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)

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

x2 = -asin(3/4)

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

Сумма и произведение корней

сумма

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

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 87.1165322215327

x2 = -14.8599011889675

x3 = 73.1046931115467

x4 = -13.4144326933407

x5 = 16.5560253469304

x6 = 91.9542490330855

x7 = 60.5383224971876

x8 = -44.8303592292386

x9 = 55.7006056856348

x10 = -82.5294710723161

x11 = -39.9926424176858

x12 = 22.83921065411

x13 = 85.6710637259059

x14 = 80.8333469143531

x15 = 68.266976299994

x16 = 99.6829028358919

x17 = -88.8126563794957

x18 = 61.9837909928144

x19 = -65.1253836464042

x20 = -57.3967298435978

x21 = -77.6917542607633

x22 = -101.379026993855

x23 = 24.2846791497369

x24 = 30.5678644569164

x25 = -8.5767158817879

x26 = -52.559013032045

x27 = -0.848062078981481

x28 = 5.43512322819811

x29 = -83.9749395679429

x30 = 156.231570600508

x31 = -2.29353057460831

x32 = -7.13124738616107

x33 = -95.0958416866753

x34 = -33.7094571105062

x35 = -69769.3377130011

x36 = -76.2462857651365

x37 = 41.6887665756488

x38 = -46.2758277248654

x39 = -58.8421983392246

x40 = 29.1223959612896

x41 = 36.851049764096

x42 = 11.7183085353777

x43 = -63.6799151507773

x44 = -25.9808033076998

x45 = -32.2639886148794

x46 = 43.1342350712756

x47 = 3.98965473257127

x48 = -27.4262718033267

x49 = 98.2374343402651

x50 = 18.0014938425573

x51 = 66.8215078043671

x52 = -38.547173922059

x53 = -69.9631004579569

x54 = 54.255137190008

x55 = -497.219701346169

x56 = 79.3878784187263

x57 = -21.1430864961471

x58 = 49.4174203784552

x59 = 47.9719518828284

x60 = 10.2728400397509

x61 = -71.4085689535838

x62 = 74.5501616071735

x63 = -90.2581248751225

x64 = -51.1135445364182

x65 = 93.3997175287123

x66 = -96.5413101823021

x67 = -19.6976180005202

x68 = 35.4055812684692

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