sin(x)=0.1 (уравнение)

Найду корень уравнения: sin(x)=0.1

Вы ввели

sin(x) = 1/10

$$\sin{\left(x \right)} = \frac{1}{10}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{1}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{10} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{10} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{10} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(1/10)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{10} \right)}$$

x2 = asin(1/10)

$$x_{2} = \operatorname{asin}{\left(\frac{1}{10} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(1/10) + asin(1/10)

$$\operatorname{asin}{\left(\frac{1}{10} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{10} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(1/10))*asin(1/10)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{10} \right)}\right) \operatorname{asin}{\left(\frac{1}{10} \right)}$$

=

(pi - asin(1/10))*asin(1/10)

$$\left(\pi - \operatorname{asin}{\left(\frac{1}{10} \right)}\right) \operatorname{asin}{\left(\frac{1}{10} \right)}$$

Численный ответ

x1 = 56.6488351857778

x2 = -91.2063543752656

x3 = -6.18301788601803

x4 = -100.430797493712

x5 = -56.4485003434547

x6 = -12.4662031931976

x7 = -87.8644268793526

x8 = 0.10016742116156

x9 = 84.7228342257629

x10 = -25.0325738075568

x11 = 69.215205800137

x12 = 40.7405370755057

x13 = 44.0824645714187

x14 = -81.5812415721731

x15 = 91.0060195329424

x16 = 6.38335272834115

x17 = 25.2329086498799

x18 = 37.7992792642391

x19 = -50.1653150362751

x20 = 88.0647617216758

x21 = 78.4396489185833

x22 = -40.9408719178289

x23 = 94.3479470288554

x24 = 97.289204840122

x25 = 28.1741664611466

x26 = 18.9497233427003

x27 = 75.4983911073166

x28 = -9.52494538193094

x29 = 34.4573517683262

x30 = -34.6576866106493

x31 = 12.6665380355207

x32 = -37.598944421916

x33 = 100.631132336035

x34 = 81.7815764144962

x35 = 3.04142523242823

x36 = 499.413064499616

x37 = 53.3069076898649

x38 = 65.8732783042241

x39 = -22.0913159962901

x40 = 31.5160939570595

x41 = 9.32461053960782

x42 = -47.2240572250085

x43 = -78.6399837609064

x44 = -28.3745013034697

x45 = 178.970613833457

x46 = -94.1476121865322

x47 = -59.7904278393676

x48 = 50.3656498785983

x49 = 62.9320204929574

x50 = -43.8821297290955

x51 = -62.7316856506343

x52 = 21.890981153967

x53 = -75.2980562649935

x54 = -69.0148709578139

x55 = -3.24176007475135

x56 = -84.923169068086

x57 = -66.0736131465472

x58 = -72.3567984537268

x59 = 59.5900929970445

x60 = -15.8081306891105

x61 = -18.7493885003772

x62 = -235.719616440396

x63 = -53.507242532188

x64 = 15.6077958467874

x65 = -31.3157591147364

x66 = 47.0237223826853

x67 = -97.4895396824452

x68 = 72.1564636114037

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