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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 53.8970324372802

x2 = 97.8793295875373

x3 = 60.1802177444598

x4 = -373.359568450932

x5 = -0.489957326253728

x6 = 85.3129589731781

x7 = 5.79322798092586

x8 = 12.0764132881054

x9 = -63.3218103980496

x10 = 56.0587104383626

x11 = -52.9171177847728

x12 = 30.9259692096442

x13 = 62.3418957455421

x14 = -57.03862509087

x15 = -216.279935771442

x16 = 41.330661822921

x17 = -31.9058838621517

x18 = -25.6226985549721

x19 = 100.04100758862

x20 = -71.7666737063115

x21 = -19.3395132477925

x22 = -38.1890691693312

x23 = -170.135960620103

x24 = -101.020922241127

x25 = -50.7554397836904

x26 = 93.7578222814401

x27 = 18.359598595285

x28 = 43.4923398240034

x29 = 87.4746369742605

x30 = -84.3330443206707

x31 = -88.4545516267679

x32 = 106.324192895799

x33 = 24.6427839024646

x34 = -27.7843765560544

x35 = 112.607378202979

x36 = -69.6049957052292

x37 = -75.8881810124088

x38 = 9.91473528702311

x39 = -2.65163532733607

x40 = 49.775525131183

x41 = -34.067561863234

x42 = -283.233296149335

x43 = -13.0563279406129

x44 = 35.0474765157415

x45 = 3.63154997984352

x46 = 22.4811059013823

x47 = -8.93482063451565

x48 = -21.5011912488748

x49 = 47.6138471301006

x50 = -5605.09125133044

x51 = -82.1713663195884

x52 = 72.746588358819

x53 = -15.2180059416952

x54 = -44.4722544765108

x55 = 68.6250810527217

x56 = 79.0297736659986

x57 = -6.77314263343331

x58 = 16.1979205942027

x59 = -94.7377369339475

x60 = -96.8994149350299

x61 = -65.4834883991319

x62 = 81.1914516670809

x63 = 91.5961442803577

x64 = 37.2091545168238

x65 = -90.6162296278503

x66 = -59.2003030919523

x67 = -46.6339324775932

x68 = -78.0498590134911

x69 = -40.3507471704136

x70 = 74.9082663599013

x71 = 66.4634030516394

x72 = 28.7642912085619

График