sin(x)=-0,6 (уравнение)

Найду корень уравнения: sin(x)=-0,6

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)

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

x2 = -asin(3/5)

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

Сумма и произведение корней

сумма

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

$$- \operatorname{asin}{\left(\frac{3}{5} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{3}{5} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -77.8963152309515

x2 = 72.9001321413585

x3 = 87.3210931917209

x4 = 81.0379078845413

x5 = 11.9228695055659

x6 = -19.493057030332

x7 = 54.0505762198198

x8 = 28.9178349911014

x9 = 35.201020298281

x10 = 74.7547225773617

x11 = 68.4715372701822

x12 = -94.8912807164871

x13 = -101.174466023667

x14 = -27.6308327735149

x15 = 55.905166655823

x16 = -88.6080954093075

x17 = -21.3476474663353

x18 = 10.0682790695627

x19 = 30.7724254271046

x20 = -52.7635740022332

x21 = -65.3299446165924

x22 = 49.6219813486434

x23 = 62.1883519630026

x24 = 85.4665027557177

x25 = 16.3514643767422

x26 = -0.643501108793284

x27 = -50.90898356623

x28 = 275.816652407109

x29 = 79.1833174485381

x30 = 18.2060548127455

x31 = 99.8874638060801

x32 = -76.0417247949483

x33 = 91.7496880628973

x34 = -84.1795005381311

x35 = -90.4626858453107

x36 = 3280205.36115037

x37 = -38.3426129518708

x38 = -13.2098717231525

x39 = -46.4803886950536

x40 = -8.7812768519761

x41 = 98.0328733700769

x42 = -96.7458711524903

x43 = 468.740806493672

x44 = -82.3249101021279

x45 = -2.49809154479651

x46 = 24.4892401199251

x47 = -59.0467593094128

x48 = -40.197203387874

x49 = -107.457651330846

x50 = 47.7673909126402

x51 = 139936.605069959

x52 = -25.7762423375116

x53 = -71.613129923772

x54 = -44.6257982590504

x55 = 60.3337615269994

x56 = 5.6396841983863

x57 = -63.4753541805892

x58 = -69.7585394877687

x59 = -15.0644621591557

x60 = -6.92668641597287

x61 = -33.9140180806944

x62 = -57.1921688734096

x63 = 22.6346496839218

x64 = 93.6042784989005

x65 = -32.0594276446912

x66 = 41.4842056054606

x67 = 66.6169468341789

x68 = 3.78509376238308

x69 = 43.3387960414638

x70 = 37.0556107342842

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