sinx=-√2/2 (уравнение)

Найду корень уравнения: sinx=-√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

Сумма и произведение корней

сумма

    pi   5*pi
0 - -- + ----
    4     4  

$$\left(- \frac{\pi}{4} + 0\right) + \frac{5 \pi}{4}$$

=

pi

$$\pi$$

произведение

  -pi  5*pi
1*----*----
   4    4  

$$\frac{5 \pi}{4} \cdot 1 \left(- \frac{\pi}{4}\right)$$

=

     2
-5*pi 
------
  16  

$$- \frac{5 \pi^{2}}{16}$$

Быстрый ответ

     -pi 
x1 = ----
      4  

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

     5*pi
x2 = ----
      4  

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

Численный ответ

x1 = -95.0331777710912

x2 = -71.4712328691678

x3 = -90.3207887907066

x4 = -44.7676953136546

x5 = -33.7721210260903

x6 = 35.3429173528852

x7 = 99.7455667514759

x8 = -82.4668071567321

x9 = 87.1791961371168

x10 = 55.7632696012188

x11 = 43.1968989868597

x12 = 73.0420291959627

x13 = 62.0464549083984

x14 = -19.6349540849362

x15 = -830.165858711103

x16 = -8.63937979737193

x17 = 98.174770424681

x18 = -14.9225651045515

x19 = -32.2013246992954

x20 = -13.3517687777566

x21 = 74.6128255227576

x22 = -101.316363078271

x23 = -371.493331286993

x24 = 47.9092879672443

x25 = -57.3340659280137

x26 = -46.3384916404494

x27 = -88.7499924639117

x28 = 93.4623814442964

x29 = 5.49778714378214

x30 = -76.1836218495525

x31 = -21.2057504117311

x32 = 79.3252145031423

x33 = 29.0597320457056

x34 = -77.7544181763474

x35 = -40.0553063332699

x36 = -215482.625507887

x37 = -27.4889357189107

x38 = 80.8960108299372

x39 = 85.6083998103219

x40 = -51.0508806208341

x41 = 10.2101761241668

x42 = -128.019900633784

x43 = -84.037603483527

x44 = -96.6039740978861

x45 = 36.9137136796801

x46 = -25.9181393921158

x47 = -0.785398163397448

x48 = 60.4756585816035

x49 = -2865.91789823729

x50 = 3.92699081698724

x51 = 652.665873783279

x52 = 11.7809724509617

x53 = -52.621676947629

x54 = -38.484510006475

x55 = 24.3473430653209

x56 = -58.9048622548086

x57 = 22.776546738526

x58 = 16.4933614313464

x59 = 30.6305283725005

x60 = 41.6261026600648

x61 = 54.1924732744239

x62 = -65.1880475619882

x63 = 91.8915851175014

x64 = 66.7588438887831

x65 = -7.06858347057703

x66 = -69.9004365423729

x67 = -63.6172512351933

x68 = 49.4800842940392

x69 = -2.35619449019234

x70 = 68.329640215578

x71 = 18.0641577581413

x72 = -704.502152567511

График