sin9x=-1/2 (уравнение)

Найду корень уравнения: sin9x=-1/2

Вы ввели

sin(9*x) = -1/2

$$\sin{\left(9 x \right)} = - \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(9 x \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$9 x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$9 x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Или
$$9 x = 2 \pi n - \frac{\pi}{6}$$
$$9 x = 2 \pi n + \frac{7 \pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$9$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{9} - \frac{\pi}{54}$$
$$x_{2} = \frac{2 \pi n}{9} + \frac{7 \pi}{54}$$

Быстрый ответ

     -pi 
x1 = ----
      54 

$$x_{1} = - \frac{\pi}{54}$$

     7*pi
x2 = ----
      54 

$$x_{2} = \frac{7 \pi}{54}$$

Сумма и произведение корней

сумма

    pi   7*pi
0 - -- + ----
    54    54 

$$\left(- \frac{\pi}{54} + 0\right) + \frac{7 \pi}{54}$$

=

pi
--
9 

$$\frac{\pi}{9}$$

произведение

  -pi  7*pi
1*----*----
   54   54 

$$\frac{7 \pi}{54} \cdot 1 \left(- \frac{\pi}{54}\right)$$

=

     2
-7*pi 
------
 2916 

$$- \frac{7 \pi^{2}}{2916}$$

Численный ответ

x1 = 43.6914089415914

x2 = -53.8143186031585

x3 = -23.794655468856

x4 = -67.7769526191131

x5 = -44.0404747919902

x6 = 4.13061256305325

x7 = 38.1063553352095

x8 = 46.0185146109172

x9 = 29.9614854925693

x10 = -88.0227719422474

x11 = 40.2007504376027

x12 = 64.1699388316582

x13 = -35.89560494935

x14 = -58.0031088079449

x15 = -21.7002603664628

x16 = -91.7461410131686

x17 = 100.240076706208

x18 = -69.8713477215063

x19 = -31.7068147445637

x20 = -79.8779020996072

x21 = 6.22500766544644

x22 = 54.1633844535574

x23 = -25.8890505712492

x24 = 92.0952068635675

x25 = 22.2820367837943

x26 = -0.0581776417331443

x27 = 98.1456816038145

x28 = -47.7638438629115

x29 = -75.6891118948208

x30 = 20.1876416814011

x31 = 48.1129097133104

x32 = -39.8516845872039

x33 = 52.3016999180967

x34 = 26.2381164216481

x35 = 68.126018469512

x36 = -15.6497856262158

x37 = 42.2951455399959

x38 = 32.0558805949625

x39 = -85.9283768398542

x40 = 73.9437826428264

x41 = -30.3105513429682

x42 = -93.8405361155618

x43 = -5.87594181504758

x44 = 70.2204135719052

x45 = 84.1830475878598

x46 = 50.2073048157035

x47 = 15.9988514766147

x48 = -49.8582389653047

x49 = 78.1325728476128

x50 = 64.6353599655233

x51 = -51.7199235007653

x52 = -41.9460796895971

x53 = 90.0008117611743

x54 = 10.1810873033003

x55 = -77.7835069972139

x56 = -3.78154671265438

x57 = 96.2839970683539

x58 = 12.9736141064912

x59 = -118.275145643482

x60 = -9.83202145290139

x61 = 87.2082849579833

x62 = -55.9087137055517

x63 = 82.0886524854666

x64 = 18.0932465790079

x65 = -99.8910108558088

x66 = 76.0381777452196

x67 = -71.9657428238995

x68 = -11.9264165552946

x69 = -81.7395866350678

x70 = -33.8012098469569

x71 = 2.03621746066005

x72 = -14.0208116576878

x73 = 36.2446707997489

x74 = -97.7966157534156

x75 = -74.0601379262927

x76 = 94.1896019659606

x77 = -27.9834456736424

x78 = -17.744180728609

x79 = 86.277442690253

x80 = 34.1502756973557

x81 = -1.68715161026119

x82 = 59.9811486268718

x83 = 24.1437213192549

x84 = -61.7264778788661

x85 = 62.075543729265

x86 = -19.8385758310022

x87 = -7.73762635050819

x88 = -83.833981737461

x89 = 66.2643339340514

x90 = 72.3148086742984

x91 = 12.2754824056935

x92 = -95.7022206510224

x93 = -63.8208729812593

x94 = -37.2918683509455

x95 = 56.2577795559506

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