sin(x)=-0,7 (уравнение)

Найду корень уравнения: sin(x)=-0,7

Вы ввели

sin(x) = -7/10

$$\sin{\left(x \right)} = - \frac{7}{10}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{7}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{7}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{7}{10} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(7/10)

$$x_{1} = \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$

x2 = -asin(7/10)

$$x_{2} = - \operatorname{asin}{\left(\frac{7}{10} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(7/10) - asin(7/10)

$$- \operatorname{asin}{\left(\frac{7}{10} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{7}{10} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi + asin(7/10))*-asin(7/10)

$$1 \left(\operatorname{asin}{\left(\frac{7}{10} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{7}{10} \right)}\right)$$

=

-(pi + asin(7/10))*asin(7/10)

$$- \left(\operatorname{asin}{\left(\frac{7}{10} \right)} + \pi\right) \operatorname{asin}{\left(\frac{7}{10} \right)}$$

Численный ответ

x1 = -107.589547718664

x2 = 68.3396408823647

x3 = -2792.10047154472

x4 = 47.8992873004577

x5 = 85.5983991435352

x6 = 24.3573437321076

x7 = 18.074158424928

x8 = 43.2068996536464

x9 = -490.863851456618

x10 = -2.36619515697904

x11 = 62.0564555751851

x12 = 66.7488432219964

x13 = 16.4833607645597

x14 = -46.3484923072361

x15 = 3.91699015020055

x16 = -25.9081387253291

x17 = 80.9060114967239

x18 = -8.64938046415863

x19 = -90.3307894574933

x20 = -77.7644188431341

x21 = 324.359440816359

x22 = -335.375016437497

x23 = 29.0497313789189

x24 = -71.4812335359545

x25 = 99.7555674182626

x26 = 74.6228261895443

x27 = 55.7732702680055

x28 = -82.4568064899454

x29 = -69.8904358755862

x30 = 91.8815844507148

x31 = -0.775397496610753

x32 = 5.50778781056883

x33 = -21.2157510785178

x34 = 98.1647697578943

x35 = 35.3329166860985

x36 = -44.7576946468679

x37 = -84.0476041503137

x38 = -14.9325657713382

x39 = -58.9148629215953

x40 = -19.6249534181495

x41 = -13.3417681109699

x42 = -33.782121692877

x43 = 41.6161019932781

x44 = -88.739991797125

x45 = -96.6139747646728

x46 = 22.7665460717393

x47 = -32.1913240325087

x48 = 73.032028529176

x49 = -65.1980482287749

x50 = 60.4656579148168

x51 = -95.0231771043046

x52 = 54.1824726076372

x53 = -157.8550301761

x54 = 10.2001754573801

x55 = -63.6072505684066

x56 = 79.3152138363556

x57 = -624.401540567758

x58 = -51.0408799540474

x59 = 30.6405290392872

x60 = 93.472382111083

x61 = -7.05858280379034

x62 = -52.6316776144157

x63 = -76.1736211827658

x64 = 996.660268684575

x65 = -101.306362411484

x66 = 11.7909731177484

x67 = -40.0653070000566

x68 = -38.4745093396883

x69 = 49.4900849608259

x70 = 36.9237143464668

x71 = 87.1891968039035

x72 = -27.4989363856974

x73 = -57.324065261227

График