sin(x)=3/7 (уравнение)

Найду корень уравнения: sin(x)=3/7

Вы ввели

sin(x) = 3/7

$$\sin{\left(x \right)} = \frac{3}{7}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{3}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{7} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{7} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(3/7)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{3}{7} \right)}$$

x2 = asin(3/7)

$$x_{2} = \operatorname{asin}{\left(\frac{3}{7} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(3/7) + asin(3/7)

$$\operatorname{asin}{\left(\frac{3}{7} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{3}{7} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(3/7))*asin(3/7)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{3}{7} \right)}\right) \operatorname{asin}{\left(\frac{3}{7} \right)}$$

=

(pi - asin(3/7))*asin(3/7)

$$\left(\pi - \operatorname{asin}{\left(\frac{3}{7} \right)}\right) \operatorname{asin}{\left(\frac{3}{7} \right)}$$

Численный ответ

x1 = -53.8499861551001

x2 = 75.8411347302287

x3 = 94.6906906517674

x4 = 38.1420228871512

x5 = 34.1146081454141

x6 = -41.283615540741

x7 = 6.72609635125323

x8 = -24.6898301846447

x9 = -30.9730154918243

x10 = -106.371239177979

x11 = 78.0969052956712

x12 = 84.3800906028508

x13 = 19.2924669656124

x14 = 21.5482375310549

x15 = 71.8137199884916

x16 = 159.778314289006

x17 = -100.0880538708

x18 = -35.0004302335614

x19 = 25.575652272792

x20 = -47.5668008479205

x21 = -97.8322833053572

x22 = 100.973875958947

x23 = -28.7172449263818

x24 = -3.58450369766343

x25 = 13.0092816584328

x26 = 2.69868160951615

x27 = 69.5579494230491

x28 = 50.7083935015103

x29 = 8.98186691669574

x30 = -5.84027426310595

x31 = -62.3889420277222

x32 = 88.4075053445878

x33 = -78.9827273838185

x34 = -91.5490979981776

x35 = 63.2747641158695

x36 = -43.5393861061835

x37 = -81.238497949261

x38 = 220.354396795359

x39 = 96.94646121721

x40 = 27.8314228382345

x41 = -60.1331714622797

x42 = -37.2562007990039

x43 = -72.6995420766389

x44 = 52.9641640669528

x45 = 82.1243200374083

x46 = 56.9915788086899

x47 = 59.2473493741324

x48 = -56.1057567205426

x49 = -87.5216832564406

x50 = 40.3977934525937

x51 = -74.9553126420814

x52 = -85.2659126909981

x53 = 46.6809787597733

x54 = -93.8048685636202

x55 = -68.6721273349018

x56 = -9.86768900484302

x57 = 0.442911044073639

x58 = 90.6632759100304

x59 = -12.1234595702855

x60 = -66.4163567694593

x61 = -22.4340596192022

x62 = 31.8588375799716

x63 = 65.530534681312

x64 = -18.4066448774651

x65 = -16.1508743120226

x66 = -122.965024534076

x67 = 44.4252081943307

x68 = 15.2650522238753

x69 = -49.8225714133631

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