sin(x)=-(1/√2) (уравнение)

Найду корень уравнения: sin(x)=-(1/√2)

Вы ввели

          -1  
sin(x) = -----
           ___
         \/ 2 

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

Подробное решение

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

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

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  

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

Численный ответ

x1 = 62.0464549083984

x2 = -32.2013246992954

x3 = 24.3473430653209

x4 = -128.019900633784

x5 = -76.1836218495525

x6 = -830.165858711103

x7 = -2.35619449019234

x8 = 3.92699081698724

x9 = 98.174770424681

x10 = -82.4668071567321

x11 = 49.4800842940392

x12 = 55.7632696012188

x13 = 11.7809724509617

x14 = -95.0331777710912

x15 = 68.329640215578

x16 = -46.3384916404494

x17 = -38.484510006475

x18 = -44.7676953136546

x19 = 66.7588438887831

x20 = 22.776546738526

x21 = 91.8915851175014

x22 = -21.2057504117311

x23 = -58.9048622548086

x24 = -63.6172512351933

x25 = -65.1880475619882

x26 = 18.0641577581413

x27 = -0.785398163397448

x28 = -84.037603483527

x29 = -2865.91789823729

x30 = -96.6039740978861

x31 = -77.7544181763474

x32 = 79.3252145031423

x33 = -215482.625507887

x34 = 30.6305283725005

x35 = 85.6083998103219

x36 = 29.0597320457056

x37 = -13.3517687777566

x38 = 73.0420291959627

x39 = -27.4889357189107

x40 = -7.06858347057703

x41 = -14.9225651045515

x42 = 10.2101761241668

x43 = 16.4933614313464

x44 = -25.9181393921158

x45 = 87.1791961371168

x46 = 99.7455667514759

x47 = -40.0553063332699

x48 = 54.1924732744239

x49 = -88.7499924639117

x50 = -704.502152567511

x51 = 5.49778714378214

x52 = -371.493331286993

x53 = -69.9004365423729

x54 = -51.0508806208341

x55 = -33.7721210260903

x56 = -57.3340659280137

x57 = -71.4712328691678

x58 = 35.3429173528852

x59 = -90.3207887907066

x60 = 74.6128255227576

x61 = 43.1968989868597

x62 = 93.4623814442964

x63 = -19.6349540849362

x64 = -52.621676947629

x65 = 60.4756585816035

x66 = 41.6261026600648

x67 = 36.9137136796801

x68 = -8.63937979737193

x69 = 80.8960108299372

x70 = 652.665873783279

x71 = -101.316363078271

x72 = 47.9092879672443

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