tgx=-√3/3 (уравнение)

Найду корень уравнения: tgx=-√3/3

Вы ввели

            ___ 
         -\/ 3  
tan(x) = -------
            3   

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

Подробное решение

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

Сумма и произведение корней

сумма

    pi
0 - --
    6 

$$- \frac{\pi}{6} + 0$$

=

-pi 
----
 6  

$$- \frac{\pi}{6}$$

произведение

  -pi 
1*----
   6  

$$1 \left(- \frac{\pi}{6}\right)$$

=

-pi 
----
 6  

$$- \frac{\pi}{6}$$

Быстрый ответ

     -pi 
x1 = ----
      6  

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

Численный ответ

x1 = 34.0339204138894

x2 = -88.4881930761125

x3 = -41.3643032722656

x4 = -94.7713783832921

x5 = 2.61799387799149

x6 = -6.80678408277789

x7 = 43.4586983746588

x8 = 8.90117918517108

x9 = -50.789081233035

x10 = 40.317105721069

x11 = 30.8923277602996

x12 = -16.2315620435473

x13 = -85.3466004225227

x14 = 62.3082542961976

x15 = -69.6386371545737

x16 = 65.4498469497874

x17 = 71.733032256967

x18 = -38.2227106186758

x19 = -75.9218224617533

x20 = -31.9395253114962

x21 = 87.4409955249159

x22 = -3.66519142918809

x23 = -60.2138591938044

x24 = 100.007366139275

x25 = 18.3259571459405

x26 = -57.0722665402146

x27 = -13.0899693899575

x28 = 96.8657734856853

x29 = 27.7507351067098

x30 = 84.2994028713261

x31 = 90.5825881785057

x32 = -22.5147473507269

x33 = -101.054563690472

x34 = -0.523598775598299

x35 = -63.3554518473942

x36 = 15.1843644923507

x37 = 12.0427718387609

x38 = 24.60914245312

x39 = 49.7418836818384

x40 = -19.3731546971371

x41 = -91.6297857297023

x42 = -79.0634151153431

x43 = -9.94837673636768

x44 = -25.6563400043166

x45 = 59.1666616426078

x46 = 68.5914396033772

x47 = -66.497044500984

x48 = -53.9306738866248

x49 = 21.4675497995303

x50 = -28.7979326579064

x51 = 74.8746249105567

x52 = 52.8834763354282

x53 = -82.2050077689329

x54 = 93.7241808320955

x55 = 81.1578102177363

x56 = -72.7802298081635

x57 = 56.025068989018

x58 = 5.75958653158129

x59 = 37.1755130674792

x60 = 78.0162175641465

x61 = -97.9129710368819

x62 = -47.6474885794452

x63 = -44.5058959258554

x64 = -35.081117965086

x65 = 46.6002910282486

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