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)

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

x2 = asin(7/10)

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

Сумма и произведение корней

сумма

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

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 46.3484923072361

x2 = 113.872733025843

x3 = 40.0653070000566

x4 = 52.6316776144157

x5 = -3.91699015020055

x6 = 7.05858280379034

x7 = -98.1647697578943

x8 = -24.3573437321076

x9 = -55.7732702680055

x10 = -49.4900849608259

x11 = 69.8904358755862

x12 = 95.0231771043046

x13 = 90.3307894574933

x14 = 58.9148629215953

x15 = 71.4812335359545

x16 = -91.8815844507148

x17 = -36.9237143464668

x18 = -16.4833607645597

x19 = 2704.1358772442

x20 = -343.208996737898

x21 = 101.306362411484

x22 = -66.7488432219964

x23 = -22.7665460717393

x24 = 84.0476041503137

x25 = 8.64938046415863

x26 = 25.9081387253291

x27 = 82.4568064899454

x28 = 63.6072505684066

x29 = 14.9325657713382

x30 = -41.6161019932781

x31 = -74.6228261895443

x32 = -93.472382111083

x33 = 8522.3654716925

x34 = -85.5983991435352

x35 = 51.0408799540474

x36 = -73.032028529176

x37 = -68.3396408823647

x38 = -80.9060114967239

x39 = -47.8992873004577

x40 = 33.782121692877

x41 = -30.6405290392872

x42 = -135.863881600972

x43 = -11.7909731177484

x44 = -79.3152138363556

x45 = 0.775397496610753

x46 = -43.2068996536464

x47 = 21.2157510785178

x48 = 76.1736211827658

x49 = 65.1980482287749

x50 = -62.0564555751851

x51 = 19.6249534181495

x52 = 88.739991797125

x53 = 27.4989363856974

x54 = -18.074158424928

x55 = -10.2001754573801

x56 = -5.50778781056883

x57 = -60.4656579148168

x58 = 32.1913240325087

x59 = -35.3329166860985

x60 = 13.3417681109699

x61 = -87.1891968039035

x62 = 3645.02287566077

x63 = 57.324065261227

x64 = -54.1824726076372

x65 = 2.36619515697904

x66 = 96.6139747646728

x67 = -236.394846515845

x68 = -2550.1978372183

x69 = -29.0497313789189

x70 = -1614.00322644854

x71 = 44.7576946468679

x72 = -99.7555674182626

x73 = 38.4745093396883

x74 = 77.7644188431341

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