cos(x)=-(1/√2) (уравнение)

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

Вы ввели

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

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

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{1}{\sqrt{2}}$$
- 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 = -335.36501577071

x2 = -65.1880475619882

x3 = -96.6039740978861

x4 = -41.6261026600648

x5 = 35.3429173528852

x6 = -29.0597320457056

x7 = 3.92699081698724

x8 = 65.1880475619882

x9 = 84.037603483527

x10 = 54.1924732744239

x11 = 255.254403104171

x12 = -3.92699081698724

x13 = -85.6083998103219

x14 = -8.63937979737193

x15 = 16.4933614313464

x16 = -16.4933614313464

x17 = 90.3207887907066

x18 = 22.776546738526

x19 = 60.4756585816035

x20 = -79.3252145031423

x21 = 91.8915851175014

x22 = -2.35619449019234

x23 = -22.776546738526

x24 = 73.0420291959627

x25 = -40.0553063332699

x26 = 58.9048622548086

x27 = 8.63937979737193

x28 = 29.0597320457056

x29 = 47.9092879672443

x30 = 52.621676947629

x31 = -90.3207887907066

x32 = -46.3384916404494

x33 = 98.174770424681

x34 = -58.9048622548086

x35 = 14.9225651045515

x36 = -98.174770424681

x37 = -47.9092879672443

x38 = -21.2057504117311

x39 = 85.6083998103219

x40 = 2584.745355741

x41 = -91.8915851175014

x42 = 41.6261026600648

x43 = 10.2101761241668

x44 = -35.3429173528852

x45 = -54.1924732744239

x46 = 2.35619449019234

x47 = -10.2101761241668

x48 = 27.4889357189107

x49 = -33.7721210260903

x50 = 104.457955731861

x51 = -27.4889357189107

x52 = -66.7588438887831

x53 = -73.0420291959627

x54 = -60.4756585816035

x55 = -84.037603483527

x56 = 33.7721210260903

x57 = -52.621676947629

x58 = 77.7544181763474

x59 = 40.0553063332699

x60 = 96.6039740978861

x61 = 21.2057504117311

x62 = 39349.2333843756

x63 = -77.7544181763474

x64 = -14.9225651045515

x65 = 71.4712328691678

x66 = 79.3252145031423

x67 = 46.3384916404494

x68 = 66.7588438887831

x69 = -71.4712328691678

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