sin(x)=0.3 (уравнение)

Найду корень уравнения: sin(x)=0.3

Вы ввели

sin(x) = 3/10

$$\sin{\left(x \right)} = \frac{3}{10}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{3}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{10} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{10} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(3/10)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{3}{10} \right)}$$

x2 = asin(3/10)

$$x_{2} = \operatorname{asin}{\left(\frac{3}{10} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(3/10) + asin(3/10)

$$\operatorname{asin}{\left(\frac{3}{10} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{3}{10} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(3/10))*asin(3/10)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{3}{10} \right)}\right) \operatorname{asin}{\left(\frac{3}{10} \right)}$$

=

(pi - asin(3/10))*asin(3/10)

$$\left(\pi - \operatorname{asin}{\left(\frac{3}{10} \right)}\right) \operatorname{asin}{\left(\frac{3}{10} \right)}$$

Численный ответ

x1 = -56.2439751106009

x2 = -5.97849265316419

x3 = 59.3855677641907

x4 = 1146.37662590626

x5 = -72.5613236865806

x6 = -22.2958412291439

x7 = -31.1112338818825

x8 = 100.835657568889

x9 = 71.9519383785498

x10 = -112.792642875217

x11 = 46.8191971498315

x12 = -75.0935310321396

x13 = -78.8445089937602

x14 = 94.5524722617092

x15 = -68.8103457249601

x16 = 90.8014943000886

x17 = -41.1453971506827

x18 = 50.5701751114521

x19 = -18.5448632675234

x20 = 0.304692654015398

x21 = 69.4197310329909

x22 = -87.6599016464988

x23 = 78.2351236857294

x24 = 44.2869898042725

x25 = -81.3767163393192

x26 = -43.6776044962417

x27 = 15.4032706139336

x28 = -12.2616779603438

x29 = 25.4374338827337

x30 = 329.562535972913

x31 = 65.6687530713703

x32 = -24.8280485747029

x33 = 84.518308992909

x34 = -85.1276943009398

x35 = 75.7029163401704

x36 = -97.694064915299

x37 = 9.12008530675398

x38 = 38.0038044970929

x39 = -91.4108796081194

x40 = -93.9430869536784

x41 = 27.9696412282927

x42 = 34.2528265354723

x43 = 88.2692869545296

x44 = 56.8533604186317

x45 = 6.58787796119498

x46 = -34.8622118435031

x47 = -62.5271604177805

x48 = 31.7206191899133

x49 = 97.0846796072682

x50 = -28.5790265363235

x51 = 40.5360118426519

x52 = -37.3944191890621

x53 = -100.226272260858

x54 = 63.1365457258113

x55 = 81.98610164735

x56 = -3.44628530760519

x57 = -16.0126559219644

x58 = 19.1542485755542

x59 = -47.4285824578623

x60 = -49.9607898034213

x61 = 21.6864559211132

x62 = -9.72947061478478

x63 = 2.8368999995744

x64 = 53.1023824570111

x65 = -59.9949530722215

x66 = -53.7117677650419

x67 = -66.2781383794011

x68 = 12.8710632683746

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