3sin(x)+cos(x)=0 (уравнение)

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

Вы ввели

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

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

Подробное решение

Дано уравнение
$$3 \sin{\left(x \right)} + \cos{\left(x \right)} = 0$$
преобразуем:
$$\frac{3 \sin{\left(x \right)}}{\cos{\left(x \right)}} = -1$$
или
$$3 \tan{\left(x \right)} = -1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$\tan{\left(x \right)} = \frac{1}{3}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{3} \right)}$$
Или
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{3} \right)}$$
, где n - любое целое число

Сумма и произведение корней

сумма

0 - atan(1/3)

$$- \operatorname{atan}{\left(\frac{1}{3} \right)} + 0$$

=

-atan(1/3)

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

произведение

1*-atan(1/3)

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

=

-atan(1/3)

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

Быстрый ответ

x1 = -atan(1/3)

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

Численный ответ

x1 = -3.46334320798644

x2 = 90.7844363997074

x3 = 53.0853245566298

x4 = 59.3685098638094

x5 = 71.9348804781686

x6 = 56.2269172102196

x7 = 15.3862127135523

x8 = 21.6693980207319

x9 = -28.5960844367048

x10 = 81.359658438938

x11 = 84.5012510925278

x12 = -94.5695301620904

x13 = -75.7199742405517

x14 = 49.9437319030401

x15 = -72.5783815869619

x16 = 34.2357686350911

x17 = -100.85271546927

x18 = 62.5101025173992

x19 = -66.2951962797823

x20 = -44.3040477046537

x21 = 100.209214360477

x22 = 43.6605465958605

x23 = -0.321750554396642

x24 = 12.2446200599625

x25 = 40.5189539422707

x26 = -25.454491783115

x27 = -53.7288256654231

x28 = -12.8881211687558

x29 = -85.1447522013211

x30 = 78.2180657853482

x31 = 68.7932878245788

x32 = 31.0941759815013

x33 = 9.10302740637274

x34 = -78.8615668941415

x35 = 5.96143475278294

x36 = -19.1713064759354

x37 = 18.5278053671421

x38 = 75.0764731317584

x39 = -69.4367889333721

x40 = -16.0297138223456

x41 = -19305.4086068637

x42 = 65.651695170989

x43 = -97.7111228156802

x44 = 87.6428437461176

x45 = -88.2863448549109

x46 = -34.8792697438844

x47 = -38.0208623974742

x48 = -60.0120109726027

x49 = -31.7376770902946

x50 = -50.5872330118333

x51 = 24.8109906743217

x52 = -41.162455051064

x53 = -6.60493586157623

x54 = 37.3773612886809

x55 = -56.8704183190129

x56 = -63.1536036261925

x57 = 27.9525833279115

x58 = -2177.44545949212

x59 = 2.81984209919315

x60 = -22.3128991295252

x61 = -91.4279375085006

x62 = -47.4456403582435

x63 = -82.0031595477313

x64 = 97.067621706887

x65 = 93.9260290532972

x66 = -9.74652851516602

x67 = 46.8021392494503

x68 = -546.958872279021

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