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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 37.4093601416415

x2 = 12.2766189129231

x3 = 93.9580279062578

x4 = -94.5375313091298

x5 = -78.2500646383088

x6 = 7825.99705179361

x7 = -27.9845821808721

x8 = -9.13502625933333

x9 = -34.2677674880517

x10 = -56.8384194660523

x11 = -37.9888635445136

x12 = -88.2543460019503

x13 = 28.5640855837442

x14 = -12.8561223157952

x15 = 85.1127533483605

x16 = 91.39593865554

x17 = 56.2589160631802

x18 = 72.5463827340013

x19 = -71.9668793311292

x20 = 41.1304561981034

x21 = -84.5332499454884

x22 = -2767.45337611117

x23 = 5.99343360574354

x24 = 49.9757307560006

x25 = 31.1261748344619

x26 = -6.57293700861563

x27 = -15.4182115665129

x28 = 22.2809002765646

x29 = 53.6968268124625

x30 = -19.1393076229748

x31 = -100.820716616309

x32 = 18.5598042201027

x33 = -59.40050871677

x34 = 78.8295680411809

x35 = 97.6791239627196

x36 = -40.5509527952313

x37 = 15.997714969385

x38 = 47.4136415052829

x39 = 62.5421013703598

x40 = -46.8341381024109

x41 = -97.0996205598475

x42 = 81.3916572918986

x43 = -2.85184095215375

x44 = -53.1173234095904

x45 = 66.2631974268217

x46 = 87.6748425990782

x47 = 43.6925454488211

x48 = -44.2720488516931

x49 = -90.816435252668

x50 = -0.289751701436047

x51 = -50.5552341588727

x52 = -75.6879753875911

x53 = 100.241213213437

x54 = -63.1216047732319

x55 = 24.8429895272823

x56 = 75.108471984719

x57 = -31.705678237334

x58 = 59.9800121196421

x59 = -25.4224929301544

x60 = -69.4047900804115

x61 = 3.43134435502584

x62 = -21.7013968736925

x63 = 34.8472708909238

x64 = -81.9711606947707

x65 = 9.71452966220543

x66 = -65.6836940239496

x67 = 68.8252866775394

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