3*sin(x)=1 (уравнение)

Найду корень уравнения: 3*sin(x)=1

Вы ввели

3*sin(x) = 1

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

Подробное решение

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

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{1}{3}$$
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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 0.339836909454122

x2 = 27.934496972854

x3 = -91.4460238635581

x4 = -78.879653249199

x5 = 84.4831647374703

x6 = 9.08494105131526

x7 = -16.0478001774031

x8 = -47.463726713301

x9 = 50.6053193668908

x10 = 172.447759037984

x11 = 21.6513116656744

x12 = 46.7840528943928

x13 = 82.0212459027887

x14 = -85.1628385563785

x15 = -72.5964679420194

x16 = -28.6141707917623

x17 = 34.2176822800336

x18 = -31.0760896264438

x19 = -9.7646148702235

x20 = 6.62302221663371

x21 = -60.0300973276602

x22 = 71.9167941231111

x23 = 100.870801824328

x24 = -68.7752014695213

x25 = 69.4548752884296

x26 = -18.5097190120846

x27 = -87.6247573910601

x28 = 65.6336088159315

x29 = 90.7663500446499

x30 = 97.0495353518295

x31 = -66.3132826348398

x32 = -34.8973560989418

x33 = -49.9256455479826

x34 = -100.191128005419

x35 = -53.7469120204806

x36 = 31.7557634453521

x37 = 15.3681263584948

x38 = 40.5008675872132

x39 = 38.0389487525316

x40 = 59.350423508752

x41 = 53.0672382015724

x42 = 88.3044312099683

x43 = -41.1805414061214

x44 = -37.3592749336234

x45 = -93.9079426982397

x46 = 12.9062075238133

x47 = -116.578765092276

x48 = 63.17168998125

x49 = 94.5876165171479

x50 = -24.7929043192642

x51 = 19.1893928309929

x52 = -12.2265337049051

x53 = 25.4725781381725

x54 = -22.3309854845827

x55 = -62.4920161623417

x56 = 44.3221340597112

x57 = -97.7292091707377

x58 = -3.48142956304392

x59 = 2.80175574413567

x60 = -75.0583867767009

x61 = 75.7380605956092

x62 = -56.2088308551622

x63 = -5.94334839772546

x64 = -43.642460240803

x65 = -81.3415720838805

x66 = 56.8885046740704

x67 = 78.1999794302907

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