2sin(x)-cos(x)=0 (уравнение)

Найду корень уравнения: 2sin(x)-cos(x)=0

Вы ввели

2*sin(x) - cos(x) = 0

$$2 \sin{\left(x \right)} - \cos{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$2 \sin{\left(x \right)} - \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}} = 1$$
или
$$2 \tan{\left(x \right)} = 1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\tan{\left(x \right)} = - \frac{1}{2}$$
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)

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

=

atan(1/2)

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

произведение

1*atan(1/2)

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

=

atan(1/2)

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

Численный ответ

x1 = 368.029988079007

x2 = -40.3770568876665

x3 = 88.428241909515

x4 = 69.5786859879763

x5 = -68.6513907699746

x6 = -15.2443156589482

x7 = 47.5875374128477

x8 = 9.88842556977019

x9 = -43.5186495412563

x10 = -8.96113035176857

x11 = 79.0034639487456

x12 = 97.8530198702844

x13 = -46.6602421948461

x14 = 50.7291300664375

x15 = -52.9434275020257

x16 = -87.5009466915134

x17 = 82.1450566023354

x18 = -24.6690936197175

x19 = 57.0123153736171

x20 = -59.2266128092053

x21 = 72.7202786415661

x22 = 100.994612523874

x23 = 53.8707227200273

x24 = -18.385908312538

x25 = 63.2955006807967

x26 = -56.0850201556155

x27 = -74.9345760771542

x28 = -30.9522789268971

x29 = -5.81953769817878

x30 = 41.3043521056681

x31 = 91.5698345631048

x32 = 0.463647609000806

x33 = 44.4459447592579

x34 = -78.076168730744

x35 = -96.9257246522828

x36 = -49.8018348484359

x37 = 25.5963888377192

x38 = -238.297394063823

x39 = 94.7114272166946

x40 = 3.6052402625906

x41 = -90.6425393451032

x42 = 35.0211667984885

x43 = -62.3682054627951

x44 = 13.03001822336

x45 = -100.067317305873

x46 = 28.7379814913089

x47 = 66.4370933343865

x48 = 4785.10925902626

x49 = 31.8795741448987

x50 = 85.2866492559252

x51 = 16.1716108769498

x52 = -93.784131998693

x53 = -34.0938715804869

x54 = 75.8618712951559

x55 = -71.7929834235644

x56 = -84.3593540379236

x57 = 60.1539080272069

x58 = 22.4547961841294

x59 = -27.8106862733073

x60 = -37.2354642340767

x61 = 6.74683291618039

x62 = -81.2177613843338

x63 = -1271.88137709487

x64 = -21.5275009661277

x65 = 38.1627594520783

x66 = -65.5097981163849

x67 = 19.3132035305396

x68 = -12.1027230053584

x69 = -2.67794504458899

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