sin(x)=-0,4 (уравнение)

Найду корень уравнения: sin(x)=-0,4

Вы ввели

sin(x) = -2/5

$$\sin{\left(x \right)} = - \frac{2}{5}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{2}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{2}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{2}{5} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{5} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(2/5)

$$x_{1} = \operatorname{asin}{\left(\frac{2}{5} \right)} + \pi$$

x2 = -asin(2/5)

$$x_{2} = - \operatorname{asin}{\left(\frac{2}{5} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(2/5) - asin(2/5)

$$- \operatorname{asin}{\left(\frac{2}{5} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{2}{5} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi + asin(2/5))*-asin(2/5)

$$1 \left(\operatorname{asin}{\left(\frac{2}{5} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{2}{5} \right)}\right)$$

=

-(pi + asin(2/5))*asin(2/5)

$$- \left(\operatorname{asin}{\left(\frac{2}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{2}{5} \right)}$$

Численный ответ

x1 = 81.2698921472671

x2 = 112.685818683165

x3 = 68.703521532908

x4 = -100.942481760941

x5 = 85.2345184929919

x6 = -88.3761111465817

x7 = 66.3849625714531

x8 = -12.9778874604267

x9 = -90.6946701080365

x10 = 100.119448068806

x11 = 47.5354066499144

x12 = -46.7123729577794

x13 = 5.8716684611121

x14 = 53.818591957094

x15 = 22.402665421196

x16 = 93.8362627616263

x17 = 9145.58773144596

x18 = -69.5265552250429

x19 = 43.5707803041896

x20 = 97.8008891073511

x21 = -63.2433699178634

x22 = 18.4380390754713

x23 = 34.9690360355552

x24 = 87.5530774544467

x25 = -21.5796317290611

x26 = -38.110628689145

x27 = 16.1194801140165

x28 = -56.9601846106838

x29 = 78.9513331858123

x30 = 60.1017772642736

x31 = -9.01326111470189

x32 = -40.4291876505998

x33 = -50.6769993035042

x34 = 62.4203362257284

x35 = 31.0044096898304

x36 = -103.261040722396

x37 = 3.55310949965728

x38 = 72.6681478786327

x39 = -15.2964464218815

x40 = -84.4114848008569

x41 = -52.995558264959

x42 = -0.411516846067488

x43 = -19.2610727676062

x44 = 91.5177038001715

x45 = 56.1371509185488

x46 = -34.1460023434202

x47 = -27.8628170362407

x48 = 12.1548537682917

x49 = -71.8451141864978

x50 = -6.69470215324707

x51 = 28.6858507283756

x52 = 37.28759499701

x53 = -31.8274433819654

x54 = -82.0929258394021

x55 = -94.6592964537613

x56 = -207.756631982994

x57 = -44.3938139963246

x58 = -78.1282994936773

x59 = 74.9867068400875

x60 = 9.83629480683687

x61 = -2.73007580752231

x62 = 24.7212243826509

x63 = -96.9778554152161

x64 = -75.8097405322225

x65 = 1121.96009417762

x66 = -65.5619288793182

x67 = 49.8539656113692

x68 = 41.2522213427348

x69 = -25.5442580747858

x70 = -59.2787435721386

График