tg(4x)=sqrt(3) (уравнение)

Найду корень уравнения: tg(4x)=sqrt(3)

Вы ввели

             ___
tan(4*x) = \/ 3 

$$\tan{\left(4 x \right)} = \sqrt{3}$$

Подробное решение

Дано уравнение
$$\tan{\left(4 x \right)} = \sqrt{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Или
$$4 x = \pi n + \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{12}$$

Быстрый ответ

     pi
x1 = --
     12

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

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

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

Численный ответ

x1 = 94.5095789954929

x2 = 50.5272818452358

x3 = -87.7027949127151

x4 = -43.720497762458

x5 = -83.7758040957278

x6 = 20.6821516361328

x7 = 70.162235930172

x8 = 14.3989663289532

x9 = 40.317105721069

x10 = 42.6733002112614

x11 = 98.4365698124802

x12 = -75.9218224617533

x13 = 18.3259571459405

x14 = 10.471975511966

x15 = 96.0803753222878

x16 = 66.2352451131848

x17 = 22.2529479629277

x18 = -35.8665161284835

x19 = -31.9395253114962

x20 = 86.6555973615185

x21 = 78.0162175641465

x22 = -51.5744793964324

x23 = 38.7463093942741

x24 = 84.2994028713261

x25 = 0.261799387799149

x26 = 74.0892267471593

x27 = -28.012534494509

x28 = -29.5833308213039

x29 = -17.8023583703422

x30 = -95.5567765466895

x31 = 60.7374579694027

x32 = 44.2440965380563

x33 = -89.27359123951

x34 = 68.5914396033772

x35 = -59.4284610304069

x36 = -45.2912940892529

x37 = -67.2824426643814

x38 = -37.4373124552784

x39 = -9.94837673636768

x40 = 82.7286065445312

x41 = -63.3554518473942

x42 = -73.565627971561

x43 = -39.7935069454707

x44 = -25.6563400043166

x45 = 2.61799387799149

x46 = 12.0427718387609

x47 = -13.8753675533549

x48 = -91.6297857297023

x49 = -23.3001455141243

x50 = 52.0980781720307

x51 = -3.66519142918809

x52 = 6.54498469497874

x53 = -53.9306738866248

x54 = -57.857664703612

x55 = 58.3812634792103

x56 = 88.2263936883134

x57 = 64.6644487863899

x58 = 32.4631240870945

x59 = 100.007366139275

x60 = -47.6474885794452

x61 = -71.9948316447661

x62 = 8.11578102177363

x63 = -11.5191730631626

x64 = 80.3724120543389

x65 = -61.7846555205993

x66 = 36.3901149040818

x67 = 92.1533845053006

x68 = -85.3466004225227

x69 = -7.59218224617533

x70 = 76.4454212373516

x71 = -15.4461638801498

x72 = -55.5014702134197

x73 = 30.1069295969022

x74 = -93.9859802198946

x75 = 48.1710873550435

x76 = 4.18879020478639

x77 = 46.6002910282486

x78 = -50.0036830696375

x79 = -79.8488132787406

x80 = -81.4196096055355

x81 = -1.30899693899575

x82 = -33.5103216382911

x83 = 24.60914245312

x84 = 15.9697626557481

x85 = -19.3731546971371

x86 = 54.4542726622231

x87 = -65.7116463375865

x88 = 34.0339204138894

x89 = -99.4837673636768

x90 = -77.4926187885482

x91 = -69.6386371545737

x92 = -97.9129710368819

x93 = 62.3082542961976

x94 = -21.7293491873294

x95 = 56.025068989018

x96 = 26.1799387799149

x97 = -41.3643032722656

x98 = 72.5184304203644

x99 = 28.5361332701073

x100 = 90.5825881785057

x101 = -6.02138591938044

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