cos(x)+3sin(x)=0 (уравнение)

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

Вы ввели

cos(x) + 3*sin(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

Быстрый ответ

x1 = -atan(1/3)

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

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)

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

Численный ответ

x1 = 65.651695170989

x2 = 84.5012510925278

x3 = -12.8881211687558

x4 = -63.1536036261925

x5 = -47.4456403582435

x6 = -72.5783815869619

x7 = 49.9437319030401

x8 = -25.454491783115

x9 = -88.2863448549109

x10 = -53.7288256654231

x11 = 81.359658438938

x12 = -91.4279375085006

x13 = -75.7199742405517

x14 = 100.209214360477

x15 = 27.9525833279115

x16 = 31.0941759815013

x17 = 71.9348804781686

x18 = -19.1713064759354

x19 = 12.2446200599625

x20 = 93.9260290532972

x21 = -44.3040477046537

x22 = 68.7932878245788

x23 = 37.3773612886809

x24 = -6.60493586157623

x25 = -60.0120109726027

x26 = -16.0297138223456

x27 = 24.8109906743217

x28 = 5.96143475278294

x29 = 97.067621706887

x30 = 40.5189539422707

x31 = 59.3685098638094

x32 = -85.1447522013211

x33 = -22.3128991295252

x34 = -19305.4086068637

x35 = -546.958872279021

x36 = -69.4367889333721

x37 = 62.5101025173992

x38 = -28.5960844367048

x39 = -31.7376770902946

x40 = 90.7844363997074

x41 = -78.8615668941415

x42 = 15.3862127135523

x43 = -0.321750554396642

x44 = 87.6428437461176

x45 = -34.8792697438844

x46 = 2.81984209919315

x47 = -9.74652851516602

x48 = -66.2951962797823

x49 = 75.0764731317584

x50 = -100.85271546927

x51 = 18.5278053671421

x52 = -94.5695301620904

x53 = -38.0208623974742

x54 = 53.0853245566298

x55 = 78.2180657853482

x56 = 34.2357686350911

x57 = 46.8021392494503

x58 = -82.0031595477313

x59 = -3.46334320798644

x60 = -56.8704183190129

x61 = 43.6605465958605

x62 = -50.5872330118333

x63 = 56.2269172102196

x64 = -2177.44545949212

x65 = 21.6693980207319

x66 = -41.162455051064

x67 = 9.10302740637274

x68 = -97.7111228156802

График