sin(x)=8/17 (уравнение)

Найду корень уравнения: sin(x)=8/17

Вы ввели

sin(x) = 8/17

$$\sin{\left(x \right)} = \frac{8}{17}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{8}{17}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{8}{17} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{8}{17} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{8}{17} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{8}{17} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(8/17)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{8}{17} \right)}$$

x2 = asin(8/17)

$$x_{2} = \operatorname{asin}{\left(\frac{8}{17} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(8/17) + asin(8/17)

$$\operatorname{asin}{\left(\frac{8}{17} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{8}{17} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(8/17))*asin(8/17)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{8}{17} \right)}\right) \operatorname{asin}{\left(\frac{8}{17} \right)}$$

=

(pi - asin(8/17))*asin(8/17)

$$\left(\pi - \operatorname{asin}{\left(\frac{8}{17} \right)}\right) \operatorname{asin}{\left(\frac{8}{17} \right)}$$

Численный ответ

x1 = -79.0297736659986

x2 = -35.0474765157415

x3 = 94.7377369339475

x4 = -91.5961442803577

x5 = 78.0498590134911

x6 = -28.7642912085619

x7 = -18.359598595285

x8 = 71.7666737063115

x9 = -41.330661822921

x10 = 8.93482063451565

x11 = 96.8994149350299

x12 = 145.003219391384

x13 = 63.3218103980496

x14 = -97.8793295875373

x15 = -3.63154997984352

x16 = -112.607378202979

x17 = -93.7578222814401

x18 = 90.6162296278503

x19 = 59.2003030919523

x20 = 15.2180059416952

x21 = -24.6427839024646

x22 = 0.489957326253728

x23 = -85.3129589731781

x24 = 50.7554397836904

x25 = -87.4746369742605

x26 = 65.4834883991319

x27 = -22.4811059013823

x28 = -12.0764132881054

x29 = -16.1979205942027

x30 = 57.03862509087

x31 = -53.8970324372802

x32 = 19.3395132477925

x33 = 258.100554920617

x34 = 38.1890691693312

x35 = -49.775525131183

x36 = 46.6339324775932

x37 = -47.6138471301006

x38 = -60.1802177444598

x39 = -81.1914516670809

x40 = 31.9058838621517

x41 = 132.436848777025

x42 = 21.5011912488748

x43 = 88.4545516267679

x44 = -477.032126019395

x45 = 84.3330443206707

x46 = -15152.3913255898

x47 = 25.6226985549721

x48 = 69.6049957052292

x49 = -62.3418957455421

x50 = -4967.34794265172

x51 = 13.0563279406129

x52 = 52.9171177847728

x53 = 75.8881810124088

x54 = 82.1713663195884

x55 = 34.067561863234

x56 = -72.746588358819

x57 = -56.0587104383626

x58 = -100.04100758862

x59 = 40.3507471704136

x60 = 44.4722544765108

x61 = 2.65163532733607

x62 = -66.4634030516394

x63 = 6.77314263343331

x64 = -37.2091545168238

x65 = 27.7843765560544

x66 = -68.6250810527217

x67 = -9.91473528702311

x68 = -5.79322798092586

x69 = -30.9259692096442

x70 = 101.020922241127

x71 = -74.9082663599013

x72 = -43.4923398240034

График