sin(x)=-1/3 (уравнение)

Найду корень уравнения: sin(x)=-1/3

Вы ввели

sin(x) = -1/3

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

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{1}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{3} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(1/3)

$$x_{1} = \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi$$

x2 = -asin(1/3)

$$x_{2} = - \operatorname{asin}{\left(\frac{1}{3} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(1/3) - asin(1/3)

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

=

pi

$$\pi$$

произведение

1*(pi + asin(1/3))*-asin(1/3)

$$1 \left(\operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{3} \right)}\right)$$

=

-(pi + asin(1/3))*asin(1/3)

$$- \left(\operatorname{asin}{\left(\frac{1}{3} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{3} \right)}$$

Численный ответ

x1 = 85.1628385563785

x2 = -94.5876165171479

x3 = -15.3681263584948

x4 = -100.870801824328

x5 = 9.7646148702235

x6 = 3047.00503707265

x7 = -25.4725781381725

x8 = -63.17168998125

x9 = 53.7469120204806

x10 = 47.463726713301

x11 = 12.2265337049051

x12 = -46.7840528943928

x13 = -69.4548752884296

x14 = 75.0583867767009

x15 = -6.62302221663371

x16 = 78.879653249199

x17 = -56.8885046740704

x18 = 5.94334839772546

x19 = 37.3592749336234

x20 = -0.339836909454122

x21 = -82.0212459027887

x22 = 97.7292091707377

x23 = 3.48142956304392

x24 = 144.173425155676

x25 = 24.7929043192642

x26 = 34.8973560989418

x27 = 68.7752014695213

x28 = 345.235354985423

x29 = -88.3044312099683

x30 = -2.80175574413567

x31 = 60.0300973276602

x32 = 16.0478001774031

x33 = -27.934496972854

x34 = 31.0760896264438

x35 = 91.4460238635581

x36 = 41.1805414061214

x37 = -358.481399418691

x38 = -34.2176822800336

x39 = -40.5008675872132

x40 = -78.1999794302907

x41 = 28.6141707917623

x42 = 66.3132826348398

x43 = -38.0389487525316

x44 = -19.1893928309929

x45 = -31.7557634453521

x46 = -90.7663500446499

x47 = 81.3415720838805

x48 = 62.4920161623417

x49 = -65.6336088159315

x50 = 18.5097190120846

x51 = 100.191128005419

x52 = -21.6513116656744

x53 = 72.5964679420194

x54 = -75.7380605956092

x55 = -71.9167941231111

x56 = 49.9256455479826

x57 = -50.6053193668908

x58 = -53.0672382015724

x59 = 87.6247573910601

x60 = -84.4831647374703

x61 = -44.3221340597112

x62 = 56.2088308551622

x63 = -9.08494105131526

x64 = -59.350423508752

x65 = 22.3309854845827

x66 = 93.9079426982397

x67 = 301.253057835166

x68 = -12.9062075238133

x69 = -97.0495353518295

x70 = 43.642460240803

График