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
- -- + ----
  54    54 

$$- \frac{\pi}{54} + \frac{7 \pi}{54}$$

=

pi
--
9 

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

произведение

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

$$- \frac{\pi}{54} \frac{7 \pi}{54}$$

=

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

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

Численный ответ

x1 = -83.833981737461

x2 = 20.1876416814011

x3 = 18.0932465790079

x4 = -1.68715161026119

x5 = -30.3105513429682

x6 = -15.6497856262158

x7 = -44.0404747919902

x8 = -25.8890505712492

x9 = -5.87594181504758

x10 = 72.3148086742984

x11 = 94.1896019659606

x12 = -67.7769526191131

x13 = 73.9437826428264

x14 = 64.1699388316582

x15 = -7.73762635050819

x16 = -21.7002603664628

x17 = 43.6914089415914

x18 = -9.83202145290139

x19 = -14.0208116576878

x20 = -33.8012098469569

x21 = -118.275145643482

x22 = -35.89560494935

x23 = 46.0185146109172

x24 = -31.7068147445637

x25 = -91.7461410131686

x26 = 36.2446707997489

x27 = 84.1830475878598

x28 = 92.0952068635675

x29 = 90.0008117611743

x30 = -23.794655468856

x31 = 52.3016999180967

x32 = 87.2082849579833

x33 = 64.6353599655233

x34 = 68.126018469512

x35 = 4.13061256305325

x36 = 50.2073048157035

x37 = -88.0227719422474

x38 = 38.1063553352095

x39 = -69.8713477215063

x40 = -39.8516845872039

x41 = -58.0031088079449

x42 = 6.22500766544644

x43 = -17.744180728609

x44 = -97.7966157534156

x45 = -53.8143186031585

x46 = -27.9834456736424

x47 = 29.9614854925693

x48 = 42.2951455399959

x49 = 70.2204135719052

x50 = 54.1633844535574

x51 = 32.0558805949625

x52 = -51.7199235007653

x53 = -0.0581776417331443

x54 = 2.03621746066005

x55 = 98.1456816038145

x56 = -71.9657428238995

x57 = 56.2577795559506

x58 = 76.0381777452196

x59 = 26.2381164216481

x60 = 96.2839970683539

x61 = -77.7835069972139

x62 = -41.9460796895971

x63 = -63.8208729812593

x64 = 24.1437213192549

x65 = 40.2007504376027

x66 = -11.9264165552946

x67 = 22.2820367837943

x68 = 15.9988514766147

x69 = -74.0601379262927

x70 = -81.7395866350678

x71 = 86.277442690253

x72 = 66.2643339340514

x73 = -49.8582389653047

x74 = 12.2754824056935

x75 = -79.8779020996072

x76 = -93.8405361155618

x77 = 48.1129097133104

x78 = -61.7264778788661

x79 = -37.2918683509455

x80 = 12.9736141064912

x81 = -99.8910108558088

x82 = -3.78154671265438

x83 = -95.7022206510224

x84 = 34.1502756973557

x85 = 82.0886524854666

x86 = -75.6891118948208

x87 = 78.1325728476128

x88 = -47.7638438629115

x89 = -55.9087137055517

x90 = -19.8385758310022

x91 = 100.240076706208

x92 = 10.1810873033003

x93 = -85.9283768398542

x94 = 59.9811486268718

x95 = 62.075543729265

График