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

Быстрый ответ

     3*pi
x1 = ----
      4  

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

     5*pi
x2 = ----
      4  

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

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  

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

Численный ответ

x1 = 98.174770424681

x2 = 3.92699081698724

x3 = -2.35619449019234

x4 = 2.35619449019234

x5 = -16.4933614313464

x6 = -85.6083998103219

x7 = -10.2101761241668

x8 = -46.3384916404494

x9 = -54.1924732744239

x10 = 66.7588438887831

x11 = 22.776546738526

x12 = 39349.2333843756

x13 = -79.3252145031423

x14 = 91.8915851175014

x15 = -21.2057504117311

x16 = -3.92699081698724

x17 = 71.4712328691678

x18 = -29.0597320457056

x19 = -65.1880475619882

x20 = 90.3207887907066

x21 = 21.2057504117311

x22 = -84.037603483527

x23 = 52.621676947629

x24 = -96.6039740978861

x25 = -77.7544181763474

x26 = 79.3252145031423

x27 = 58.9048622548086

x28 = 77.7544181763474

x29 = 85.6083998103219

x30 = 29.0597320457056

x31 = 46.3384916404494

x32 = 27.4889357189107

x33 = 73.0420291959627

x34 = -27.4889357189107

x35 = 40.0553063332699

x36 = -14.9225651045515

x37 = 10.2101761241668

x38 = 16.4933614313464

x39 = -73.0420291959627

x40 = -335.36501577071

x41 = -40.0553063332699

x42 = 255.254403104171

x43 = 54.1924732744239

x44 = -66.7588438887831

x45 = -60.4756585816035

x46 = -98.174770424681

x47 = -33.7721210260903

x48 = 33.7721210260903

x49 = -71.4712328691678

x50 = -91.8915851175014

x51 = 2584.745355741

x52 = 65.1880475619882

x53 = 35.3429173528852

x54 = 8.63937979737193

x55 = -90.3207887907066

x56 = 14.9225651045515

x57 = -41.6261026600648

x58 = 104.457955731861

x59 = -35.3429173528852

x60 = -52.621676947629

x61 = 60.4756585816035

x62 = 96.6039740978861

x63 = 41.6261026600648

x64 = -47.9092879672443

x65 = -22.776546738526

x66 = -8.63937979737193

x67 = 84.037603483527

x68 = -58.9048622548086

x69 = 47.9092879672443

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