sin(x)=3/5 (уравнение)

Найду корень уравнения: sin(x)=3/5

Вы ввели

sin(x) = 3/5

$$\sin{\left(x \right)} = \frac{3}{5}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{3}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{5} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{3}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{3}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(3/5)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{3}{5} \right)}$$

x2 = asin(3/5)

$$x_{2} = \operatorname{asin}{\left(\frac{3}{5} \right)}$$

Сумма и произведение корней

сумма

pi - asin(3/5) + asin(3/5)

$$\operatorname{asin}{\left(\frac{3}{5} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{3}{5} \right)}\right)$$

=

pi

$$\pi$$

произведение

(pi - asin(3/5))*asin(3/5)

$$\left(\pi - \operatorname{asin}{\left(\frac{3}{5} \right)}\right) \operatorname{asin}{\left(\frac{3}{5} \right)}$$

=

(pi - asin(3/5))*asin(3/5)

$$\left(\pi - \operatorname{asin}{\left(\frac{3}{5} \right)}\right) \operatorname{asin}{\left(\frac{3}{5} \right)}$$

Численный ответ

x1 = 77.8963152309515

x2 = 44.6257982590504

x3 = 52.7635740022332

x4 = 76.0417247949483

x5 = -24.4892401199251

x6 = -37.0556107342842

x7 = -62.1883519630026

x8 = 84.1795005381311

x9 = 32.0594276446912

x10 = 8.7812768519761

x11 = -87.3210931917209

x12 = -72.9001321413585

x13 = 50.90898356623

x14 = -85.4665027557177

x15 = 6.92668641597287

x16 = -91.7496880628973

x17 = 21.3476474663353

x18 = -16.3514643767422

x19 = -49.6219813486434

x20 = -18.2060548127455

x21 = -93.6042784989005

x22 = -60.3337615269994

x23 = 46.4803886950536

x24 = -55.905166655823

x25 = -79.1833174485381

x26 = 94.8912807164871

x27 = -74.7547225773617

x28 = 90.4626858453107

x29 = 27.6308327735149

x30 = 101.174466023667

x31 = 69.7585394877687

x32 = -99.8874638060801

x33 = -116.882429291616

x34 = -68.4715372701822

x35 = 65.3299446165924

x36 = -47.7673909126402

x37 = 33.9140180806944

x38 = 13.2098717231525

x39 = 1177.45374398738

x40 = -30.7724254271046

x41 = 2.49809154479651

x42 = 0.643501108793284

x43 = -5358.91356591539

x44 = 96.7458711524903

x45 = -5.6396841983863

x46 = -98.0328733700769

x47 = 57.1921688734096

x48 = -142.015170520334

x49 = -22.6346496839218

x50 = -35.201020298281

x51 = 40.197203387874

x52 = 19.493057030332

x53 = 82.3249101021279

x54 = -54.0505762198198

x55 = 71.613129923772

x56 = 63.4753541805892

x57 = -28.9178349911014

x58 = 59.0467593094128

x59 = -449.891250572134

x60 = -41.4842056054606

x61 = 88.6080954093075

x62 = -3.78509376238308

x63 = 15.0644621591557

x64 = -81.0379078845413

x65 = -10.0682790695627

x66 = 25.7762423375116

x67 = 38.3426129518708

x68 = -11.9228695055659

x69 = -43.3387960414638

x70 = -66.6169468341789

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