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

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

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

=

pi

$$\pi$$

произведение

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

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

=

-(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 = 79.1833174485381

x2 = -88.6080954093075

x3 = -46.4803886950536

x4 = -8.7812768519761

x5 = 93.6042784989005

x6 = -96.7458711524903

x7 = 16.3514643767422

x8 = 55.905166655823

x9 = -94.8912807164871

x10 = -21.3476474663353

x11 = -107.457651330846

x12 = -63.4753541805892

x13 = -57.1921688734096

x14 = 49.6219813486434

x15 = -101.174466023667

x16 = 43.3387960414638

x17 = 87.3210931917209

x18 = 62.1883519630026

x19 = -59.0467593094128

x20 = 68.4715372701822

x21 = -84.1795005381311

x22 = -13.2098717231525

x23 = -90.4626858453107

x24 = -25.7762423375116

x25 = 74.7547225773617

x26 = 91.7496880628973

x27 = 85.4665027557177

x28 = -52.7635740022332

x29 = 81.0379078845413

x30 = 41.4842056054606

x31 = -69.7585394877687

x32 = -27.6308327735149

x33 = 18.2060548127455

x34 = 22.6346496839218

x35 = 60.3337615269994

x36 = 66.6169468341789

x37 = 35.201020298281

x38 = 54.0505762198198

x39 = 47.7673909126402

x40 = 468.740806493672

x41 = 30.7724254271046

x42 = -44.6257982590504

x43 = -32.0594276446912

x44 = -71.613129923772

x45 = 37.0556107342842

x46 = -6.92668641597287

x47 = 11.9228695055659

x48 = -50.90898356623

x49 = -2.49809154479651

x50 = 98.0328733700769

x51 = 24.4892401199251

x52 = -77.8963152309515

x53 = -38.3426129518708

x54 = 3.78509376238308

x55 = 10.0682790695627

x56 = -33.9140180806944

x57 = 275.816652407109

x58 = -82.3249101021279

x59 = 99.8874638060801

x60 = -15.0644621591557

x61 = 139936.605069959

x62 = 28.9178349911014

x63 = 5.6396841983863

x64 = -19.493057030332

x65 = -65.3299446165924

x66 = 72.9001321413585

x67 = -0.643501108793284

x68 = -40.197203387874

x69 = 3280205.36115037

x70 = -76.0417247949483

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