sinx=3cosx (уравнение)

Найду корень уравнения: sinx=3cosx

Вы ввели

sin(x) = 3*cos(x)

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = 3 \cos{\left(x \right)}$$
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)

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

=

atan(3)

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

произведение

1*atan(3)

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

=

atan(3)

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

Численный ответ

x1 = 32.6649723082962

x2 = 35.806564961886

x3 = -55.299621992218

x4 = -89.8571411817058

x5 = -23.8836954563201

x6 = -1.89254688119154

x7 = 1.24904577239825

x8 = -64.7243999529874

x9 = 67.2224914977839

x10 = 95.496825380092

x11 = 92.3552327265023

x12 = -5.03413953478133

x13 = 60.9393061906043

x14 = -8.17573218837112

x15 = 79.7888621121431

x16 = 64.0808988441941

x17 = -77.2907705673466

x18 = 73.5056768049635

x19 = -42.7332513778588

x20 = 551.027760150612

x21 = -33.3084734170895

x22 = -96.1403264888853

x23 = 98.6384180336818

x24 = 51.5145282298349

x25 = -83.5739558745262

x26 = 86.0720474193227

x27 = 20.098601693937

x28 = 10.6738237331676

x29 = 16.9570090403472

x30 = -36.4500660706793

x31 = 13.8154163867574

x32 = -99.2819191424751

x33 = -17.6005101491405

x34 = 82.9304547657329

x35 = 57.7977135370145

x36 = -39.5916587242691

x37 = 101.780010687272

x38 = -52.1580293386282

x39 = 70.3640841513737

x40 = 7.53223107957784

x41 = -118.131475064014

x42 = -58.4412146458078

x43 = 23.2401943475268

x44 = -30.1668807634997

x45 = -71.007585260167

x46 = -80.4323632209364

x47 = 38.9481576154758

x48 = -20.7421028027303

x49 = -27.0252881099099

x50 = 45.2313429226554

x51 = 42.0897502690656

x52 = -86.715548528116

x53 = 48.3729355762452

x54 = -74.1491779137568

x55 = 54.6561208834247

x56 = 186.603012334196

x57 = 89.2136400729125

x58 = 4.39063842598805

x59 = -49.0164366850384

x60 = -45.8748440314486

x61 = -14.4589174955507

x62 = 26.3817870011166

x63 = -61.5828072993976

x64 = -92.9987338352955

x65 = 29.5233796547064

x66 = 76.6472694585533

x67 = -11.3173248419609

x68 = -67.8659926065772

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