cos(x)=-(√3/2) (уравнение)

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

Вы ввели

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

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

Подробное решение

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

Быстрый ответ

     5*pi
x1 = ----
      6  

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

     7*pi
x2 = ----
      6  

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

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  

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

Численный ответ

x1 = 35.081117965086

x2 = -857.131195654415

x3 = -8.90117918517108

x4 = 34.0339204138894

x5 = 192.160750644576

x6 = -41.3643032722656

x7 = 2.61799387799149

x8 = 53.9306738866248

x9 = 85.3466004225227

x10 = 8.90117918517108

x11 = 40.317105721069

x12 = -71.733032256967

x13 = 97.9129710368819

x14 = -16.2315620435473

x15 = -85.3466004225227

x16 = -40.317105721069

x17 = -4697.20461589234

x18 = 65.4498469497874

x19 = 91.6297857297023

x20 = 71.733032256967

x21 = -3.66519142918809

x22 = -60.2138591938044

x23 = 96.8657734856853

x24 = 203.679923707738

x25 = 3.66519142918809

x26 = 27.7507351067098

x27 = 84.2994028713261

x28 = 90.5825881785057

x29 = -22.5147473507269

x30 = -96.8657734856853

x31 = 66.497044500984

x32 = -2.61799387799149

x33 = -90.5825881785057

x34 = 15.1843644923507

x35 = 79.0634151153431

x36 = 216.246294322097

x37 = -91.6297857297023

x38 = -79.0634151153431

x39 = -59.1666616426078

x40 = -9.94837673636768

x41 = 9.94837673636768

x42 = -21.4675497995303

x43 = -46.6002910282486

x44 = 22.5147473507269

x45 = 59.1666616426078

x46 = -66.497044500984

x47 = 16.2315620435473

x48 = -53.9306738866248

x49 = -15.1843644923507

x50 = -28.7979326579064

x51 = 21.4675497995303

x52 = -78.0162175641465

x53 = -65.4498469497874

x54 = 28.7979326579064

x55 = 52.8834763354282

x56 = 60.2138591938044

x57 = -72.7802298081635

x58 = 47.6474885794452

x59 = 78.0162175641465

x60 = -27.7507351067098

x61 = -84.2994028713261

x62 = -34.0339204138894

x63 = 72.7802298081635

x64 = -128.281700021583

x65 = -97.9129710368819

x66 = -47.6474885794452

x67 = 41.3643032722656

x68 = -52.8834763354282

x69 = -35.081117965086

x70 = 46.6002910282486

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