sin(x) + 0.2 = 0 (уравнение)

Найду корень уравнения: sin(x) + 0.2 = 0

Вы ввели

sin(x) + 1/5 = 0

$$\sin{\left(x \right)} + \frac{1}{5} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} + \frac{1}{5} = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём 1/5 в правую часть ур-ния

с изменением знака при 1/5

Получим:
$$\sin{\left(x \right)} = - \frac{1}{5}$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(1/5)

$$x_{1} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$

x2 = -asin(1/5)

$$x_{2} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Численный ответ

x1 = 4024.58154716932

x2 = 31.2145686151076

x3 = 37.4977539222872

x4 = -31.6172844566883

x5 = -94.4491375284841

x6 = -44.1836550710474

x7 = 56.3473098438259

x8 = -59.4889024974157

x9 = 15.9093211887393

x10 = -90.9048290333137

x11 = 100.329606994083

x12 = -37.9004697638678

x13 = 43.7809392294668

x14 = -84.6216437261341

x15 = -53.2057171902362

x16 = 66.174803646176

x17 = -97.1880143404933

x18 = 78.7411742605352

x19 = -69.3163962997658

x20 = -75.5995816069454

x21 = 34.7588771102781

x22 = 59.8916183389964

x23 = 94.0464216869035

x24 = -279.400388248701

x25 = 75.1968657653647

x26 = 68.9136804581851

x27 = 72.4579889533556

x28 = -0.201357920790331

x29 = 9.62613588155971

x30 = 129.006656717972

x31 = 172.988953868229

x32 = -34.3561612686974

x33 = 3.34295057438012

x34 = 22.1925064959189

x35 = 50.0641245366464

x36 = -78.3384584189545

x37 = 28.4756918030985

x38 = 81.4800510725443

x39 = -21.7897906543382

x40 = -6.48454322796992

x41 = -63.0332109925862

x42 = 62.6304951510055

x43 = -40.639346575877

x44 = 41.0420624174576

x45 = 97.5907301820739

x46 = -50.466840378227

x47 = 3845.10805007312

x48 = -19.0509138423291

x49 = -15.5066053471586

x50 = -46.9225318830566

x51 = -107.015508142843

x52 = -100.732322835664

x53 = -81.882766914125

x54 = -12.7677285351495

x55 = -9.22342003997905

x56 = 87.7632363797239

x57 = 9845.55001842962

x58 = 24.931383307928

x59 = -65.7720878045953

x60 = -2.94023473279946

x61 = 6.08182738638926

x62 = -28.0729759615178

x63 = -25.3340991495087

x64 = -72.0552731117749

x65 = 225.993313137675

x66 = 12.3650126935688

x67 = 91.3075448748943

x68 = 18.6481980007484

x69 = -56.7500256854066

x70 = 47.3252477246372

x71 = 85.0243595677148

x72 = -88.1659522213045

x73 = 53.6084330318168

График