sinx=-0.6 (уравнение)

Найду корень уравнения: sinx=-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 = 74.7547225773617

x2 = -25.7762423375116

x3 = 91.7496880628973

x4 = 30.7724254271046

x5 = 85.4665027557177

x6 = 43.3387960414638

x7 = 68.4715372701822

x8 = 79.1833174485381

x9 = 3.78509376238308

x10 = -8.7812768519761

x11 = 11.9228695055659

x12 = 72.9001321413585

x13 = -101.174466023667

x14 = 87.3210931917209

x15 = -52.7635740022332

x16 = 139936.605069959

x17 = -65.3299446165924

x18 = -27.6308327735149

x19 = -33.9140180806944

x20 = -59.0467593094128

x21 = -77.8963152309515

x22 = -38.3426129518708

x23 = -44.6257982590504

x24 = -107.457651330846

x25 = -76.0417247949483

x26 = 468.740806493672

x27 = 41.4842056054606

x28 = 16.3514643767422

x29 = 35.201020298281

x30 = -32.0594276446912

x31 = 22.6346496839218

x32 = 28.9178349911014

x33 = -46.4803886950536

x34 = -57.1921688734096

x35 = -40.197203387874

x36 = -94.8912807164871

x37 = -84.1795005381311

x38 = -63.4753541805892

x39 = 66.6169468341789

x40 = 3280205.36115037

x41 = 98.0328733700769

x42 = 93.6042784989005

x43 = -82.3249101021279

x44 = -21.3476474663353

x45 = 24.4892401199251

x46 = -2.49809154479651

x47 = -88.6080954093075

x48 = -50.90898356623

x49 = 47.7673909126402

x50 = -19.493057030332

x51 = -90.4626858453107

x52 = -69.7585394877687

x53 = -6.92668641597287

x54 = -15.0644621591557

x55 = 275.816652407109

x56 = 55.905166655823

x57 = 99.8874638060801

x58 = -13.2098717231525

x59 = 49.6219813486434

x60 = 60.3337615269994

x61 = 18.2060548127455

x62 = 81.0379078845413

x63 = 37.0556107342842

x64 = 54.0505762198198

x65 = -71.613129923772

x66 = -0.643501108793284

x67 = 5.6396841983863

x68 = 62.1883519630026

x69 = -96.7458711524903

x70 = 10.0682790695627

График