tgx=-0,5 (уравнение)

Найду корень уравнения: tgx=-0,5

Вы ввели

tan(x) = -1/2

$$\tan{\left(x \right)} = - \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\tan{\left(x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{2} \right)}$$
Или
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -atan(1/2)

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

Сумма и произведение корней

сумма

0 - atan(1/2)

$$- \operatorname{atan}{\left(\frac{1}{2} \right)} + 0$$

=

-atan(1/2)

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

произведение

1*-atan(1/2)

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

=

-atan(1/2)

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

Численный ответ

x1 = 30.9522789268971

x2 = -6.74683291618039

x3 = -75.8618712951559

x4 = -0.463647609000806

x5 = 78.076168730744

x6 = -25.5963888377192

x7 = -19.3132035305396

x8 = 100.067317305873

x9 = 5.81953769817878

x10 = -28.7379814913089

x11 = 81.2177613843338

x12 = 8.96113035176857

x13 = 68.6513907699746

x14 = 24.6690936197175

x15 = 62.3682054627951

x16 = 90.6425393451032

x17 = -94.7114272166946

x18 = -13.03001822336

x19 = 59.2266128092053

x20 = 18.385908312538

x21 = -31.8795741448987

x22 = 74.9345760771542

x23 = -9.88842556977019

x24 = -38.1627594520783

x25 = -47.5875374128477

x26 = -100.994612523874

x27 = 43.5186495412563

x28 = -53.8707227200273

x29 = 40.3770568876665

x30 = -60.1539080272069

x31 = -41.3043521056681

x32 = 49.8018348484359

x33 = -72.7202786415661

x34 = -79.0034639487456

x35 = -69.5786859879763

x36 = 96.9257246522828

x37 = -88.428241909515

x38 = -57.0123153736171

x39 = 56.0850201556155

x40 = -66.4370933343865

x41 = 15.2443156589482

x42 = 87.5009466915134

x43 = -35.0211667984885

x44 = 46.6602421948461

x45 = 27.8106862733073

x46 = -82.1450566023354

x47 = 84.3593540379236

x48 = -85.2866492559252

x49 = -97.8530198702844

x50 = -16.1716108769498

x51 = -22.4547961841294

x52 = -3.6052402625906

x53 = 34.0938715804869

x54 = -63.2955006807967

x55 = 52.9434275020257

x56 = 37.2354642340767

x57 = -44.4459447592579

x58 = 12.1027230053584

x59 = 93.784131998693

x60 = 71.7929834235644

x61 = 2.67794504458899

x62 = 65.5097981163849

x63 = 21.5275009661277

x64 = -50.7291300664375

x65 = -91.5698345631048

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