sin(10*x)=1 (уравнение)

Найду корень уравнения: sin(10*x)=1

Вы ввели

sin(10*x) = 1

$$\sin{\left(10 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(10 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$10 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$10 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$10 x = 2 \pi n + \frac{\pi}{2}$$
$$10 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$10$$
получим ответ:
$$x_{1} = \frac{\pi n}{5} + \frac{\pi}{20}$$
$$x_{2} = \frac{\pi n}{5} + \frac{\pi}{20}$$

Быстрый ответ

     pi
x1 = --
     20

$$x_{1} = \frac{\pi}{20}$$

Сумма и произведение корней

сумма

    pi
0 + --
    20

$$0 + \frac{\pi}{20}$$

=

pi
--
20

$$\frac{\pi}{20}$$

произведение

  pi
1*--
  20

$$1 \frac{\pi}{20}$$

=

pi
--
20

$$\frac{\pi}{20}$$

Численный ответ

x1 = 68.0154809279967

x2 = 79.953533066717

x3 = 54.1924733263404

x4 = -19.9491134606349

x5 = 62.3606141648078

x6 = 76.1836219103648

x7 = 8.32522049939218

x8 = -43.8252174485564

x9 = -30.0022098391916

x10 = 2.04203514142486

x11 = -89.6924702518419

x12 = -41.9402620479968

x13 = -13.6659280746332

x14 = 25.9181394256657

x15 = -8.01106125490105

x16 = -76.497781212056

x17 = -1.72787597427359

x18 = 91.8915851497169

x19 = 52.3075176519326

x20 = 44.7676953057635

x21 = -94.0906999450817

x22 = -97.232292636607

x23 = 12.7234502260327

x24 = -40.0553062983706

x25 = -67.7013217124545

x26 = -51.9933584255165

x27 = 69.9004365659765

x28 = -57.6482252146897

x29 = -35.657076646377

x30 = -11.780972425067

x31 = 74.2986662298085

x32 = 96.2898148085112

x33 = -50.1084028120048

x34 = 91.8915851302345

x35 = 30.316369075045

x36 = 42.2544211875615

x37 = -72.099551376271

x38 = -89.6924702903292

x39 = 30.316369197705

x40 = -62.0464548755453

x41 = 47.9092879971704

x42 = -28.1172542560358

x43 = 13.9800873276515

x44 = -21.8340688676231

x45 = -95.9756556060289

x46 = -72.0995514491497

x47 = 35.9712359086794

x48 = -79.6393737774286

x49 = 64.245569769264

x50 = 10.2101761584315

x51 = -38.7986692706729

x52 = 86.236718351454

x53 = 24.0331837408851

x54 = 3.92699085234414

x55 = 84.3517627275565

x56 = 98.1747704937124

x57 = 22.1482282201248

x58 = 15.865042802169

x59 = -84.0376034539302

x60 = -73.9845070142824

x61 = 20.2632726063718

x62 = -55.7632695908146

x63 = 57.9623844883337

x64 = -18.0641577223908

x65 = -23.7190245543336

x66 = 0.157079704797132

x67 = -77.7544181730039

x68 = -3.61283143575334

x69 = 32.2013247422744

x70 = 65.5022066835525

x71 = 100.059725894233

x72 = -87.8075146159305

x73 = 90.0066295167589

x74 = -99.7455667547058

x75 = -6.12610571544417

x76 = 18.3783170771162

x77 = -33.7721210081607

x78 = 3.92699091808855

x79 = 40.3694656118613

x80 = -45.7101731337528

x81 = 46.0243323362547

x82 = -65.8163660319057

График