sin(2x) = 0.7 (уравнение)

Найду корень уравнения: sin(2x) = 0.7

Вы ввели

sin(2*x) = 7/10

$$\sin{\left(2 x \right)} = \frac{7}{10}$$

Подробное решение

Дано уравнение
$$\sin{\left(2 x \right)} = \frac{7}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
Или
$$2 x = 2 \pi n + \operatorname{asin}{\left(\frac{7}{10} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(\frac{7}{10} \right)} + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n + \frac{\operatorname{asin}{\left(\frac{7}{10} \right)}}{2}$$
$$x_{2} = \pi n - \frac{\operatorname{asin}{\left(\frac{7}{10} \right)}}{2} + \frac{\pi}{2}$$

Быстрый ответ

     pi   asin(7/10)
x1 = -- - ----------
     2        2     

$$x_{1} = - \frac{\operatorname{asin}{\left(\frac{7}{10} \right)}}{2} + \frac{\pi}{2}$$

     asin(7/10)
x2 = ----------
         2     

$$x_{2} = \frac{\operatorname{asin}{\left(\frac{7}{10} \right)}}{2}$$

Численный ответ

x1 = -762.22391724383

x2 = 29.4574314607977

x3 = 13.7494681928487

x4 = -27.8866351340028

x5 = 20.0326535000283

x6 = 79.7229139182344

x7 = 31.8036252842033

x8 = -58.5071628397165

x9 = 66.361144473691

x10 = 100.918663663179

x11 = -21.6034498268232

x12 = 60.0779591665114

x13 = -83.6399040684349

x14 = 9.81247670907476

x15 = -17.6664583430492

x16 = 6.67088405548496

x17 = 34.9452179377931

x18 = -45.9407922253574

x19 = 75.7859224344604

x20 = 28.6620326306135

x21 = -14.5248656894594

x22 = -39.6576069181778

x23 = -100.143266166568

x24 = 42.0238020751568

x25 = -52.223977532537

x26 = 35.7406167679772

x27 = 88.3522930488196

x28 = 89.1476918790037

x29 = -42.7991995717676

x30 = -96.2062746827941

x31 = 44.3699958985625

x32 = 12.9540693626645

x33 = -34.1698204411824

x34 = 92.2892845325935

x35 = -8.24168038227986

x36 = -89.9230893756145

x37 = 38.0868105913829

x38 = -1.95849507510027

x39 = -23.9496436502288

x40 = -67.9319408004859

x41 = 53.7947738593319

x42 = -97.0016735129782

x43 = -78.1521175914394

x44 = 292.555815532156

x45 = -59.3025616699007

x46 = 22.3788473234339

x47 = -31.0282277875926

x48 = 50.6531812057421

x49 = 64.0149506502854

x50 = 95.4308771861833

x51 = -5.89548655887421

x52 = 86.0060992254139

x53 = -9.037079212464

x54 = -75.0105249378497

x55 = 51.4485800359262

x56 = -33.3744216109982

x57 = -74.2151261076655

x58 = -43.5945984019517

x59 = 16.0956620162543

x60 = 72.6443297808706

x61 = -93.8600808593884

x62 = 48.3069873823364

x63 = -37.3114130947721

x64 = -15.3202645196436

x65 = -81.2937102450292

x66 = -49.8777837091313

x67 = -65.5857469770803

x68 = -71.8689322842599

x69 = -36.516014264588

x70 = 70.298135957465

x71 = -12.1786718660538

x72 = -30.2328289574084

x73 = 56.9363665129217

x74 = 4.32469023207931

x75 = 7.46628288566911

x76 = 78.9275150880502

x77 = -53.0193763627211

x78 = 97.777071009589

x79 = 82.06910774164

x80 = 26.3158388072079

x81 = 73.4397286110548

x82 = -61.6487554933063

x83 = -56.1609690163109

x84 = -80.4983114148451

x85 = 57.7317653431058

x86 = 0.387698748305377

x87 = 94.6354783559992

x88 = -87.5768955522088

x89 = 2645.60871307091

График