sin(x+1)=2/3 (уравнение)

Найду корень уравнения: sin(x+1)=2/3

Вы ввели

sin(x + 1) = 2/3

$$\sin{\left(x + 1 \right)} = \frac{2}{3}$$

Подробное решение

Дано уравнение
$$\sin{\left(x + 1 \right)} = \frac{2}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x + 1 = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x + 1 = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
Или
$$x + 1 = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x + 1 = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
, где n - любое целое число
Перенесём
$$1$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = 2 \pi n - 1 + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$x = 2 \pi n - 1 - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$

Быстрый ответ

x1 = -1 + asin(2/3)

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

x2 = -1 + pi - asin(2/3)

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

Численный ответ

x1 = -19.1198282653118

x2 = -136.818211760588

x3 = -17.4376909241759

x4 = 108.226015219416

x5 = 39.1109768404403

x6 = -86.5527293031514

x7 = 45.3941621476199

x8 = 87.6943219567412

x9 = 27760.5245521168

x10 = -48.8536174600739

x11 = -88.2348666442873

x12 = -37.9693841868506

x13 = 31.1456541921249

x14 = -11.1545056169963

x15 = 12.2960982705861

x16 = 83.0932739906975

x17 = -73.9863586887922

x18 = 26.5446062260812

x19 = -0.270272343773034

x20 = -6.55345765095262

x21 = -31.686198879671

x22 = -25.4030135724914

x23 = -30.0040615385351

x24 = -12.8366429581322

x25 = -99.1190999175106

x26 = 24.8624688849453

x27 = -80.2695439959718

x28 = 93.9775072639208

x29 = 1.41186499736283

x30 = 13.978235611722

x31 = 89.376459297877

x32 = -94.5180519514668

x33 = 177.341053598391

x34 = -63.1021254155689

x35 = 95.6596446050566

x36 = 57.9605327619791

x37 = 18.5792835777657

x38 = 49.9952101136637

x39 = 37.4288394993045

x40 = -44.2525694940301

x41 = 81.4111366495616

x42 = 1283.181667662

x43 = -23.7208762313555

x44 = 51.6773474547995

x45 = -50.5357548012097

x46 = 56.2783954208432

x47 = 64.2437180691587

x48 = -67.7031733816126

x49 = 6.01291296340655

x50 = 7.69505030454241

x51 = 271.588833206085

x52 = 62.5615807280228

x53 = 100.2606925711

x54 = -36.2872468457147

x55 = 32.8277915332608

x56 = -92.835914610331

x57 = -42.5704321528943

x58 = -81.9516813371077

x59 = -4.87132030981676

x60 = 76.8100886835179

x61 = 43.7120248064841

x62 = 68.8447660352024

x63 = -56.8189401083893

x64 = 10852.4728904965

x65 = 20.2614209189016

x66 = -75.6684960299281

x67 = -69.3853107227485

x68 = 70.5269033763383

x69 = 75.127951342382

x70 = -61.419988074433

x71 = -55.1368027672534

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