sin(x)=5/6 (уравнение)

Найду корень уравнения: sin(x)=5/6

Вы ввели

sin(x) = 5/6

$$\sin{\left(x \right)} = \frac{5}{6}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{5}{6}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{5}{6} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{5}{6} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{5}{6} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{5}{6} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(5/6)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{5}{6} \right)}$$

x2 = asin(5/6)

$$x_{2} = \operatorname{asin}{\left(\frac{5}{6} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(5/6) + asin(5/6)

$$\operatorname{asin}{\left(\frac{5}{6} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{5}{6} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(5/6))*asin(5/6)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{5}{6} \right)}\right) \operatorname{asin}{\left(\frac{5}{6} \right)}$$

=

(pi - asin(5/6))*asin(5/6)

$$\left(\pi - \operatorname{asin}{\left(\frac{5}{6} \right)}\right) \operatorname{asin}{\left(\frac{5}{6} \right)}$$

Численный ответ

x1 = -99.5458541315356

x2 = 63.8169638551336

x3 = -48.1090005871846

x4 = -55.5635569812785

x5 = 13893.1078249574

x6 = -16.6930740512867

x7 = -54.3921858943642

x8 = 57.533778547954

x9 = -30.4308157525602

x10 = -29.2594446656459

x11 = 26.1178520120561

x12 = -990.586796664123

x13 = -11.5812598310214

x14 = 7.26829609051733

x15 = 52.4219643276887

x16 = -92.0912977374417

x17 = -5.29807452384184

x18 = 32.4010373192357

x19 = -4.12670343692754

x20 = -85.8081124302622

x21 = -49.2803716740989

x22 = -73.241741815903

x23 = -68.1299275956377

x24 = -98.3744830446213

x25 = -41.8258152800051

x26 = 126.648816926929

x27 = -17.864445138201

x28 = 95.2328903910315

x29 = -24.1476304453806

x30 = 685.852309265913

x31 = -10.4098887441071

x32 = 70.1001491623132

x33 = -93.2626688243561

x34 = 19.8346667048765

x35 = -211.471818573854

x36 = -42.9971863669194

x37 = 76.3833344694928

x38 = 38.6842226264153

x39 = 14.7228524846112

x40 = 88.949705083852

x41 = 77.5547055564071

x42 = 51.2505932407744

x43 = -36.7140010597398

x44 = 58.7051496348683

x45 = 2.15648187025205

x46 = -35.5426299728255

x47 = -60.6753712015438

x48 = 38304.454114437

x49 = -80.6962982099969

x50 = 0.985110783337746

x51 = 44.9674079335948

x52 = 27.2892230989704

x53 = 82.6665197766724

x54 = 96.4042614779459

x55 = 46.1387790205092

x56 = 13.5514813976969

x57 = -66.9585565087234

x58 = 39.8555937133296

x59 = 1623.21829112259

x60 = -2617.93179122364

x61 = 71.2715202492275

x62 = 101.516075698211

x63 = -22.9762593584663

x64 = 2564.52471611261

x65 = 64.9883349420479

x66 = 33.57240840615

x67 = -61.8467422884581

x68 = -86.9794835171765

x69 = -79.5249271230826

x70 = 83.8378908635867

x71 = 21.0060377917908

x72 = -74.4131129028173

x73 = 8.43966717743163

x74 = 90.1210761707663

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