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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 21.5796317290611

x2 = -49.8539656113692

x3 = 44.3938139963246

x4 = -5.8716684611121

x5 = -62.4203362257284

x6 = -24.7212243826509

x7 = 6.69470215324707

x8 = 71.8451141864978

x9 = -85.2345184929919

x10 = 84.4114848008569

x11 = -78.9513331858123

x12 = 59.2787435721386

x13 = 19.2610727676062

x14 = 100.942481760941

x15 = 27.8628170362407

x16 = -91.5177038001715

x17 = 52.995558264959

x18 = 75.8097405322225

x19 = 2.73007580752231

x20 = -31.0044096898304

x21 = -43.5707803041896

x22 = 69.5265552250429

x23 = 96.9778554152161

x24 = -97.8008891073511

x25 = -68.703521532908

x26 = 90.6946701080365

x27 = 9.01326111470189

x28 = 56.9601846106838

x29 = -100.119448068806

x30 = -53.818591957094

x31 = -22.402665421196

x32 = -12.1548537682917

x33 = 65.5619288793182

x34 = -56.1371509185488

x35 = -18.4380390754713

x36 = 25.5442580747858

x37 = -47.5354066499144

x38 = -81.2698921472671

x39 = 78.1282994936773

x40 = 50.6769993035042

x41 = -34.9690360355552

x42 = 88.3761111465817

x43 = 46.7123729577794

x44 = 40.4291876505998

x45 = -93.8362627616263

x46 = -66.3849625714531

x47 = -37.28759499701

x48 = -16.1194801140165

x49 = 31.8274433819654

x50 = 38.110628689145

x51 = 15.2964464218815

x52 = 94.6592964537613

x53 = 34.1460023434202

x54 = -28.6858507283756

x55 = -60.1017772642736

x56 = -41.2522213427348

x57 = 12.9778874604267

x58 = -87.5530774544467

x59 = -9.83629480683687

x60 = 63.2433699178634

x61 = 82.0929258394021

x62 = -74.9867068400875

x63 = -72.6681478786327

x64 = 697.845085943002

x65 = -3.55310949965728

x66 = 0.411516846067488

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