tg2x=1 (уравнение)

Найду корень уравнения: tg2x=1

Вы ввели

tan(2*x) = 1

$$\tan{\left(2 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\tan{\left(2 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$2 x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$

Быстрый ответ

     pi
x1 = --
     8 

$$x_{1} = \frac{\pi}{8}$$

Сумма и произведение корней

сумма

    pi
0 + --
    8 

$$0 + \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

произведение

  pi
1*--
  8 

$$1 \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

Численный ответ

x1 = 5.10508806208341

x2 = 66.3661448070844

x3 = -71.8639319508665

x4 = -5.89048622548086

x5 = -73.4347282776614

x6 = -79.717913584841

x7 = 96.2112750161874

x8 = -96.9966731795849

x9 = -93.8550805259951

x10 = -21.5984494934298

x11 = -75.0055246044563

x12 = -68.7223392972767

x13 = -37.3064127613788

x14 = 88.3572933822129

x15 = 58.5121631731099

x16 = -100.138265833175

x17 = 30.2378292908018

x18 = -95.42587685279

x19 = 78.9325154214436

x20 = -23.1692458202247

x21 = -13.7444678594553

x22 = 85.2157007286231

x23 = 60.0829594999048

x24 = -87.5718952188155

x25 = -45.1603943953533

x26 = 42.8041999051609

x27 = -60.8683576633022

x28 = 20.8130513300324

x29 = -9.03207887907065

x30 = 52.2289778659303

x31 = -2.74889357189107

x32 = -90.7134878724053

x33 = 12.9590696960579

x34 = 63.2245521534946

x35 = -15.3152641862502

x36 = 82.0741080750334

x37 = 36.5210145979813

x38 = -24.7400421470196

x39 = 31.8086256175967

x40 = 56.941366846315

x41 = 94.6404786893925

x42 = -78.1471172580461

x43 = 38.0918109247762

x44 = 64.7953484802895

x45 = -82.8595062384308

x46 = 74.2201264410589

x47 = -31.0232274541992

x48 = 28.6670329640069

x49 = 100.923663996572

x50 = 72.649330114264

x51 = -46.7311907221482

x52 = 22.3838476568273

x53 = 8.24668071567321

x54 = 34.9502182711865

x55 = 53.7997741927252

x56 = -67.1515429704818

x57 = -43.5895980685584

x58 = 41.233403578366

x59 = 14.5298660228528

x60 = -16.8860605130451

x61 = 44.3749962319558

x62 = -81.2887099116359

x63 = 67.9369411338793

x64 = -38.8772090881737

x65 = 19.2422550032375

x66 = 1.96349540849362

x67 = -20.0276531666349

x68 = -35.7356164345839

x69 = -56.1559686829176

x70 = 27.096236637212

x71 = -64.009950316892

x72 = 80.5033117482384

x73 = -42.0188017417635

x74 = -51.4435797025329

x75 = 97.7820713429823

x76 = -65.5807466436869

x77 = 9.8174770424681

x78 = 45.9457925587507

x79 = 16.1006623496477

x80 = -29.4524311274043

x81 = -57.7267650097125

x82 = -53.0143760293278

x83 = 86.786497055418

x84 = 50.6581815391354

x85 = -1.17809724509617

x86 = -27.8816348006094

x87 = 89.9280897090078

x88 = 49.0873852123405

x89 = -7.46128255227576

x90 = 23.9546439836222

x91 = -34.164820107789

x92 = -89.1426915456104

x93 = 0.392699081698724

x94 = -12.1736715326604

x95 = 71.0785337874691

x96 = -49.872783375738

x97 = -86.0010988920206

x98 = 75.7909227678538

x99 = 6.67588438887831

x100 = 93.0696823625976

x101 = -59.2975613365073

График