tg(2x)=-√3 (уравнение)

Найду корень уравнения: tg(2x)=-√3

Вы ввели

              ___
tan(2*x) = -\/ 3 

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

Подробное решение

Дано уравнение
$$\tan{\left(2 x \right)} = - \sqrt{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Или
$$2 x = \pi n - \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} - \frac{\pi}{6}$$

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 = 63.8790506229925

x2 = 81.1578102177363

x3 = -83.7758040957278

x4 = 70.162235930172

x5 = -50.789081233035

x6 = 45.0294947014537

x7 = -52.3598775598299

x8 = 40.317105721069

x9 = 98.4365698124802

x10 = -75.9218224617533

x11 = 30.8923277602996

x12 = 18.3259571459405

x13 = -79.0634151153431

x14 = -31.9395253114962

x15 = 78.0162175641465

x16 = 87.4409955249159

x17 = 79.5870138909414

x18 = 85.870199198121

x19 = -16.2315620435473

x20 = -82.2050077689329

x21 = -74.3510261349584

x22 = -88.4881930761125

x23 = 84.2994028713261

x24 = 8.90117918517108

x25 = -20.943951023932

x26 = 37.1755130674792

x27 = 51.3126800086333

x28 = -17.8023583703422

x29 = -66.497044500984

x30 = -68.0678408277789

x31 = -96.342174710087

x32 = -14.6607657167524

x33 = 41.8879020478639

x34 = -9.94837673636768

x35 = 59.1666616426078

x36 = -38.2227106186758

x37 = -39.7935069454707

x38 = 71.733032256967

x39 = -25.6563400043166

x40 = 12.0427718387609

x41 = -91.6297857297023

x42 = -3.66519142918809

x43 = 49.7418836818384

x44 = -53.9306738866248

x45 = 27.7507351067098

x46 = 13.6135681655558

x47 = 57.5958653158129

x48 = 74.8746249105567

x49 = 67.0206432765823

x50 = 52.8834763354282

x51 = -94.7713783832921

x52 = 23.0383461263252

x53 = 35.6047167406843

x54 = 100.007366139275

x55 = 65.4498469497874

x56 = -47.6474885794452

x57 = 21.4675497995303

x58 = 43.4586983746588

x59 = 73.3038285837618

x60 = -72.7802298081635

x61 = 29.3215314335047

x62 = -61.7846555205993

x63 = 15.1843644923507

x64 = -2.0943951023932

x65 = 92.1533845053006

x66 = -80.634211442138

x67 = -22.5147473507269

x68 = -57.0722665402146

x69 = -90.0589894029074

x70 = -13.0899693899575

x71 = -58.6430628670095

x72 = 48.1710873550435

x73 = 4.18879020478639

x74 = -101.054563690472

x75 = -46.0766922526503

x76 = -24.0855436775217

x77 = -60.2138591938044

x78 = 1.0471975511966

x79 = 19.8967534727354

x80 = -0.523598775598299

x81 = 34.0339204138894

x82 = 89.0117918517108

x83 = 93.7241808320955

x84 = -35.081117965086

x85 = 7.33038285837618

x86 = -8.37758040957278

x87 = -69.6386371545737

x88 = -97.9129710368819

x89 = -36.6519142918809

x90 = 62.3082542961976

x91 = 56.025068989018

x92 = -28.7979326579064

x93 = -64.9262481741891

x94 = 26.1799387799149

x95 = -6.80678408277789

x96 = 95.2949771588904

x97 = -44.5058959258554

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