2sinx+cosx=0 (уравнение)

Найду корень уравнения: 2sinx+cosx=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

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)

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

Быстрый ответ

x1 = -atan(1/2)

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

Численный ответ

x1 = -50.7291300664375

x2 = -13.03001822336

x3 = -69.5786859879763

x4 = -72.7202786415661

x5 = 87.5009466915134

x6 = 27.8106862733073

x7 = -25.5963888377192

x8 = 74.9345760771542

x9 = 21.5275009661277

x10 = 15.2443156589482

x11 = -16.1716108769498

x12 = -88.428241909515

x13 = 52.9434275020257

x14 = -97.8530198702844

x15 = -57.0123153736171

x16 = 84.3593540379236

x17 = 81.2177613843338

x18 = 100.067317305873

x19 = 2.67794504458899

x20 = -60.1539080272069

x21 = -75.8618712951559

x22 = 40.3770568876665

x23 = -0.463647609000806

x24 = -286.348579085672

x25 = -41.3043521056681

x26 = -53.8707227200273

x27 = -85.2866492559252

x28 = 5.81953769817878

x29 = -28.7379814913089

x30 = -82.1450566023354

x31 = -19.3132035305396

x32 = 49.8018348484359

x33 = 68.6513907699746

x34 = -44.4459447592579

x35 = -9.88842556977019

x36 = -35.0211667984885

x37 = 12.1027230053584

x38 = 59.2266128092053

x39 = 65.5097981163849

x40 = 24.6690936197175

x41 = 90.6425393451032

x42 = -91.5698345631048

x43 = -141.835317020542

x44 = 93.784131998693

x45 = -94.7114272166946

x46 = -79.0034639487456

x47 = -63.2955006807967

x48 = 34.0938715804869

x49 = 30.9522789268971

x50 = -66.4370933343865

x51 = -100.994612523874

x52 = 191.173504259977

x53 = 56.0850201556155

x54 = 78.076168730744

x55 = -31.8795741448987

x56 = 835.199998245884

x57 = 37.2354642340767

x58 = -3.6052402625906

x59 = 18.385908312538

x60 = -22.4547961841294

x61 = 46.6602421948461

x62 = 96.9257246522828

x63 = 8.96113035176857

x64 = -38.1627594520783

x65 = -47.5875374128477

x66 = 71.7929834235644

x67 = -6.74683291618039

x68 = 43.5186495412563

x69 = 62.3682054627951

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