sin(6x)=-1/2 (уравнение)

Найду корень уравнения: sin(6x)=-1/2

Вы ввели

sin(6*x) = -1/2

$$\sin{\left(6 x \right)} = - \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(6 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$6 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Или
$$6 x = 2 \pi n - \frac{\pi}{6}$$
$$6 x = 2 \pi n + \frac{7 \pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{36}$$
$$x_{2} = \frac{\pi n}{3} + \frac{7 \pi}{36}$$

Быстрый ответ

     -pi 
x1 = ----
      36 

$$x_{1} = - \frac{\pi}{36}$$

     7*pi
x2 = ----
      36 

$$x_{2} = \frac{7 \pi}{36}$$

Сумма и произведение корней

сумма

    pi   7*pi
0 - -- + ----
    36    36 

$$\left(- \frac{\pi}{36} + 0\right) + \frac{7 \pi}{36}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

произведение

  -pi  7*pi
1*----*----
   36   36 

$$\frac{7 \pi}{36} \cdot 1 \left(- \frac{\pi}{36}\right)$$

=

     2
-7*pi 
------
 1296 

$$- \frac{7 \pi^{2}}{1296}$$

Численный ответ

x1 = -66.0607121879854

x2 = 30.2814625221016

x3 = 34.1211868764891

x4 = 94.1605131450941

x5 = 12.1300383013606

x6 = 28.1870674197084

x7 = -15.7952297305487

x8 = 1816.4514190131

x9 = -31.8522588488965

x10 = 40.7534380340676

x11 = -55.9378025264183

x12 = 36.2155819788823

x13 = -97.8257045742822

x14 = -58.0321976288115

x15 = -99.9200996766754

x16 = 10.0356431989674

x17 = -80.02334620394

x18 = 82.2922742315326

x19 = 89.9717229403077

x20 = -53.8434074240251

x21 = 26.0926723173152

x22 = -41.9751685104636

x23 = -5.67232006898157

x24 = -68.5041731407774

x25 = -63.9663170855922

x26 = -39.8807734080704

x27 = -77.9289511015468

x28 = 76.0090889243531

x29 = 67.9805743651791

x30 = 65.8861792627859

x31 = 43.8950306876574

x32 = -0.0872664625997165

x33 = -88.0518607631139

x34 = -44.0695636128568

x35 = -17.8896248329419

x36 = 499.076899607779

x37 = -51.7490123216319

x38 = -7.76671517137477

x39 = -61.871921983199

x40 = 96.2549082474873

x41 = -83.8630705583275

x42 = -49.6546172192387

x43 = 21.9038821125288

x44 = 58.2067305540109

x45 = -90.1462558655071

x46 = 48.0838208924438

x47 = -81.7686754559343

x48 = 70.0749694675723

x49 = 72.1693645699655

x50 = 32.0267917740959

x51 = -22.0784150377283

x52 = -36.7391807544806

x53 = 4.10152374218667

x54 = -33.9466539512897

x55 = -93.6369143694958

x56 = -71.6457657943672

x57 = 62.3955207587973

x58 = 100.094632601875

x59 = 2.00712863979348

x60 = 50.178215994837

x61 = -75.8345559991536

x62 = 56.1123354516177

x63 = 45.9894257900506

x64 = -46.5130245656489

x65 = 80.1978791291394

x66 = -37.7863783056772

x67 = 87.8773278379145

x68 = -29.7578637465033

x69 = 74.2637596723587

x70 = 14.2244334037538

x71 = -59.7775268808058

x72 = -11.9555053761612

x73 = -85.9574656607207

x74 = 52.2726110972302

x75 = -73.7401608967604

x76 = 98.0002374994816

x77 = -71.2966999439684

x78 = -27.6634686441101

x79 = -4.27605666738611

x80 = 92.0661180427009

x81 = -9.86111027376796

x82 = -19.9840199353351

x83 = -95.731309471889

x84 = -24.5218759905203

x85 = 60.3011256564041

x86 = 54.0179403492245

x87 = 84.3866693339258

x88 = 18.762289458939

x89 = 16.318828506147

x90 = -3.22885911618951

x91 = 38.3099770812755

x92 = 78.1034840267462

x93 = 6.19591884457987

x94 = 23.998277214922

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