tan(2x)=-1 (уравнение)

Найду корень уравнения: tan(2x)=-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 

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

=

-pi 
----
 8  

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

произведение

  -pi 
1*----
   8  

$$1 \left(- \frac{\pi}{8}\right)$$

=

-pi 
----
 8  

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

Численный ответ

x1 = 15.3152641862502

x2 = -39.6626072515711

x3 = 4.31968989868597

x4 = 81.2887099116359

x5 = 71.8639319508665

x6 = 56.1559686829176

x7 = -58.5121631731099

x8 = 79.717913584841

x9 = -91.4988860358027

x10 = -17.6714586764426

x11 = -22.3838476568273

x12 = 96.9966731795849

x13 = -36.5210145979813

x14 = -72.649330114264

x15 = 73.4347282776614

x16 = -3.53429173528852

x17 = 12.1736715326604

x18 = -31.8086256175967

x19 = 87.5718952188155

x20 = 53.0143760293278

x21 = 20.0276531666349

x22 = -42.8041999051609

x23 = -16.1006623496477

x24 = -61.6537558266997

x25 = -56.941366846315

x26 = 35.7356164345839

x27 = 100.138265833175

x28 = 48.3019870489431

x29 = 92.2842841992002

x30 = 26.3108384738145

x31 = -64.7953484802895

x32 = 65.5807466436869

x33 = 62.4391539900971

x34 = 13.7444678594553

x35 = 42.0188017417635

x36 = 34.164820107789

x37 = 49.872783375738

x38 = 45.1603943953533

x39 = -34.9502182711865

x40 = -28.6670329640069

x41 = 59.2975613365073

x42 = -44.3749962319558

x43 = 64.009950316892

x44 = 37.3064127613788

x45 = -23.9546439836222

x46 = -82.0741080750334

x47 = -30.2378292908018

x48 = -6.67588438887831

x49 = -50.6581815391354

x50 = 1.17809724509617

x51 = 95.42587685279

x52 = 18.45685683984

x53 = -47.5165888855456

x54 = -86.786497055418

x55 = 27.8816348006094

x56 = 84.4303025652257

x57 = -38.0918109247762

x58 = -96.2112750161874

x59 = 5.89048622548086

x60 = 9.03207887907065

x61 = 67.1515429704818

x62 = 29.4524311274043

x63 = 78.1471172580461

x64 = 57.7267650097125

x65 = -83.6449044018282

x66 = 7.46128255227576

x67 = 93.8550805259951

x68 = -89.9280897090078

x69 = -69.5077374606742

x70 = 86.0010988920206

x71 = -67.9369411338793

x72 = -88.3572933822129

x73 = -8.24668071567321

x74 = -60.0829594999048

x75 = -80.5033117482384

x76 = 70.2931356240716

x77 = -12.9590696960579

x78 = 43.5895980685584

x79 = -75.7909227678538

x80 = 51.4435797025329

x81 = -66.3661448070844

x82 = -9.8174770424681

x83 = -1.96349540849362

x84 = 21.5984494934298

x85 = -14.5298660228528

x86 = -52.2289778659303

x87 = -20.8130513300324

x88 = -45.9457925587507

x89 = 31.0232274541992

x90 = -97.7820713429823

x91 = 23.1692458202247

x92 = -25.5254403104171

x93 = -0.392699081698724

x94 = 89.1426915456104

x95 = -100.923663996572

x96 = -94.6404786893925

x97 = -74.2201264410589

x98 = -78.9325154214436

x99 = 40.4480054149686

x100 = -53.7997741927252

x101 = 75.0055246044563

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