tan(3*x+pi/6)=1 (уравнение)

Найду корень уравнения: tan(3*x+pi/6)=1

Вы ввели

   /      pi\    
tan|3*x + --| = 1
   \      6 /    

$$\tan{\left(3 x + \frac{\pi}{6} \right)} = 1$$

Подробное решение

Дано уравнение
$$\tan{\left(3 x + \frac{\pi}{6} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$3 x + \frac{\pi}{6} = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Перенесём
$$\frac{\pi}{6}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = \pi n + \frac{\pi}{12}$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{36}$$

Быстрый ответ

     pi
x1 = --
     36

$$x_{1} = \frac{\pi}{36}$$

Сумма и произведение корней

сумма

    pi
0 + --
    36

$$0 + \frac{\pi}{36}$$

=

pi
--
36

$$\frac{\pi}{36}$$

произведение

  pi
1*--
  36

$$1 \frac{\pi}{36}$$

=

pi
--
36

$$\frac{\pi}{36}$$

Численный ответ

x1 = -67.9805743651791

x2 = -95.2077106962907

x3 = 38.8335758568738

x4 = 46.16395871525

x5 = 41.9751685104636

x6 = -71.1221670187689

x7 = -93.1133155938975

x8 = 52.4471440224296

x9 = -61.6973890579996

x10 = -31.3286600732982

x11 = 72.343897495165

x12 = 58.7303293296092

x13 = -92.0661180427009

x14 = -26.0926723173152

x15 = 30.4559954473011

x16 = -83.6885376331281

x17 = 6.3704517697793

x18 = -79.4997474283417

x19 = 70.2495023927718

x20 = 19.9840199353351

x21 = -29.234264970905

x22 = -45.9894257900506

x23 = -51.2254135460336

x24 = -57.5085988532132

x25 = 61.871921983199

x26 = -39.706240482871

x27 = 80.7214779047377

x28 = -48.0838208924438

x29 = 90.1462558655071

x30 = -23.998277214922

x31 = -99.3965009010771

x32 = 17.8896248329419

x33 = 22.0784150377283

x34 = -11.4319066005629

x35 = -85.7829327355213

x36 = 56.635934227216

x37 = -77.4053523259485

x38 = 4.27605666738611

x39 = -75.3109572235553

x40 = 36.7391807544806

x41 = 82.8158730071309

x42 = 32.5503905496942

x43 = 92.2406509679003

x44 = -21.9038821125288

x45 = 84.9102681095241

x46 = -2.00712863979348

x47 = 44.0695636128568

x48 = 78.6270828023445

x49 = 66.0607121879854

x50 = -63.7917841603927

x51 = 28.3616003449079

x52 = 96.4294411726867

x53 = 98.5238362750799

x54 = 85.9574656607207

x55 = 14.7480321793521

x56 = -4.10152374218667

x57 = 94.3350460702935

x58 = 26.2672052425147

x59 = -55.41420375082

x60 = 16.8424272817453

x61 = 100.618231377473

x62 = -7.24311639577647

x63 = -41.8006355852642

x64 = -19.8094870101356

x65 = -5.14872129338327

x66 = 0.0872664625997165

x67 = -37.6118453804778

x68 = 39.8807734080704

x69 = 48.2583538176432

x70 = -15.6206968053492

x71 = -49.1310184436404

x72 = 76.5326876999514

x73 = -97.3021057986839

x74 = -27.1398698685118

x75 = 50.3527489200364

x76 = -87.8773278379145

x77 = -89.9717229403077

x78 = 8.4648468721725

x79 = -70.0749694675723

x80 = 2.18166156499291

x81 = -33.4230551756914

x82 = 74.4382925975582

x83 = -81.5941425307349

x84 = -9.33751149816966

x85 = 54.5415391248228

x86 = 12.6536370769589

x87 = 63.9663170855922

x88 = -59.6029939556064

x89 = 10.5592419745657

x90 = 60.8247244320024

x91 = -43.8950306876574

x92 = -17.7150919077424

x93 = 88.0518607631139

x94 = -13.5263017029561

x95 = 68.1551072903786

x96 = 34.6447856520874

x97 = -35.5174502780846

x98 = -65.8861792627859

x99 = -73.2165621211621

x100 = -53.3198086484268

x101 = 24.1728101401215

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