tan(x)=-2/3 (уравнение)

Найду корень уравнения: tan(x)=-2/3

Вы ввели

tan(x) = -2/3

$$\tan{\left(x \right)} = - \frac{2}{3}$$

Подробное решение

Дано уравнение
$$\tan{\left(x \right)} = - \frac{2}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(- \frac{2}{3} \right)}$$
Или
$$x = \pi n - \operatorname{atan}{\left(\frac{2}{3} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -atan(2/3)

$$x_{1} = - \operatorname{atan}{\left(\frac{2}{3} \right)}$$

Сумма и произведение корней

сумма

0 - atan(2/3)

$$- \operatorname{atan}{\left(\frac{2}{3} \right)} + 0$$

=

-atan(2/3)

$$- \operatorname{atan}{\left(\frac{2}{3} \right)}$$

произведение

1*-atan(2/3)

$$1 \left(- \operatorname{atan}{\left(\frac{2}{3} \right)}\right)$$

=

-atan(2/3)

$$- \operatorname{atan}{\left(\frac{2}{3} \right)}$$

Численный ответ

x1 = -13.1543732179067

x2 = 24.5447386251708

x3 = 21.403145971581

x4 = -10.0127805643169

x5 = 46.5358872002993

x6 = -53.9950777145741

x7 = -82.2694115968822

x8 = -75.9862262897026

x9 = 99.9429623113258

x10 = -47.7118924073945

x11 = 52.8190725074789

x12 = 87.3765916969666

x13 = 90.5181843505564

x14 = -19.4375585250863

x15 = 8.83677535722181

x16 = -66.5614483289332

x17 = -41.4287071002149

x18 = -50.8534850609843

x19 = -57.1366703681638

x20 = -69.703040982523

x21 = -63.4198556753434

x22 = -28.8623364858557

x23 = 49.6774798538891

x24 = -97.9773748648312

x25 = 37.11110923953

x26 = 65.3854431218381

x27 = -72.8446336361128

x28 = -101.118967518421

x29 = -16.2959658714965

x30 = -25.7207438322659

x31 = -35.1455217930353

x32 = 55.9606651610687

x33 = 5.69518270363202

x34 = 62.2438504682483

x35 = -79.1278189432924

x36 = 18.2615533179912

x37 = -88.5525969040618

x38 = 43.3942945467095

x39 = 11.9783680108116

x40 = -85.411004250472

x41 = 2.55359005004223

x42 = 71.6686284290177

x43 = 33.9695165859402

x44 = 30.8279239323504

x45 = 93.6597770041462

x46 = -44.5702997538047

x47 = -38.2871144466251

x48 = 81.0934063897871

x49 = -6.87118791072715

x50 = 15.1199606644014

x51 = 84.2349990433768

x52 = -60.2782630217536

x53 = 96.801369657736

x54 = 59.1022578146585

x55 = -0.588002603547568

x56 = 40.2527018931197

x57 = 27.6863312787606

x58 = -3.72959525713736

x59 = 77.9518137361973

x60 = -94.8357822112414

x61 = 74.8102210826075

x62 = -91.6941895576516

x63 = 68.5270357754279

x64 = -32.0039291394455

x65 = -22.5791511786761

График