tg2x=√3 (уравнение)

Найду корень уравнения: tg2x=√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 

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

=

pi
--
6 

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

произведение

  pi
1*--
  6 

$$1 \frac{\pi}{6}$$

=

pi
--
6 

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

Численный ответ

x1 = -23.0383461263252

x2 = -71.733032256967

x3 = 74.3510261349584

x4 = 0.523598775598299

x5 = -68.5914396033772

x6 = 57.0722665402146

x7 = -37.1755130674792

x8 = -2.61799387799149

x9 = -90.5825881785057

x10 = -16.7551608191456

x11 = 42.9350995990605

x12 = -59.1666616426078

x13 = -85.870199198121

x14 = 13.0899693899575

x15 = 68.0678408277789

x16 = -49.7418836818384

x17 = -34.0339204138894

x18 = -5.75958653158129

x19 = 27.2271363311115

x20 = -12.0427718387609

x21 = -51.3126800086333

x22 = 85.3466004225227

x23 = -38.7463093942741

x24 = 2.0943951023932

x25 = 31.9395253114962

x26 = -79.5870138909414

x27 = -43.4586983746588

x28 = -87.4409955249159

x29 = 38.2227106186758

x30 = 19.3731546971371

x31 = 93.2005820564972

x32 = -74.8746249105567

x33 = 22.5147473507269

x34 = 71.2094334813686

x35 = 16.2315620435473

x36 = 82.2050077689329

x37 = -65.4498469497874

x38 = 28.7979326579064

x39 = 60.2138591938044

x40 = 72.7802298081635

x41 = -27.7507351067098

x42 = -63.8790506229925

x43 = 86.9173967493176

x44 = 41.3643032722656

x45 = 80.634211442138

x46 = 35.081117965086

x47 = 90.0589894029074

x48 = 53.9306738866248

x49 = -35.6047167406843

x50 = 96.342174710087

x51 = 8.37758040957278

x52 = -89.0117918517108

x53 = 24.0855436775217

x54 = 50.789081233035

x55 = -7.33038285837618

x56 = -13.6135681655558

x57 = -81.1578102177363

x58 = 66.497044500984

x59 = 94.7713783832921

x60 = 79.0634151153431

x61 = -82.7286065445312

x62 = -19.8967534727354

x63 = -41.8879020478639

x64 = -21.4675497995303

x65 = -15.1843644923507

x66 = -78.0162175641465

x67 = -56.025068989018

x68 = -29.3215314335047

x69 = 52.3598775598299

x70 = 101.054563690472

x71 = -45.0294947014537

x72 = 75.9218224617533

x73 = -93.7241808320955

x74 = -52.8834763354282

x75 = -73.3038285837618

x76 = -8.90117918517108

x77 = 5.23598775598299

x78 = -57.5958653158129

x79 = -1.0471975511966

x80 = 97.9129710368819

x81 = 58.6430628670095

x82 = -67.0206432765823

x83 = 44.5058959258554

x84 = -24.60914245312

x85 = -100.007366139275

x86 = 20.943951023932

x87 = 88.4881930761125

x88 = -96.8657734856853

x89 = -95.2949771588904

x90 = 30.3687289847013

x91 = 9.94837673636768

x92 = 36.6519142918809

x93 = 63.3554518473942

x94 = -30.8923277602996

x95 = 46.0766922526503

x96 = 64.9262481741891

x97 = 14.6607657167524

x98 = 49.2182849062401

x99 = -60.7374579694027

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