tan(x)=0.5 (уравнение)

Найду корень уравнения: tan(x)=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

atan(1/2)

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

=

atan(1/2)

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

произведение

atan(1/2)

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

=

atan(1/2)

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

Численный ответ

x1 = -18.385908312538

x2 = 66.4370933343865

x3 = 3.6052402625906

x4 = -40.3770568876665

x5 = 50.7291300664375

x6 = 94.7114272166946

x7 = 35.0211667984885

x8 = -93.784131998693

x9 = -84.3593540379236

x10 = 69.5786859879763

x11 = -81.2177613843338

x12 = 91.5698345631048

x13 = -8.96113035176857

x14 = -68.6513907699746

x15 = -37.2354642340767

x16 = 44.4459447592579

x17 = -87.5009466915134

x18 = 57.0123153736171

x19 = -52.9434275020257

x20 = 28.7379814913089

x21 = -56.0850201556155

x22 = 6.74683291618039

x23 = 88.428241909515

x24 = -30.9522789268971

x25 = 82.1450566023354

x26 = -27.8106862733073

x27 = -62.3682054627951

x28 = -46.6602421948461

x29 = -21.5275009661277

x30 = -59.2266128092053

x31 = 85.2866492559252

x32 = 13.03001822336

x33 = 31.8795741448987

x34 = -100.067317305873

x35 = 79.0034639487456

x36 = -71.7929834235644

x37 = 25.5963888377192

x38 = -12.1027230053584

x39 = -96.9257246522828

x40 = -74.9345760771542

x41 = 47.5875374128477

x42 = -78.076168730744

x43 = -65.5097981163849

x44 = 53.8707227200273

x45 = 41.3043521056681

x46 = -49.8018348484359

x47 = 16.1716108769498

x48 = -2.67794504458899

x49 = 100.994612523874

x50 = -34.0938715804869

x51 = -24.6690936197175

x52 = 22.4547961841294

x53 = -5.81953769817878

x54 = -15.2443156589482

x55 = 72.7202786415661

x56 = 60.1539080272069

x57 = -90.6425393451032

x58 = 0.463647609000806

x59 = 9.88842556977019

x60 = 75.8618712951559

x61 = 97.8530198702844

x62 = 38.1627594520783

x63 = 19.3132035305396

x64 = -43.5186495412563

x65 = 63.2955006807967

График