6sin(x)=1/6 (уравнение)

Найду корень уравнения: 6sin(x)=1/6

Вы ввели

6*sin(x) = 1/6

$$6 \sin{\left(x \right)} = \frac{1}{6}$$

Подробное решение

Дано уравнение
$$6 \sin{\left(x \right)} = \frac{1}{6}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 6

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{1}{36}$$
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{36} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{36} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{36} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{36} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(1/36)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{36} \right)}$$

x2 = asin(1/36)

$$x_{2} = \operatorname{asin}{\left(\frac{1}{36} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(1/36) + asin(1/36)

$$\operatorname{asin}{\left(\frac{1}{36} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{36} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(1/36))*asin(1/36)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{36} \right)}\right) \operatorname{asin}{\left(\frac{1}{36} \right)}$$

=

(pi - asin(1/36))*asin(1/36)

$$\left(\pi - \operatorname{asin}{\left(\frac{1}{36} \right)}\right) \operatorname{asin}{\left(\frac{1}{36} \right)}$$

Численный ответ

x1 = 12.594151965623

x2 = -84.8507829981882

x3 = 21.9633672238648

x4 = 100.558746266137

x5 = -25.1049598774546

x6 = -9.45255931203318

x7 = 59.6624790669423

x8 = -18.821774570275

x9 = -100.50318356361

x10 = 56.5764491158801

x11 = 28.2465525310443

x12 = 44.0100785015209

x13 = 87.992375651778

x14 = 65.9456643741219

x15 = 34.5297378382239

x16 = 40.8129231454035

x17 = 9.39699660950559

x18 = 735.160462291275

x19 = -43.9545157989933

x20 = -37.6713304918137

x21 = -40.8684858479311

x22 = -91.1339683053678

x23 = -50.2377011061729

x24 = 18.8773372728026

x25 = -28.3021152335719

x26 = -87.9368129492504

x27 = -53.4348564622903

x28 = 94.2755609589576

x29 = -34.5853005407515

x30 = 97.3615909100198

x31 = -47.1516711551107

x32 = -78.5675976910086

x33 = 47.0961084525831

x34 = -15.7357446192128

x35 = -66.0012270766495

x36 = 207.37289648819

x37 = -97.4171536125474

x38 = 62.8596344230597

x39 = -22.0189299263923

x40 = -3.16937400485359

x41 = 72.2288496813015

x42 = 84.7952202956606

x43 = 53.3792937597627

x44 = 0.0277813512637952

x45 = -59.7180417694699

x46 = -75.3704423348912

x47 = -94.21999825643

x48 = 91.0784056028402

x49 = 69.1428197302393

x50 = 78.512034988481

x51 = 31.4437078871617

x52 = 81.7091903445984

x53 = -72.284412383829

x54 = -69.0872570277117

x55 = 25.1605225799821

x56 = 15.6801819166852

x57 = -81.6536276420708

x58 = 6.31096665844338

x59 = -62.8040717205321

x60 = -6.25540395591579

x61 = 75.4260050374188

x62 = 3.113811302326

x63 = -188.467777864124

x64 = -12.5385892630954

x65 = 37.7268931943413

x66 = 50.2932638087005

x67 = -56.5208864133525

x68 = -31.3881451846341

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