4sin(x)=3 (уравнение)

Найду корень уравнения: 4sin(x)=3

Вы ввели

4*sin(x) = 3

$$4 \sin{\left(x \right)} = 3$$

Подробное решение

Дано уравнение
$$4 \sin{\left(x \right)} = 3$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 4

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{3}{4}$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{4} \right)} + \pi$$
, где n - любое целое число

Сумма и произведение корней

сумма

0 + pi - asin(3/4) + asin(3/4)

$$\operatorname{asin}{\left(\frac{3}{4} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(3/4))*asin(3/4)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right) \operatorname{asin}{\left(\frac{3}{4} \right)}$$

=

(pi - asin(3/4))*asin(3/4)

$$\left(\pi - \operatorname{asin}{\left(\frac{3}{4} \right)}\right) \operatorname{asin}{\left(\frac{3}{4} \right)}$$

Быстрый ответ

x1 = pi - asin(3/4)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{3}{4} \right)}$$

x2 = asin(3/4)

$$x_{2} = \operatorname{asin}{\left(\frac{3}{4} \right)}$$

Численный ответ

x1 = -148.502916797702

x2 = -91.9542490330855

x3 = 32.2639886148794

x4 = -22.83921065411

x5 = -24.2846791497369

x6 = 8.5767158817879

x7 = -30.5678644569164

x8 = -18.0014938425573

x9 = -98.2374343402651

x10 = 58.8421983392246

x11 = 13.4144326933407

x12 = -36.851049764096

x13 = -2279.94820442721

x14 = -87.1165322215327

x15 = 7.13124738616107

x16 = -60.5383224971876

x17 = 7202.82389260241

x18 = -74.5501616071735

x19 = 14.8599011889675

x20 = -41.6887665756488

x21 = 0.848062078981481

x22 = 21.1430864961471

x23 = 25.9808033076998

x24 = -1606.20190806337

x25 = 17010.8761571097

x26 = -68.266976299994

x27 = 69.9631004579569

x28 = 83.9749395679429

x29 = 27.4262718033267

x30 = -47.9719518828284

x31 = -462.662182156681

x32 = 76.2462857651365

x33 = -16.5560253469304

x34 = -124.81564406461

x35 = -35.4055812684692

x36 = 71.4085689535838

x37 = 46.2758277248654

x38 = 52.559013032045

x39 = 19.6976180005202

x40 = 101.379026993855

x41 = 2.29353057460831

x42 = 33.7094571105062

x43 = 77.6917542607633

x44 = 51.1135445364182

x45 = -29.1223959612896

x46 = -3.98965473257127

x47 = 95.0958416866753

x48 = 88.8126563794957

x49 = -73.1046931115467

x50 = 82.5294710723161

x51 = -93.3997175287123

x52 = -99.6829028358919

x53 = 96.5413101823021

x54 = -54.255137190008

x55 = 164.210880065651

x56 = -43.1342350712756

x57 = 57.3967298435978

x58 = -55.7006056856348

x59 = -11.7183085353777

x60 = 63.6799151507773

x61 = 272.470498783331

x62 = -5.43512322819811

x63 = -80.8333469143531

x64 = 44.8303592292386

x65 = 65.1253836464042

x66 = -66.8215078043671

x67 = -49.4174203784552

x68 = -3792.75039496186

x69 = -79.3878784187263

x70 = 38.547173922059

x71 = -10.2728400397509

x72 = 90.2581248751225

x73 = -61.9837909928144

x74 = 39.9926424176858

x75 = -85.6710637259059

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