cos(x)=-√(3)/2 (уравнение)

Найду корень уравнения: cos(x)=-√(3)/2

Вы ввели

            ___ 
         -\/ 3  
cos(x) = -------
            2   

$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{2} \right)}$$
Или
$$x = \pi n + \frac{5 \pi}{6}$$
$$x = \pi n - \frac{\pi}{6}$$
, где n - любое целое число

Сумма и произведение корней

сумма

    5*pi   7*pi
0 + ---- + ----
     6      6  

$$\left(0 + \frac{5 \pi}{6}\right) + \frac{7 \pi}{6}$$

=

2*pi

$$2 \pi$$

произведение

  5*pi 7*pi
1*----*----
   6    6  

$$\frac{7 \pi}{6} \cdot 1 \cdot \frac{5 \pi}{6}$$

=

     2
35*pi 
------
  36  

$$\frac{35 \pi^{2}}{36}$$

Быстрый ответ

     5*pi
x1 = ----
      6  

$$x_{1} = \frac{5 \pi}{6}$$

     7*pi
x2 = ----
      6  

$$x_{2} = \frac{7 \pi}{6}$$

Численный ответ

x1 = 35.081117965086

x2 = 8.90117918517108

x3 = 60.2138591938044

x4 = 16.2315620435473

x5 = 65.4498469497874

x6 = -71.733032256967

x7 = -90.5825881785057

x8 = 27.7507351067098

x9 = 3.66519142918809

x10 = -60.2138591938044

x11 = -8.90117918517108

x12 = 78.0162175641465

x13 = -9.94837673636768

x14 = 90.5825881785057

x15 = -53.9306738866248

x16 = -21.4675497995303

x17 = 15.1843644923507

x18 = 84.2994028713261

x19 = -91.6297857297023

x20 = -41.3643032722656

x21 = -65.4498469497874

x22 = -28.7979326579064

x23 = 53.9306738866248

x24 = 21.4675497995303

x25 = -16.2315620435473

x26 = -84.2994028713261

x27 = -59.1666616426078

x28 = -66.497044500984

x29 = 40.317105721069

x30 = -52.8834763354282

x31 = -35.081117965086

x32 = 79.0634151153431

x33 = 72.7802298081635

x34 = 192.160750644576

x35 = 216.246294322097

x36 = 41.3643032722656

x37 = -857.131195654415

x38 = -15.1843644923507

x39 = -72.7802298081635

x40 = -22.5147473507269

x41 = -78.0162175641465

x42 = 52.8834763354282

x43 = -34.0339204138894

x44 = -47.6474885794452

x45 = 96.8657734856853

x46 = -96.8657734856853

x47 = -128.281700021583

x48 = 85.3466004225227

x49 = 66.497044500984

x50 = 28.7979326579064

x51 = 22.5147473507269

x52 = 46.6002910282486

x53 = -97.9129710368819

x54 = -2.61799387799149

x55 = -46.6002910282486

x56 = -40.317105721069

x57 = 71.733032256967

x58 = -3.66519142918809

x59 = 47.6474885794452

x60 = -85.3466004225227

x61 = -27.7507351067098

x62 = -4697.20461589234

x63 = 203.679923707738

x64 = 91.6297857297023

x65 = 9.94837673636768

x66 = 97.9129710368819

x67 = 59.1666616426078

x68 = -79.0634151153431

x69 = 34.0339204138894

x70 = 2.61799387799149

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