

x59 = 11.7809724509617

x60 = -13.3517687777566

x61 = -33.7721210260903

x62 = 93.4623814442964

x63 = -57.3340659280137

x64 = -69.9004365423729

x65 = -63.6172512351933

x66 = -40.0553063332699

x67 = 43.1968989868597

x68 = -77.7544181763474

x69 = -65.1880475619882

x70 = 35.3429173528852

x71 = -27.4889357189107

x72 = 74.6128255227576

График