tg3x=√3 (уравнение)

Найду корень уравнения: tg3x=√3

Вы ввели

             ___
tan(3*x) = \/ 3 

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

Подробное решение

Дано уравнение
$$\tan{\left(3 x \right)} = \sqrt{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Или
$$3 x = \pi n + \frac{\pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{9}$$

Быстрый ответ

     pi
x1 = --
     9 

$$x_{1} = \frac{\pi}{9}$$

Сумма и произведение корней

сумма

    pi
0 + --
    9 

$$0 + \frac{\pi}{9}$$

=

pi
--
9 

$$\frac{\pi}{9}$$

произведение

  pi
1*--
  9 

$$1 \frac{\pi}{9}$$

=

pi
--
9 

$$\frac{\pi}{9}$$

Численный ответ

x1 = -71.9075651821664

x2 = 22.3402144255274

x3 = 6.63225115757845

x4 = -8.02851455917392

x5 = 32.8121899374934

x6 = -33.1612557878923

x7 = -1.74532925199433

x8 = 88.3136601509131

x9 = 78.8888821901437

x10 = -53.0580092606276

x11 = 68.4169066781777

x12 = -30.0196631343025

x13 = -63.5299847725936

x14 = 48.5201532054424

x15 = 94.5968454580927

x16 = 44.331363000656

x17 = -93.8987137572949

x18 = -87.6155284501153

x19 = 66.3225115757845

x20 = -13.2645023151569

x21 = 28.623399732707

x22 = 90.4080552533063

x23 = 16.0570291183478

x24 = -83.4267382453289

x25 = 24.4346095279206

x26 = 18.151424220741

x27 = -59.3411945678072

x28 = 74.7000919853573

x29 = -47.8220215046446

x30 = -27.9252680319093

x31 = -65.6243798749868

x32 = 10.8210413623648

x33 = -85.5211333477222

x34 = 13.9626340159546

x35 = -21.6420827247297

x36 = -69.8131700797732

x37 = 20.2458193231342

x38 = -19.5476876223365

x39 = 12.915436464758

x40 = -11.1701072127637

x41 = -91.8043186549017

x42 = 35.9537825910832

x43 = -3.83972435438753

x44 = 92.5024503556995

x45 = 70.5113017805709

x46 = 57.9449311662117

x47 = 4.53785605518526

x48 = 72.6056968829641

x49 = 2.44346095279206

x50 = 38.0481776934764

x51 = 86.2192650485199

x52 = -55.1524043630208

x53 = -41.538836197465

x54 = 8.72664625997165

x55 = 40.1425727958696

x56 = -25.8308729295161

x57 = -75.0491578357562

x58 = -15.3588974175501

x59 = -17.4532925199433

x60 = 34.9065850398866

x61 = -79.2379480405426

x62 = 60.0393262686049

x63 = -37.3500459926787

x64 = 42.2369678982628

x65 = -99.1347015132779

x66 = -43.6332312998582

x67 = 100.880030765272

x68 = 64.2281164733913

x69 = -31.0668606854991

x70 = -67.71877497738

x71 = -97.0403064108847

x72 = 96.6912405604859

x73 = 50.6145483078356

x74 = -74.0019602845596

x75 = -89.7099235525085

x76 = 62.1337213709981

x77 = 84.1248699461267

x78 = 98.7856356628791

x79 = -61.4355896702004

x80 = -95.9931088596881

x81 = 30.7177948351002

x82 = 76.7944870877505

x83 = 0.349065850398866

x84 = 56.8977336150151

x85 = 54.8033385126219

x86 = 82.0304748437335

x87 = -5.93411945678072

x88 = 26.5290046303138

x89 = -81.3323431429358

x90 = -23.7364778271229

x91 = -45.7276264022514

x92 = -35.2556508902855

x93 = -49.9164166070378

x94 = -39.4444410950718

x95 = -57.246799465414

x96 = -52.010811709431

x97 = 52.7089434102288

x98 = -77.1435529381494

x99 = 46.4257581030492

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