tan(x)=-1/3 (уравнение)

Найду корень уравнения: tan(x)=-1/3

Вы ввели

tan(x) = -1/3

$$\tan{\left(x \right)} = - \frac{1}{3}$$

Подробное решение

Дано уравнение
$$\tan{\left(x \right)} = - \frac{1}{3}$$
- это простейшее тригонометрическое ур-ние
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 = 78.2180657853482

x2 = 27.9525833279115

x3 = -97.7111228156802

x4 = 71.9348804781686

x5 = -69.4367889333721

x6 = 90.7844363997074

x7 = 68.7932878245788

x8 = -82.0031595477313

x9 = 31.0941759815013

x10 = -53.7288256654231

x11 = 21.6693980207319

x12 = 87.6428437461176

x13 = 75.0764731317584

x14 = 40.5189539422707

x15 = -75.7199742405517

x16 = 97.067621706887

x17 = -16.0297138223456

x18 = -38.0208623974742

x19 = 24.8109906743217

x20 = -6.60493586157623

x21 = -31.7376770902946

x22 = -50.5872330118333

x23 = -88.2863448549109

x24 = -60.0120109726027

x25 = 59.3685098638094

x26 = 81.359658438938

x27 = -9.74652851516602

x28 = 46.8021392494503

x29 = 12.2446200599625

x30 = 93.9260290532972

x31 = 37.3773612886809

x32 = 34.2357686350911

x33 = -100.85271546927

x34 = 49.9437319030401

x35 = -85.1447522013211

x36 = 56.2269172102196

x37 = -19.1713064759354

x38 = -0.321750554396642

x39 = 84.5012510925278

x40 = 2.81984209919315

x41 = 15.3862127135523

x42 = -47.4456403582435

x43 = -28.5960844367048

x44 = -44.3040477046537

x45 = 100.209214360477

x46 = -34.8792697438844

x47 = 65.651695170989

x48 = 9.10302740637274

x49 = 53.0853245566298

x50 = -25.454491783115

x51 = -12.8881211687558

x52 = -3.46334320798644

x53 = -22.3128991295252

x54 = 5.96143475278294

x55 = -94.5695301620904

x56 = -63.1536036261925

x57 = -91.4279375085006

x58 = -78.8615668941415

x59 = 62.5101025173992

x60 = -66.2951962797823

x61 = -72.5783815869619

x62 = -56.8704183190129

x63 = -41.162455051064

x64 = 18.5278053671421

x65 = 43.6605465958605

График