sin(x)=1/6 (уравнение)

Найду корень уравнения: sin(x)=1/6

Вы ввели

sin(x) = 1/6

$$\sin{\left(x \right)} = \frac{1}{6}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{1}{6}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{6} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{6} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{6} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{6} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(1/6)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{6} \right)}$$

x2 = asin(1/6)

$$x_{2} = \operatorname{asin}{\left(\frac{1}{6} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(1/6) + asin(1/6)

$$\operatorname{asin}{\left(\frac{1}{6} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{6} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(1/6))*asin(1/6)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{6} \right)}\right) \operatorname{asin}{\left(\frac{1}{6} \right)}$$

=

(pi - asin(1/6))*asin(1/6)

$$\left(\pi - \operatorname{asin}{\left(\frac{1}{6} \right)}\right) \operatorname{asin}{\left(\frac{1}{6} \right)}$$

Численный ответ

x1 = 15.5405151887293

x2 = 100.698412994093

x3 = 65.805997646166

x4 = 62.9993011510156

x5 = 56.716115843836

x6 = -43.8148490710374

x7 = -94.0803315284741

x8 = -72.4240791117849

x9 = -848.062568390024

x10 = 44.1497452294768

x11 = 0.167448079219689

x12 = -81.5139609141149

x13 = -56.3812196853966

x14 = -91.2736350333237

x15 = -62.6644049925762

x16 = 50.4329305366564

x17 = 59.5228123389864

x18 = 40.6732564174476

x19 = -15.8754113471687

x20 = 19.0170040007584

x21 = -75.2307756069354

x22 = -97.5568203405033

x23 = 53.2396270318068

x24 = 25.300189307938

x25 = -47.2913378830666

x26 = -41.008152575887

x27 = -53.5745231902462

x28 = -34.7249672687074

x29 = 37.8665599222972

x30 = 9.25732988154969

x31 = -28.4417819615278

x32 = -18.6821078423191

x33 = 31.5833746151176

x34 = -12.3989225351395

x35 = 84.6555535677047

x36 = -22.1585966543482

x37 = 75.5656717653747

x38 = 97.2219241820639

x39 = 46.9564417246272

x40 = -87.7971462212945

x41 = -84.9904497261441

x42 = 78.3723682605251

x43 = 28.1068858030884

x44 = -37.5316637638578

x45 = -100.363516835654

x46 = 69.2824864581951

x47 = 88.1320423797339

x48 = -24.9652931494987

x49 = -78.7072644189645

x50 = -116.406376262042

x51 = -50.098034378217

x52 = 72.0891829533456

x53 = 21.8237004959089

x54 = 81.8488570725543

x55 = 34.390071110268

x56 = 90.9387388748843

x57 = -3.30904073280948

x58 = -59.8577084974258

x59 = -31.2484784566782

x60 = 6.45063338639928

x61 = -66.1408938046053

x62 = 94.4152276869135

x63 = -68.9475902997558

x64 = 2.9741445743701

x65 = -6.1157372279599

x66 = -9.59222603998907

x67 = 12.7338186935789

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