tan(3x)=-1 (уравнение)

Найду корень уравнения: tan(3x)=-1

Вы ввели

tan(3*x) = -1

$$\tan{\left(3 x \right)} = -1$$

Подробное решение

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

Быстрый ответ

     -pi 
x1 = ----
      12 

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

Сумма и произведение корней

сумма

    pi
0 - --
    12

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

=

-pi 
----
 12 

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

произведение

  -pi 
1*----
   12 

$$1 \left(- \frac{\pi}{12}\right)$$

=

-pi 
----
 12 

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

Численный ответ

x1 = 3.92699081698724

x2 = -57.857664703612

x3 = 56.2868683768171

x4 = -18.0641577581413

x5 = 100.269165527074

x6 = -90.3207887907066

x7 = 47.9092879672443

x8 = 30.1069295969022

x9 = -2.35619449019234

x10 = 28.012534494509

x11 = 50.0036830696375

x12 = -79.8488132787406

x13 = 15.4461638801498

x14 = 17.540558982543

x15 = 63.6172512351933

x16 = 45.8148928648512

x17 = 23.8237442897226

x18 = 81.4196096055355

x19 = -73.565627971561

x20 = -68.329640215578

x21 = -59.9520598060052

x22 = -53.6688744988256

x23 = -31.6777259236971

x24 = 91.8915851175014

x25 = -6.54498469497874

x26 = -92.4151838930998

x27 = -35.8665161284835

x28 = -88.2263936883134

x29 = -51.5744793964324

x30 = -77.7544181763474

x31 = 80.3724120543389

x32 = 25.9181393921158

x33 = -29.5833308213039

x34 = -66.2352451131848

x35 = -11.7809724509617

x36 = -33.7721210260903

x37 = 32.2013246992954

x38 = 8.11578102177363

x39 = -64.1408500107916

x40 = 58.3812634792103

x41 = 43.720497762458

x42 = -84.037603483527

x43 = 87.7027949127151

x44 = -20.1585528605345

x45 = 37.4373124552784

x46 = 98.174770424681

x47 = -50.5272818452358

x48 = -28.5361332701073

x49 = -24.3473430653209

x50 = 83.5140047079287

x51 = 36.3901149040818

x52 = 61.5228561328001

x53 = -72.5184304203644

x54 = -81.9432083811338

x55 = 69.9004365423729

x56 = -26.4417381677141

x57 = 39.5317075576716

x58 = 59.4284610304069

x59 = 78.2780169519457

x60 = 10.2101761241668

x61 = -55.7632696012188

x62 = -70.4240353179712

x63 = -7.59218224617533

x64 = 96.0803753222878

x65 = 54.1924732744239

x66 = -42.1497014356631

x67 = -40.0553063332699

x68 = 93.9859802198946

x69 = 52.0980781720307

x70 = 85.6083998103219

x71 = -13.8753675533549

x72 = -44.2440965380563

x73 = -62.0464549083984

x74 = -99.7455667514759

x75 = 14.3989663289532

x76 = 6.02138591938044

x77 = -37.9609112308767

x78 = 65.7116463375865

x79 = -75.6600230739542

x80 = -97.6511716490827

x81 = 67.8060414399797

x82 = 89.7971900151083

x83 = 76.1836218495525

x84 = 34.2957198016886

x85 = -22.2529479629277

x86 = -48.4328867428426

x87 = 1.83259571459405

x88 = -46.3384916404494

x89 = -94.5095789954929

x90 = 71.9948316447661

x91 = 19.6349540849362

x92 = 21.7293491873294

x93 = 74.0892267471593

x94 = -9.68657734856853

x95 = -15.9697626557481

x96 = 41.6261026600648

x97 = 12.30457122656

x98 = -0.261799387799149

x99 = -96.6039740978861

x100 = -4.45058959258554

x101 = -86.1319985859202

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