sin(x)=3/10 (уравнение)

Найду корень уравнения: sin(x)=3/10

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 = 69.4197310329909

x2 = 6.58787796119498

x3 = -41.1453971506827

x4 = -3.44628530760519

x5 = 97.0846796072682

x6 = 0.304692654015398

x7 = 71.9519383785498

x8 = 75.7029163401704

x9 = -31.1112338818825

x10 = 34.2528265354723

x11 = 90.8014943000886

x12 = 50.5701751114521

x13 = -75.0935310321396

x14 = 81.98610164735

x15 = -12.2616779603438

x16 = -72.5613236865806

x17 = -97.694064915299

x18 = -37.3944191890621

x19 = 44.2869898042725

x20 = -91.4108796081194

x21 = 63.1365457258113

x22 = 27.9696412282927

x23 = 40.5360118426519

x24 = 15.4032706139336

x25 = -62.5271604177805

x26 = 84.518308992909

x27 = 88.2692869545296

x28 = 31.7206191899133

x29 = -56.2439751106009

x30 = -53.7117677650419

x31 = 1146.37662590626

x32 = 78.2351236857294

x33 = 59.3855677641907

x34 = -24.8280485747029

x35 = 65.6687530713703

x36 = -43.6776044962417

x37 = -18.5448632675234

x38 = 53.1023824570111

x39 = -68.8103457249601

x40 = -93.9430869536784

x41 = -47.4285824578623

x42 = -78.8445089937602

x43 = -85.1276943009398

x44 = -16.0126559219644

x45 = 2.8368999995744

x46 = 12.8710632683746

x47 = -100.226272260858

x48 = 21.6864559211132

x49 = 19.1542485755542

x50 = -81.3767163393192

x51 = -34.8622118435031

x52 = 329.562535972913

x53 = 9.12008530675398

x54 = -87.6599016464988

x55 = -5.97849265316419

x56 = -28.5790265363235

x57 = 56.8533604186317

x58 = 46.8191971498315

x59 = 38.0038044970929

x60 = 94.5524722617092

x61 = -66.2781383794011

x62 = -22.2958412291439

x63 = 25.4374338827337

x64 = -59.9949530722215

x65 = -49.9607898034213

x66 = -9.72947061478478

x67 = -112.792642875217

x68 = 100.835657568889

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