4sinx=√8 (уравнение)

Найду корень уравнения: 4sinx=√8

Вы ввели

             ___
4*sin(x) = \/ 8 

$$4 \sin{\left(x \right)} = \sqrt{8}$$

Подробное решение

Дано уравнение
$$4 \sin{\left(x \right)} = \sqrt{8}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 4

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{\sqrt{2}}{2}$$
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
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{3 \pi}{4}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     4 

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

     3*pi
x2 = ----
      4  

$$x_{2} = \frac{3 \pi}{4}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 + -- + ----
    4     4  

$$\left(0 + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$

=

pi

$$\pi$$

произведение

  pi 3*pi
1*--*----
  4   4  

$$\frac{3 \pi}{4} \cdot 1 \frac{\pi}{4}$$

=

    2
3*pi 
-----
  16 

$$\frac{3 \pi^{2}}{16}$$

Численный ответ

x1 = -11.7809724509617

x2 = 69.9004365423729

x3 = 65.1880475619882

x4 = 95.0331777710912

x5 = 40.0553063332699

x6 = -118.595122673015

x7 = 51.0508806208341

x8 = -16.4933614313464

x9 = 25.9181393921158

x10 = 0.785398163397448

x11 = -93.4623814442964

x12 = 2.35619449019234

x13 = 90.3207887907066

x14 = 2151.20556954561

x15 = -18.0641577581413

x16 = 19.6349540849362

x17 = -186.139364725195

x18 = 6964.12551484517

x19 = -55.7632696012188

x20 = 96.6039740978861

x21 = 46.3384916404494

x22 = 7.06858347057703

x23 = -43.1968989868597

x24 = 57.3340659280137

x25 = -91.8915851175014

x26 = -1160.03308733803

x27 = -237.975643509427

x28 = 21.2057504117311

x29 = -74.6128255227576

x30 = -10.2101761241668

x31 = -35.3429173528852

x32 = 77.7544181763474

x33 = -54.1924732744239

x34 = 52.621676947629

x35 = -29.0597320457056

x36 = -30.6305283725005

x37 = -68.329640215578

x38 = -99.7455667514759

x39 = 33.7721210260903

x40 = 8.63937979737193

x41 = -60.4756585816035

x42 = 13.3517687777566

x43 = 2476.36040919215

x44 = -85.6083998103219

x45 = 14.9225651045515

x46 = -73.0420291959627

x47 = -36.9137136796801

x48 = -47.9092879672443

x49 = 32.2013246992954

x50 = 84.037603483527

x51 = -62.0464549083984

x52 = 27.4889357189107

x53 = -98.174770424681

x54 = -79.3252145031423

x55 = -41.6261026600648

x56 = -66.7588438887831

x57 = 128.019900633784

x58 = -17680.09805624

x59 = -80.8960108299372

x60 = 71.4712328691678

x61 = 101.316363078271

x62 = -49.4800842940392

x63 = 82.4668071567321

x64 = -5.49778714378214

x65 = 76.1836218495525

x66 = -3.92699081698724

x67 = -87.1791961371168

x68 = -24.3473430653209

x69 = 63.6172512351933

x70 = -22.776546738526

x71 = 38.484510006475

x72 = 58.9048622548086

x73 = 44.7676953136546

x74 = 88.7499924639117

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