sin(5x)=1 (уравнение)

Найду корень уравнения: sin(5x)=1

Вы ввели

sin(5*x) = 1

$$\sin{\left(5 x \right)} = 1$$

Подробное решение

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

Быстрый ответ

     pi
x1 = --
     10

$$x_{1} = \frac{\pi}{10}$$

Сумма и произведение корней

сумма

    pi
0 + --
    10

$$0 + \frac{\pi}{10}$$

=

pi
--
10

$$\frac{\pi}{10}$$

произведение

  pi
1*--
  10

$$1 \frac{\pi}{10}$$

=

pi
--
10

$$\frac{\pi}{10}$$

Численный ответ

x1 = -23.5619449885447

x2 = -33.6150414656421

x3 = 17.9070781942786

x4 = 88.2787535460736

x5 = 24.1902634875252

x6 = -53.7212346026701

x7 = 85.7654795375399

x8 = 21.67698935198

x9 = 36.7566342760199

x10 = 64.4026493205741

x11 = 78.2256570938614

x12 = 30.4734486494869

x13 = -63.7743308484076

x14 = -80.1106125902406

x15 = -100.216805553554

x16 = 95.8185760288222

x17 = 68.1725606607797

x18 = 81.9955682638526

x19 = 88.2787533397037

x20 = 10.3672556912883

x21 = 29.21681174899

x22 = 51.8362788758192

x23 = -77.5973386216882

x24 = -60.0044196784197

x25 = -70.0575161253882

x26 = 98.3318500076337

x27 = -56.2345084047172

x28 = 84.5088422945471

x29 = -46.1814119134379

x30 = 61.8893753520228

x31 = 54.3495528490555

x32 = -49.9513232902855

x33 = 31.7300858868767

x34 = 16.6504412743164

x35 = -19.7920336817869

x36 = -32.3584043768638

x37 = 94.5619388168119

x38 = 65.6592864690668

x39 = -12.2522112577381

x40 = 17.9070782948399

x41 = -36.1283154337195

x42 = -3.45575199070453

x43 = 48.0663674154127

x44 = -37.3849525044987

x45 = 7.85398172163012

x46 = -9.73893723410038

x47 = 50.579641691231

x48 = -87.6504350932086

x49 = 55.6061897240307

x50 = -29.8451301030746

x51 = -26.0752189647962

x52 = 6.59734458065606

x53 = -97.7035315572951

x54 = -73.8274272814964

x55 = 74.4557458008934

x56 = 20.4203521654844

x57 = -34.8716784592049

x58 = -76.3407014731634

x59 = 0.31415922475457

x60 = -16.0221225103299

x61 = 11.623892685602

x62 = 34.243359929156

x63 = 71.9424718168781

x64 = -22.3053077773099

x65 = -86.3937982181784

x66 = 92.048664652016

x67 = 40.5265451499163

x68 = 14.1371670477357

x69 = 75.7123830282674

x70 = 38.0132710906981

x71 = -13.5088485001991

x72 = 44.2964563849706

x73 = -43.6681379346309

x74 = -91.4203462510066

x75 = 71.9424718164574

x76 = -57.4911456477088

x77 = 41.7831823887039

x78 = -2.19911476168457

x79 = 27.9601746544561

x80 = -67.5442421413666

x81 = -47.4380491254335

x82 = -66.2876049139838

x83 = -81.3672495508249

x84 = 60.6327383913504

x85 = -53.7212343961928

x86 = -93.9336205269205

x87 = -90.1637090664418

x88 = -5.96902609116739

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