cos9x=-1 (уравнение)

Найду корень уравнения: cos9x=-1

Вы ввели

cos(9*x) = -1

$$\cos{\left(9 x \right)} = -1$$

Подробное решение

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

Быстрый ответ

     pi
x1 = --
     9 

$$x_{1} = \frac{\pi}{9}$$

Сумма и произведение корней

сумма

    pi
0 + --
    9 

$$0 + \frac{\pi}{9}$$

=

pi
--
9 

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

произведение

  pi
1*--
  9 

$$1 \frac{\pi}{9}$$

=

pi
--
9 

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

Численный ответ

x1 = -82.0304748164276

x2 = -95.9931088685753

x3 = 33.8593874870198

x4 = -24.085543634654

x5 = 5.93411945787349

x6 = -35.9537826857019

x7 = 49.9164166499969

x8 = -75.7472895385462

x9 = -90.4080552794313

x10 = 28.2743338659518

x11 = 100.181899127779

x12 = 79.9360797825443

x13 = 60.3883921153078

x14 = 95.993108867423

x15 = -8.02851453314641

x16 = 26.8780703938441

x17 = -31.7649923745212

x18 = -29.6705973223797

x19 = -91.8043186062168

x20 = -40.1425727846458

x21 = -45.7276264174202

x22 = 35.953782626709

x23 = -73.6528944731872

x24 = 14.3116998322756

x25 = -57.5958652612883

x26 = 26.8780705565623

x27 = 82.0304747925099

x28 = -61.7846554914422

x29 = 5.93411949836991

x30 = -77.8416845567304

x31 = -65.9734457679684

x32 = 21.9911485848755

x33 = -43.6332313319376

x34 = -84.1248699208298

x35 = -47.8220214371937

x36 = -40.1425728028779

x37 = 12.2173047912859

x38 = 42.2369679084262

x39 = 16.4060950349246

x40 = -54.1052067731032

x41 = 38.048177592468

x42 = 58.293996989696

x43 = -1.74532925540132

x44 = 74.3510260965278

x45 = -68.0678407858503

x46 = -52.0108116977499

x47 = -98.0875039193568

x48 = -21.9911485867805

x49 = -84.1248699566507

x50 = -79.9360798712708

x51 = 77.8416845591782

x52 = 8.0285145123667

x53 = 68.0678407944026

x54 = 63.8790506521453

x55 = 30.3687289540014

x56 = 56.1996019588514

x57 = 72.2566310277657

x58 = 86.2192650740357

x59 = -59.690260451614

x60 = -87.615528461787

x61 = 19.8967535121777

x62 = 88.3136601161986

x63 = 90.4080553323618

x64 = 65.9734457500772

x65 = 70.1622360113718

x66 = -89.7099235775224

x67 = 52.0108116949

x68 = -17.8023583236913

x69 = 26.1799388453017

x70 = -70.1622360375375

x71 = -10.1229096342445

x72 = -3.83972427242607

x73 = 3.83972426108974

x74 = 48.5201531894717

x75 = 0.349065811631025

x76 = -15.7079632939265

x77 = 93.8987137973797

x78 = -5.93411956563942

x79 = 44.3313629619014

x80 = -26.8780705097624

x81 = -38.0481776570432

x82 = 58.9921287215078

x83 = -13.6135681734592

График