sin(x)=(3/4) (уравнение)

Найду корень уравнения: sin(x)=(3/4)

Вы ввели

sin(x) = 3/4

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

Подробное решение

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

Быстрый ответ

x1 = pi - asin(3/4)

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

x2 = asin(3/4)

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

Сумма и произведение корней

сумма

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

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -85.6710637259059

x2 = -98.2374343402651

x3 = -5.43512322819811

x4 = 38.547173922059

x5 = 0.848062078981481

x6 = 51.1135445364182

x7 = 95.0958416866753

x8 = -124.81564406461

x9 = 83.9749395679429

x10 = -99.6829028358919

x11 = 96.5413101823021

x12 = -43.1342350712756

x13 = 65.1253836464042

x14 = -36.851049764096

x15 = 17010.8761571097

x16 = 58.8421983392246

x17 = 52.559013032045

x18 = -29.1223959612896

x19 = -61.9837909928144

x20 = 33.7094571105062

x21 = -49.4174203784552

x22 = 90.2581248751225

x23 = -462.662182156681

x24 = -91.9542490330855

x25 = 57.3967298435978

x26 = -16.5560253469304

x27 = -30.5678644569164

x28 = -11.7183085353777

x29 = -54.255137190008

x30 = -3792.75039496186

x31 = 44.8303592292386

x32 = -55.7006056856348

x33 = 8.5767158817879

x34 = -2279.94820442721

x35 = 27.4262718033267

x36 = -93.3997175287123

x37 = -18.0014938425573

x38 = 14.8599011889675

x39 = -3.98965473257127

x40 = -10.2728400397509

x41 = 25.9808033076998

x42 = 13.4144326933407

x43 = 39.9926424176858

x44 = 101.379026993855

x45 = 77.6917542607633

x46 = -35.4055812684692

x47 = 7.13124738616107

x48 = -1606.20190806337

x49 = -68.266976299994

x50 = 71.4085689535838

x51 = 19.6976180005202

x52 = -148.502916797702

x53 = -74.5501616071735

x54 = 7202.82389260241

x55 = -80.8333469143531

x56 = 2.29353057460831

x57 = 21.1430864961471

x58 = 76.2462857651365

x59 = 272.470498783331

x60 = 82.5294710723161

x61 = -87.1165322215327

x62 = -66.8215078043671

x63 = 46.2758277248654

x64 = 63.6799151507773

x65 = 32.2639886148794

x66 = -79.3878784187263

x67 = 88.8126563794957

x68 = -41.6887665756488

x69 = -22.83921065411

x70 = 164.210880065651

x71 = -60.5383224971876

x72 = -73.1046931115467

x73 = 69.9631004579569

x74 = -24.2846791497369

x75 = -47.9719518828284

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