sin(9*x)=1 (уравнение)

Найду корень уравнения: sin(9*x)=1

Вы ввели

sin(9*x) = 1

$$\sin{\left(9 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(9 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$9 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$9 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$9 x = 2 \pi n + \frac{\pi}{2}$$
$$9 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$9$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{9} + \frac{\pi}{18}$$
$$x_{2} = \frac{2 \pi n}{9} + \frac{\pi}{18}$$

Быстрый ответ

     pi
x1 = --
     18

$$x_{1} = \frac{\pi}{18}$$

Сумма и произведение корней

сумма

    pi
0 + --
    18

$$0 + \frac{\pi}{18}$$

=

pi
--
18

$$\frac{\pi}{18}$$

произведение

  pi
1*--
  18

$$1 \frac{\pi}{18}$$

=

pi
--
18

$$\frac{\pi}{18}$$

Численный ответ

x1 = -29.8451301283469

x2 = 12.042771754898

x3 = 29.4960643236131

x4 = -94.0732466398687

x5 = 78.3652833815258

x6 = 97.9129710796459

x7 = 34.3829862500245

x8 = -64.0535835097806

x9 = -13.7881010583263

x10 = 86.0447320334194

x11 = -43.8077641727596

x12 = 14.8352986647884

x13 = 7.85398161599041

x14 = -57.7703982246775

x15 = 83.9503370579401

x16 = -91.9788516119509

x17 = -20.0712863555213

x18 = -66.1479786758594

x19 = 32.2885911376289

x20 = -50.0909494898951

x21 = 37.873644791895

x22 = 76.2708882978988

x23 = 48.3456202410697

x24 = 23.9110107949028

x25 = -9.59931084907568

x26 = -61.9591885238521

x27 = -4.01425726468606

x28 = 51.8362786663579

x29 = 81.8559419070607

x30 = -47.9965544341325

x31 = -41.7133691459212

x32 = 16.2315620582096

x33 = 56.0250689495141

x34 = 20.4203522229268

x35 = -69.6386371896856

x36 = 39.9680398989072

x37 = 2.26892801456772

x38 = 100.007366129728

x39 = 64.402649445087

x40 = 90.2335223411186

x41 = 67.893307940698

x42 = -17.9768913311353

x43 = -8.90117922107669

x44 = -53.5816079130873

x45 = 46.251225176944

x46 = -85.6956663043161

x47 = -71.7330322687403

x48 = 92.3279173922657

x49 = 44.1568301574075

x50 = -31.9395254476516

x51 = -39.6189740376435

x52 = -36.1283154950913

x53 = -80.1106126302666

x54 = -11.6937060205141

x55 = 53.9306739287799

x56 = -96.1676419219425

x57 = 42.0624348377035

x58 = 100.705497840381

x59 = 69.9877030180693

x60 = 74.1764932787559

x61 = -6.10865234473588

x62 = 60.2138592243636

x63 = -73.827427286404

x64 = 4.36332309585286

x65 = -99.6583003282472

x66 = 62.308254263319

x67 = 9.94837677410343

x68 = -78.016217547512

x69 = -22.1656816304647

x70 = -27.7507351061623

x71 = 30.1941961097389

x72 = -34.0339203844719

x73 = 18.3259571080643

x74 = -87.7900613409949

x75 = -83.6012711422021

x76 = 0.174532996202717

x77 = 26.0054058478504

x78 = -25.6563400436219

x79 = -55.6760031760944

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