3cos(x)+sin(x)=0 (уравнение)

Найду корень уравнения: 3cos(x)+sin(x)=0

Вы ввели

3*cos(x) + sin(x) = 0

$$\sin{\left(x \right)} + 3 \cos{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} + 3 \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} = -3$$
или
$$\tan{\left(x \right)} = -3$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
Или
$$x = \pi n + \operatorname{atan}{\left(3 \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -atan(3)

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

Сумма и произведение корней

сумма

0 - atan(3)

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

=

-atan(3)

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

произведение

1*-atan(3)

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

=

-atan(3)

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

Численный ответ

x1 = 30.1668807634997

x2 = -32.6649723082962

x3 = -23.2401943475268

x4 = -86.0720474193227

x5 = 80.4323632209364

x6 = -60.9393061906043

x7 = -51.5145282298349

x8 = 17.6005101491405

x9 = -38.9481576154758

x10 = 27.0252881099099

x11 = -4.39063842598805

x12 = -42.0897502690656

x13 = 92.9987338352955

x14 = 5.03413953478133

x15 = -92.3552327265023

x16 = 23.8836954563201

x17 = -16.9570090403472

x18 = 14.4589174955507

x19 = -114.346381301631

x20 = -35.806564961886

x21 = 36.4500660706793

x22 = 42.7332513778588

x23 = -57.7977135370145

x24 = -45.2313429226554

x25 = 20.7421028027303

x26 = 52.1580293386282

x27 = 67.8659926065772

x28 = -64.0808988441941

x29 = -629.567576490357

x30 = -73.5056768049635

x31 = -70.3640841513737

x32 = 262.644737129144

x33 = -54.6561208834247

x34 = -20.098601693937

x35 = 86.715548528116

x36 = 1.89254688119154

x37 = 8.17573218837112

x38 = 99.2819191424751

x39 = -76.6472694585533

x40 = -29.5233796547064

x41 = -10.6738237331676

x42 = 83.5739558745262

x43 = -95.496825380092

x44 = 11.3173248419609

x45 = -1.24904577239825

x46 = -82.9304547657329

x47 = -89.2136400729125

x48 = 96.1403264888853

x49 = 71.007585260167

x50 = 74.1491779137568

x51 = 45.8748440314486

x52 = 49.0164366850384

x53 = 33.3084734170895

x54 = -67.2224914977839

x55 = 77.2907705673466

x56 = 58.4412146458078

x57 = 61.5828072993976

x58 = -7.53223107957784

x59 = -13.8154163867574

x60 = -26.3817870011166

x61 = -1226.47018067242

x62 = 55.299621992218

x63 = -48.3729355762452

x64 = 39.5916587242691

x65 = -98.6384180336818

x66 = 64.7243999529874

x67 = -79.7888621121431

x68 = 89.8571411817058

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