sin(x)=-1/10 (уравнение)

Найду корень уравнения: sin(x)=-1/10

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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 97.4895396824452

x2 = -12.6665380355207

x3 = 40.9408719178289

x4 = -84.7228342257629

x5 = 94.1476121865322

x6 = 367.666507891167

x7 = -21.890981153967

x8 = -31.5160939570595

x9 = -28.1741664611466

x10 = -103.572390147302

x11 = 87.8644268793526

x12 = 78.6399837609064

x13 = -69.215205800137

x14 = 53.507242532188

x15 = -97.289204840122

x16 = 84.923169068086

x17 = -6.38335272834115

x18 = 81.5812415721731

x19 = 3.24176007475135

x20 = 31.3157591147364

x21 = -65.8732783042241

x22 = 75.2980562649935

x23 = -100.631132336035

x24 = 6.18301788601803

x25 = -88.0647617216758

x26 = 56.4485003434547

x27 = 25.0325738075568

x28 = -18.9497233427003

x29 = 9.52494538193094

x30 = -81.7815764144962

x31 = 69.0148709578139

x32 = -50.3656498785983

x33 = 59.7904278393676

x34 = 47.2240572250085

x35 = 66.0736131465472

x36 = 22.0913159962901

x37 = -153.837872604738

x38 = -0.10016742116156

x39 = 72.3567984537268

x40 = -40.7405370755057

x41 = -3.04142523242823

x42 = 15.8081306891105

x43 = -47.0237223826853

x44 = 100.430797493712

x45 = -62.9320204929574

x46 = -53.3069076898649

x47 = -34.4573517683262

x48 = -59.5900929970445

x49 = 244.944059558842

x50 = 91.2063543752656

x51 = -78.4396489185833

x52 = 18.7493885003772

x53 = 34.6576866106493

x54 = -94.3479470288554

x55 = -44.0824645714187

x56 = -91.0060195329424

x57 = 28.3745013034697

x58 = -9.32461053960782

x59 = -56.6488351857778

x60 = -15.6077958467874

x61 = 12.4662031931976

x62 = -25.2329086498799

x63 = 50.1653150362751

x64 = -72.1564636114037

x65 = 62.7316856506343

x66 = 37.598944421916

x67 = 43.8821297290955

x68 = -75.4983911073166

x69 = -37.7992792642391

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