sin(x)=2/7 (уравнение)

Найду корень уравнения: sin(x)=2/7

Вы ввели

sin(x) = 2/7

$$\sin{\left(x \right)} = \frac{2}{7}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{2}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{7} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{7} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(2/7)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{2}{7} \right)}$$

x2 = asin(2/7)

$$x_{2} = \operatorname{asin}{\left(\frac{2}{7} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(2/7) + asin(2/7)

$$\operatorname{asin}{\left(\frac{2}{7} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{2}{7} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(2/7))*asin(2/7)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{2}{7} \right)}\right) \operatorname{asin}{\left(\frac{2}{7} \right)}$$

=

(pi - asin(2/7))*asin(2/7)

$$\left(\pi - \operatorname{asin}{\left(\frac{2}{7} \right)}\right) \operatorname{asin}{\left(\frac{2}{7} \right)}$$

Численный ответ

x1 = 63.1216047732319

x2 = -68.8252866775394

x3 = -34.8472708909238

x4 = 78.2500646383088

x5 = 2.85184095215375

x6 = -72.5463827340013

x7 = 12.8561223157952

x8 = 69.4047900804115

x9 = -24.8429895272823

x10 = 75.6879753875911

x11 = 90.816435252668

x12 = -28.5640855837442

x13 = 34.2677674880517

x14 = -12.2766189129231

x15 = -37.4093601416415

x16 = -91.39593865554

x17 = 88.2543460019503

x18 = 25.4224929301544

x19 = 71.9668793311292

x20 = -81.3916572918986

x21 = 31.705678237334

x22 = -18.5598042201027

x23 = 15.4182115665129

x24 = -56.2589160631802

x25 = 59.40050871677

x26 = -15.997714969385

x27 = -53.6968268124625

x28 = 44.2720488516931

x29 = -87.6748425990782

x30 = -112.807583827797

x31 = -5.99343360574354

x32 = -85.1127533483605

x33 = 81.9711606947707

x34 = 21.7013968736925

x35 = -75.108471984719

x36 = 50.5552341588727

x37 = -3.43134435502584

x38 = 9.13502625933333

x39 = 94.5375313091298

x40 = -62.5421013703598

x41 = -97.6791239627196

x42 = 100.820716616309

x43 = 84.5332499454884

x44 = -47.4136415052829

x45 = 19.1393076229748

x46 = 46.8341381024109

x47 = 37.9888635445136

x48 = -31.1261748344619

x49 = 53.1173234095904

x50 = -93.9580279062578

x51 = 97.0996205598475

x52 = 0.289751701436047

x53 = -49.9757307560006

x54 = -43.6925454488211

x55 = 40.5509527952313

x56 = -100.241213213437

x57 = 65.6836940239496

x58 = -9.71452966220543

x59 = -78.8295680411809

x60 = -59.9800121196421

x61 = -41.1304561981034

x62 = 291.878365082415

x63 = 6.57293700861563

x64 = 56.8384194660523

x65 = 27.9845821808721

x66 = -66.2631974268217

x67 = -22.2809002765646

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