sin(x)=-2/3 (уравнение)

Найду корень уравнения: sin(x)=-2/3

Вы ввели

sin(x) = -2/3

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

Подробное решение

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

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 36.9693841868506

x2 = -63.5615807280228

x3 = 41.5704321528943

x4 = 80.9516813371077

x5 = -46.3941621476199

x6 = 60.419988074433

x7 = 49.5357548012097

x8 = -44.7120248064841

x9 = -58.9605327619791

x10 = -0.729727656226966

x11 = 87.2348666442873

x12 = 85.5527293031514

x13 = 79.2695439959718

x14 = 66.7031733816126

x15 = 1216.52608459548

x16 = 62.1021254155689

x17 = 5.55345765095262

x18 = -13.2960982705861

x19 = -25.8624688849453

x20 = 24.4030135724914

x21 = -38.4288394993045

x22 = -107.54387787828

x23 = -27.5446062260812

x24 = 175.199460944801

x25 = 99.8012372586464

x26 = -52.6773474547995

x27 = 35.2872468457147

x28 = -8.69505030454241

x29 = 22.7208762313555

x30 = 16.4376909241759

x31 = 72.9863586887922

x32 = -76.127951342382

x33 = 93.5180519514668

x34 = -77.8100886835179

x35 = 18.1198282653118

x36 = 11.8366429581322

x37 = 10.1545056169963

x38 = -40.1109768404403

x39 = -21.2614209189016

x40 = -90.376459297877

x41 = -88.6943219567412

x42 = 30.686198879671

x43 = 91.835914610331

x44 = -84.0932739906975

x45 = -7.01291296340655

x46 = -101.2606925711

x47 = 68.3853107227485

x48 = -94.9775072639208

x49 = 47.8536174600739

x50 = -32.1456541921249

x51 = 29.0040615385351

x52 = -82.4111366495616

x53 = 74.6684960299281

x54 = -836.393373511112

x55 = 55.8189401083893

x56 = -302.322622400847

x57 = -19.5792835777657

x58 = 54.1368027672534

x59 = -57.2783954208432

x60 = 3.87132030981676

x61 = 43.2525694940301

x62 = -69.8447660352024

x63 = -71.5269033763383

x64 = -1979.9330994178

x65 = -96.6596446050566

x66 = -1755.42056570047

x67 = -65.2437180691587

x68 = 98.1190999175106

x69 = -14.978235611722

x70 = -2.41186499736283

x71 = -50.9952101136637

x72 = -33.8277915332608

x73 = 412.27836527649

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