3tg2x=√3 (уравнение)

Найду корень уравнения: 3tg2x=√3

Вы ввели

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

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

Подробное решение

Дано уравнение
$$3 \tan{\left(2 x \right)} = \sqrt{3}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$\tan{\left(2 x \right)} = \frac{\sqrt{3}}{3}$$
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Или
$$2 x = \pi n + \frac{\pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{12}$$

Сумма и произведение корней

сумма

    pi
0 + --
    12

$$0 + \frac{\pi}{12}$$

=

pi
--
12

$$\frac{\pi}{12}$$

произведение

  pi
1*--
  12

$$1 \frac{\pi}{12}$$

=

pi
--
12

$$\frac{\pi}{12}$$

Быстрый ответ

     pi
x1 = --
     12

$$x_{1} = \frac{\pi}{12}$$

Численный ответ

x1 = 42.6733002112614

x2 = 56.8104671524154

x3 = -46.8620904160477

x4 = 48.9564855184409

x5 = -45.2912940892529

x6 = 1.83259571459405

x7 = -23.3001455141243

x8 = -95.5567765466895

x9 = 58.3812634792103

x10 = 31.6777259236971

x11 = 8.11578102177363

x12 = -78.2780169519457

x13 = 9.68657734856853

x14 = 86.6555973615185

x15 = 92.9387826686981

x16 = -59.4284610304069

x17 = -39.0081087820733

x18 = -43.720497762458

x19 = -100.269165527074

x20 = 45.8148928648512

x21 = 52.0980781720307

x22 = -34.2957198016886

x23 = -21.7293491873294

x24 = 50.5272818452358

x25 = -28.012534494509

x26 = -1.30899693899575

x27 = -60.9992573572018

x28 = 80.3724120543389

x29 = 89.7971900151083

x30 = 53.6688744988256

x31 = -51.5744793964324

x32 = 85.0848010347236

x33 = -50.0036830696375

x34 = 0.261799387799149

x35 = 41.1025038844665

x36 = -67.2824426643814

x37 = -24.8709418409192

x38 = -68.8532389911763

x39 = 22.2529479629277

x40 = 26.9653369433124

x41 = 23.8237442897226

x42 = -53.1452757232273

x43 = -82.9904059323304

x44 = -75.1364242983559

x45 = -15.4461638801498

x46 = -31.1541271480988

x47 = -65.7116463375865

x48 = -17.0169602069447

x49 = 59.9520598060052

x50 = 34.8193185772869

x51 = 88.2263936883134

x52 = 70.9476340935695

x53 = 100.792764302673

x54 = 67.8060414399797

x55 = -37.4373124552784

x56 = -2.87979326579064

x57 = -20.1585528605345

x58 = 28.5361332701073

x59 = 44.2440965380563

x60 = 75.6600230739542

x61 = -71.9948316447661

x62 = -12.30457122656

x63 = -6.02138591938044

x64 = -81.4196096055355

x65 = 72.5184304203644

x66 = 74.0892267471593

x67 = -86.1319985859202

x68 = 66.2352451131848

x69 = 94.5095789954929

x70 = -73.565627971561

x71 = 15.9697626557481

x72 = -42.1497014356631

x73 = -29.5833308213039

x74 = 96.0803753222878

x75 = 14.3989663289532

x76 = 12.8281700021583

x77 = 30.1069295969022

x78 = 63.093652459595

x79 = -57.857664703612

x80 = -64.1408500107916

x81 = 19.1113553093379

x82 = -93.9859802198946

x83 = 97.6511716490827

x84 = -90.8443875663049

x85 = -56.2868683768171

x86 = 81.9432083811338

x87 = -9.16297857297023

x88 = -89.27359123951

x89 = 20.6821516361328

x90 = 37.9609112308767

x91 = 78.801615727544

x92 = -97.1275728734844

x93 = 6.54498469497874

x94 = -87.7027949127151

x95 = -7.59218224617533

x96 = -35.8665161284835

x97 = 4.97418836818384

x98 = 36.3901149040818

x99 = -79.8488132787406

x100 = -13.8753675533549

x101 = 64.6644487863899

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