3sinx=2 (уравнение)

Найду корень уравнения: 3sinx=2

Вы ввели

3*sin(x) = 2

$$3 \sin{\left(x \right)} = 2$$

Подробное решение

Дано уравнение
$$3 \sin{\left(x \right)} = 2$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 3

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

Быстрый ответ

x1 = pi - asin(2/3)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{2}{3} \right)}$$

x2 = asin(2/3)

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

Сумма и произведение корней

сумма

0 + pi - asin(2/3) + asin(2/3)

$$\operatorname{asin}{\left(\frac{2}{3} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{2}{3} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(2/3))*asin(2/3)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{2}{3} \right)}\right) \operatorname{asin}{\left(\frac{2}{3} \right)}$$

=

(pi - asin(2/3))*asin(2/3)

$$\left(\pi - \operatorname{asin}{\left(\frac{2}{3} \right)}\right) \operatorname{asin}{\left(\frac{2}{3} \right)}$$

Численный ответ

x1 = -62.1021254155689

x2 = 50.9952101136637

x3 = -72.9863586887922

x4 = -91.835914610331

x5 = -49.5357548012097

x6 = -123.251841146229

x7 = 25.8624688849453

x8 = -93.5180519514668

x9 = -10.1545056169963

x10 = 21.2614209189016

x11 = -47.8536174600739

x12 = -104.40228522469

x13 = -24.4030135724914

x14 = 32.1456541921249

x15 = -85.5527293031514

x16 = -43.2525694940301

x17 = -3.87132030981676

x18 = 33.8277915332608

x19 = -66.7031733816126

x20 = 47300.5487201042

x21 = -35.2872468457147

x22 = 0.729727656226966

x23 = 71.5269033763383

x24 = 76.127951342382

x25 = -68.3853107227485

x26 = -87.2348666442873

x27 = 90.376459297877

x28 = 352.588104858284

x29 = 94.9775072639208

x30 = -5.55345765095262

x31 = 84.0932739906975

x32 = 1596.65879567984

x33 = -74.6684960299281

x34 = 222.323350748648

x35 = 2.41186499736283

x36 = 77.8100886835179

x37 = 46.3941621476199

x38 = 82.4111366495616

x39 = -98.1190999175106

x40 = 38.4288394993045

x41 = -30.686198879671

x42 = 69.8447660352024

x43 = 52.6773474547995

x44 = -29.0040615385351

x45 = -80.9516813371077

x46 = 40.1109768404403

x47 = -41.5704321528943

x48 = 101.2606925711

x49 = 7.01291296340655

x50 = 96.6596446050566

x51 = -99.8012372586464

x52 = 44.7120248064841

x53 = 8.69505030454241

x54 = 58.9605327619791

x55 = -22.7208762313555

x56 = -36.9693841868506

x57 = -54.1368027672534

x58 = 27.5446062260812

x59 = -79.2695439959718

x60 = -1241.6588258242

x61 = 63.5615807280228

x62 = -16.4376909241759

x63 = 57.2783954208432

x64 = -11.8366429581322

x65 = 88.6943219567412

x66 = 13.2960982705861

x67 = 19.5792835777657

x68 = -55.8189401083893

x69 = 65.2437180691587

x70 = -18.1198282653118

x71 = -60.419988074433

x72 = 14.978235611722

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