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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -31.7206191899133

x2 = 34.8622118435031

x3 = 3.44628530760519

x4 = -78.2351236857294

x5 = -647.472779293513

x6 = 91.4108796081194

x7 = -44.2869898042725

x8 = 37.3944191890621

x9 = -0.304692654015398

x10 = -25.4374338827337

x11 = -21.6864559211132

x12 = 75.0935310321396

x13 = -40.5360118426519

x14 = 56.2439751106009

x15 = 78.8445089937602

x16 = 66.2781383794011

x17 = -50.5701751114521

x18 = 24.8280485747029

x19 = 59.9949530722215

x20 = 16.0126559219644

x21 = 31.1112338818825

x22 = -71.9519383785498

x23 = -2.8368999995744

x24 = -34.2528265354723

x25 = -12.8710632683746

x26 = -81.98610164735

x27 = 826.543560548131

x28 = 93.9430869536784

x29 = -100.835657568889

x30 = 81.3767163393192

x31 = 68.8103457249601

x32 = 53.7117677650419

x33 = -56.8533604186317

x34 = 100.226272260858

x35 = 28.5790265363235

x36 = -90.8014943000886

x37 = -97.0846796072682

x38 = -53.1023824570111

x39 = 22.2958412291439

x40 = -63.1365457258113

x41 = 41.1453971506827

x42 = -19.1542485755542

x43 = -46.8191971498315

x44 = 49.9607898034213

x45 = -59.3855677641907

x46 = 18.5448632675234

x47 = 87.6599016464988

x48 = 85.1276943009398

x49 = -6.58787796119498

x50 = 47.4285824578623

x51 = 12.2616779603438

x52 = 5.97849265316419

x53 = -15.4032706139336

x54 = -65.6687530713703

x55 = -4225.13742642426

x56 = -84.518308992909

x57 = 43.6776044962417

x58 = -27.9696412282927

x59 = 97.694064915299

x60 = -38.0038044970929

x61 = -75.7029163401704

x62 = -88.2692869545296

x63 = -94.5524722617092

x64 = 62.5271604177805

x65 = 9.72947061478478

x66 = -69.4197310329909

x67 = 72.5613236865806

x68 = -9.12008530675398

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