cosx=-√2/2 (уравнение)

Найду корень уравнения: cosx=-√2/2

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Или
$$x = \pi n + \frac{3 \pi}{4}$$
$$x = \pi n - \frac{\pi}{4}$$
, где n - любое целое число

Сумма и произведение корней

сумма

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

$$\left(0 + \frac{3 \pi}{4}\right) + \frac{5 \pi}{4}$$

=

2*pi

$$2 \pi$$

произведение

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

$$\frac{5 \pi}{4} \cdot 1 \cdot \frac{3 \pi}{4}$$

=

     2
15*pi 
------
  16  

$$\frac{15 \pi^{2}}{16}$$

Быстрый ответ

     3*pi
x1 = ----
      4  

$$x_{1} = \frac{3 \pi}{4}$$

     5*pi
x2 = ----
      4  

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

Численный ответ

x1 = 65.1880475619882

x2 = 2.35619449019234

x3 = -10.2101761241668

x4 = 40.0553063332699

x5 = -90.3207887907066

x6 = -16.4933614313464

x7 = -71.4712328691678

x8 = -33.7721210260903

x9 = 90.3207887907066

x10 = 35.3429173528852

x11 = 96.6039740978861

x12 = 73.0420291959627

x13 = -14.9225651045515

x14 = -91.8915851175014

x15 = 98.174770424681

x16 = -8.63937979737193

x17 = -335.36501577071

x18 = 39349.2333843756

x19 = 21.2057504117311

x20 = 2584.745355741

x21 = 47.9092879672443

x22 = -46.3384916404494

x23 = 255.254403104171

x24 = -35.3429173528852

x25 = 77.7544181763474

x26 = -54.1924732744239

x27 = 52.621676947629

x28 = -29.0597320457056

x29 = -21.2057504117311

x30 = 79.3252145031423

x31 = 29.0597320457056

x32 = 33.7721210260903

x33 = -77.7544181763474

x34 = 8.63937979737193

x35 = -27.4889357189107

x36 = -84.037603483527

x37 = 85.6083998103219

x38 = -96.6039740978861

x39 = -60.4756585816035

x40 = 10.2101761241668

x41 = 104.457955731861

x42 = -85.6083998103219

x43 = 14.9225651045515

x44 = 60.4756585816035

x45 = 3.92699081698724

x46 = -73.0420291959627

x47 = -47.9092879672443

x48 = -52.621676947629

x49 = 84.037603483527

x50 = -58.9048622548086

x51 = 27.4889357189107

x52 = 22.776546738526

x53 = -98.174770424681

x54 = 16.4933614313464

x55 = -79.3252145031423

x56 = -41.6261026600648

x57 = -66.7588438887831

x58 = 41.6261026600648

x59 = 54.1924732744239

x60 = 71.4712328691678

x61 = -65.1880475619882

x62 = 66.7588438887831

x63 = -3.92699081698724

x64 = -2.35619449019234

x65 = 46.3384916404494

x66 = 58.9048622548086

x67 = -22.776546738526

x68 = 91.8915851175014

x69 = -40.0553063332699

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