sin(7x)=-1 (уравнение)

Найду корень уравнения: sin(7x)=-1

Вы ввели

sin(7*x) = -1

$$\sin{\left(7 x \right)} = -1$$

Подробное решение

Дано уравнение
$$\sin{\left(7 x \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$7 x = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$7 x = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Или
$$7 x = 2 \pi n - \frac{\pi}{2}$$
$$7 x = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$7$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{7} - \frac{\pi}{14}$$
$$x_{2} = \frac{2 \pi n}{7} + \frac{3 \pi}{14}$$

Быстрый ответ

     -pi 
x1 = ----
      14 

$$x_{1} = - \frac{\pi}{14}$$

     3*pi
x2 = ----
      14 

$$x_{2} = \frac{3 \pi}{14}$$

Сумма и произведение корней

сумма

    pi   3*pi
0 - -- + ----
    14    14 

$$\left(- \frac{\pi}{14} + 0\right) + \frac{3 \pi}{14}$$

=

pi
--
7 

$$\frac{\pi}{7}$$

произведение

  -pi  3*pi
1*----*----
   14   14 

$$\frac{3 \pi}{14} \cdot 1 \left(- \frac{\pi}{14}\right)$$

=

     2
-3*pi 
------
 196  

$$- \frac{3 \pi^{2}}{196}$$

Численный ответ

x1 = -21.7667490867332

x2 = 66.1978452470166

x3 = 7.85398169495316

x4 = 69.7882368066005

x5 = 67.9930410105944

x6 = -13.6883680280288

x7 = -3.81479101884417

x8 = -62.1586545882655

x9 = -5.60998693951112

x10 = 15.9323627936885

x11 = 76.0714219867554

x12 = 100.306565404686

x13 = -72.0322315269287

x14 = -85.4962001961162

x15 = 30.293929131297

x16 = 12.3419710894768

x17 = 95.8185759802228

x18 = 28.4987335331749

x19 = 61.709855798655

x20 = -89.9841895997492

x21 = 72.4810305791346

x22 = 59.9146599502416

x23 = -99.8577664110223

x24 = 2.46839424485093

x25 = 48.2458871832247

x26 = -54.0802734815868

x27 = 94.023380097403

x28 = 92.2281843477919

x29 = 46.4506913541324

x30 = 43.7578975329286

x31 = -29.8451301122563

x32 = -26.254738653815

x33 = -46.001892425326

x34 = 13.2395690634871

x35 = 4.26359002020643

x36 = -31.6403260657234

x37 = -39.7187071414127

x38 = 24.0107438382386

x39 = -19.9715533428935

x40 = -88.1889937368012

x41 = -34.33311961254

x42 = 50.0410829061044

x43 = -63.0562527372411

x44 = -49.5922838608809

x45 = 56.3242682463445

x46 = -29.8451300798499

x47 = 52.7338764603268

x48 = -91.7793853558147

x49 = 20.4203521965023

x50 = -36.1283154535468

x51 = -0.224399514512687

x52 = 40.1675061533025

x53 = 33.8843208261029

x54 = 41.9627019069089

x55 = -47.7970881885378

x56 = -38.8211093539582

x57 = -83.7010043016944

x58 = 38.3723102119433

x59 = 90.4329884842009

x60 = 86.8425968691975

x61 = 25.8059396877581

x62 = -70.2370358625256

x63 = -75.6226232189275

x64 = -2.01959525710412

x65 = -81.0082105020289

x66 = -98.0625706387998

x67 = 77.8666179764942

x68 = -28.0499343652511

x69 = 22.215548079095

x70 = -18.1763574464374

x71 = 85.9449990677518

x72 = -63.9538505397178

x73 = 51.8362788401232

x74 = 6.05878569168424

x75 = -80.1106126046346

x76 = -93.574581231161

x77 = 31.1915270258916

x78 = 82.3546073657633

x79 = -57.6706651859628

x80 = 11.4443733932631

x81 = 84.1498033202441

x82 = 74.2762262919595

x83 = -23.5619449416433

x84 = 64.4026493415306

x85 = -65.7490462508355

x86 = -67.5442420672257

x87 = -73.8274272833876

x88 = -41.5139028204363

x89 = -10.0979763266333

x90 = -44.2066966123235

x91 = -49.592284087747

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