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

Быстрый ответ

     -pi 
x1 = ----
      6  

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

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  

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

Численный ответ

x1 = 37.1755130674792

x2 = 74.8746249105567

x3 = -101.054563690472

x4 = -66.497044500984

x5 = 52.8834763354282

x6 = 81.1578102177363

x7 = -60.2138591938044

x8 = -94.7713783832921

x9 = -50.789081233035

x10 = 24.60914245312

x11 = 100.007366139275

x12 = -19.3731546971371

x13 = 68.5914396033772

x14 = 65.4498469497874

x15 = 43.4586983746588

x16 = 21.4675497995303

x17 = 40.317105721069

x18 = -47.6474885794452

x19 = -72.7802298081635

x20 = -0.523598775598299

x21 = -75.9218224617533

x22 = 34.0339204138894

x23 = -9.94837673636768

x24 = 30.8923277602996

x25 = 18.3259571459405

x26 = -79.0634151153431

x27 = 15.1843644923507

x28 = -63.3554518473942

x29 = -85.3466004225227

x30 = 59.1666616426078

x31 = -38.2227106186758

x32 = 93.7241808320955

x33 = 71.733032256967

x34 = -22.5147473507269

x35 = -25.6563400043166

x36 = -31.9395253114962

x37 = -35.081117965086

x38 = 2.61799387799149

x39 = -69.6386371545737

x40 = 12.0427718387609

x41 = 78.0162175641465

x42 = 87.4409955249159

x43 = -57.0722665402146

x44 = -97.9129710368819

x45 = -16.2315620435473

x46 = -13.0899693899575

x47 = 46.6002910282486

x48 = -82.2050077689329

x49 = -91.6297857297023

x50 = 62.3082542961976

x51 = 49.7418836818384

x52 = -28.7979326579064

x53 = -3.66519142918809

x54 = 56.025068989018

x55 = 5.75958653158129

x56 = -53.9306738866248

x57 = -6.80678408277789

x58 = 84.2994028713261

x59 = -88.4881930761125

x60 = 96.8657734856853

x61 = -41.3643032722656

x62 = 8.90117918517108

x63 = 27.7507351067098

x64 = -44.5058959258554

x65 = 90.5825881785057

График