sin(18x)=1/2 (уравнение)

Найду корень уравнения: sin(18x)=1/2

Вы ввели

sin(18*x) = 1/2

$$\sin{\left(18 x \right)} = \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(18 x \right)} = \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$18 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$18 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Или
$$18 x = 2 \pi n + \frac{\pi}{6}$$
$$18 x = 2 \pi n + \frac{5 \pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$18$$
получим ответ:
$$x_{1} = \frac{\pi n}{9} + \frac{\pi}{108}$$
$$x_{2} = \frac{\pi n}{9} + \frac{5 \pi}{108}$$

Быстрый ответ

      pi
x1 = ---
     108

$$x_{1} = \frac{\pi}{108}$$

     5*pi
x2 = ----
     108 

$$x_{2} = \frac{5 \pi}{108}$$

Сумма и произведение корней

сумма

 pi   5*pi
--- + ----
108   108 

$$\frac{\pi}{108} + \frac{5 \pi}{108}$$

=

pi
--
18

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

произведение

 pi 5*pi
---*----
108 108 

$$\frac{\pi}{108} \frac{5 \pi}{108}$$

=

    2
5*pi 
-----
11664

$$\frac{5 \pi^{2}}{11664}$$

Численный ответ

x1 = 32.2595023410285

x2 = -77.8125958180805

x3 = 51.807189963365

x4 = -82.0013860228669

x5 = -31.7359035654302

x6 = 2.23983920672606

x7 = -61.7555666997327

x8 = -63.7336065186596

x9 = -81.3032543220692

x10 = 8.17395866350678

x11 = 16.0861179392144

x12 = -53.9597627074914

x13 = -3.81063553352095

x14 = 4.21787902565296

x15 = 24.2309877818546

x16 = -55.821447242952

x17 = -93.7532696529621

x18 = 81.0123661134035

x19 = 54.9487826169548

x20 = -9.74475499030167

x21 = 12.2463935848269

x22 = -33.8302986678234

x23 = -22.1947703211946

x24 = 84.2703140504595

x25 = 40.1716616167362

x26 = -45.9312481483174

x27 = -8.69755743910508

x28 = -79.5579250700749

x29 = 66.0025345462522

x30 = -71.7621210778335

x31 = -7.99942573830734

x32 = -19.7513093684025

x33 = 98.2329480664142

x34 = 839.648814313605

x35 = 100.210987885341

x36 = -99.8037443932091

x37 = -25.8017841086495

x38 = -91.7752298340352

x39 = 94.2768684285604

x40 = -83.7467152748612

x41 = 78.2198393102125

x42 = 58.0903752705446

x43 = 36.099226695416

x44 = -5.55596478551528

x45 = 48.2001761759101

x46 = 42.9641884199271

x47 = 46.2221363569832

x48 = 70.1913247510386

x49 = 76.2417994912856

x50 = 54.2506509161571

x51 = -96.1967306057541

x52 = 18.1805130416076

x53 = 73.1002068376958

x54 = -15.911585014015

x55 = -89.9135452985745

x56 = 20.2749081440008

x57 = -85.7247550937882

x58 = -41.7424579435311

x59 = 6.07956356111358

x60 = 86.2483538693864

x61 = -47.7929326837781

x62 = 13.9917228368212

x63 = 42.2660567191293

x64 = -30.2232848803685

x65 = 64.0244947273253

x66 = -17.7732695494756

x67 = 87.9936831213808

x68 = 80.0815238456732

x69 = -29.5251531795707

x70 = -49.770972502705

x71 = 10.2683537659

x72 = -67.922396723446

x73 = 26.2090276007815

x74 = -27.7798239275764

x75 = -37.9027335891435

x76 = -69.7840812589066

x77 = 7.12676111231018

x78 = -1.59988514766147

x79 = 68.4459954990443

x80 = 92.1824733261672

x81 = 28.0707121362421

x82 = 64.2572052942579

x83 = -53.7270521405588

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