sin(x)=3/8 (уравнение)

Найду корень уравнения: sin(x)=3/8

Вы ввели

sin(x) = 3/8

$$\sin{\left(x \right)} = \frac{3}{8}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{3}{8}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{8} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{8} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(3/8)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{3}{8} \right)}$$

x2 = asin(3/8)

$$x_{2} = \operatorname{asin}{\left(\frac{3}{8} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(3/8) + asin(3/8)

$$\operatorname{asin}{\left(\frac{3}{8} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{3}{8} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(3/8))*asin(3/8)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{3}{8} \right)}\right) \operatorname{asin}{\left(\frac{3}{8} \right)}$$

=

(pi - asin(3/8))*asin(3/8)

$$\left(\pi - \operatorname{asin}{\left(\frac{3}{8} \right)}\right) \operatorname{asin}{\left(\frac{3}{8} \right)}$$

Численный ответ

x1 = -75.0138269116594

x2 = -60.0746571927017

x3 = -81.297012218839

x4 = -5.89878853268395

x5 = -85.2073984214201

x6 = -31.0315297614023

x7 = 71.8722342580696

x8 = -100.146568140378

x9 = -3.52598942808543

x10 = 9.04038118627374

x11 = -28.6587306568038

x12 = 15.3235664934533

x13 = 38.0835086175732

x14 = -12.1819738398635

x15 = 12.9507673888548

x16 = -68.7306416044798

x17 = -72.6410278070609

x18 = 53.0226783365308

x19 = 65.58904895089

x20 = 63.2162498462915

x21 = 6.66758208167523

x22 = 75.7826204606507

x23 = 27.8899371078125

x24 = -53.7914718855221

x25 = -91.4905837285996

x26 = 78.1554195652492

x27 = -47.5082865783425

x28 = -43.5979003757615

x29 = 82.0658057678303

x30 = 2.75719587909415

x31 = 84.4386048724288

x32 = -22.3755453496242

x33 = 100.915361689369

x34 = -9.80917473526502

x35 = 59.3058636437104

x36 = -37.3147150685819

x37 = 90.7217901796084

x38 = -1249.96947935424

x39 = 34.1731224149921

x40 = 201.446326604242

x41 = -34.9419159639834

x42 = 56.9330645391119

x43 = 31.8003233103936

x44 = 25.517138003214

x45 = 44.3666939247527

x46 = 40.4563077221717

x47 = 88.3489910750098

x48 = -62.4474562973002

x49 = -78.9242131142405

x50 = -18.4651591470431

x51 = -56.1642709901206

x52 = 97.004975486788

x53 = 21.6067518006329

x54 = -93.8633828331982

x55 = 46.7394930293513

x56 = -66.3578424998813

x57 = -24.7483444542227

x58 = 50.6498792319323

x59 = -200.677533055251

x60 = -87.5801975260186

x61 = -16.0923600424446

x62 = 0.384396774495639

x63 = -97.7737690357792

x64 = -41.2251012711629

x65 = 69.4994351534711

x66 = -49.8810856829411

x67 = 19.2339526960344

x68 = 94.6321763821894

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