cos(4x)=-1 (уравнение)

Найду корень уравнения: cos(4x)=-1

Вы ввели

cos(4*x) = -1

$$\cos{\left(4 x \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(4 x \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$4 x = \pi n + \pi$$
$$4 x = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{4}$$

Быстрый ответ

     pi
x1 = --
     4 

$$x_{1} = \frac{\pi}{4}$$

Сумма и произведение корней

сумма

    pi
0 + --
    4 

$$0 + \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

произведение

  pi
1*--
  4 

$$1 \frac{\pi}{4}$$

=

pi
--
4 

$$\frac{\pi}{4}$$

Численный ответ

x1 = 90.3207887457625

x2 = -38.4845100906754

x3 = -5.49778725647941

x4 = -84.0376034471411

x5 = 8.63937970041344

x6 = -3.92699105526517

x7 = 77.7544182976932

x8 = -13.3517688688202

x9 = 24.347343006498

x10 = 18.0641575853046

x11 = 62.0464548185713

x12 = 19.6349541951516

x13 = 66.7588441131007

x14 = -11.780972425667

x15 = -16.4933615591447

x16 = 91.8915851975093

x17 = -77.7544181730257

x18 = 32.2013247418649

x19 = -33.7721210085549

x20 = 49.4800839996026

x21 = -68.3296400953708

x22 = -63.6172513104641

x23 = 27.4889354808973

x24 = -90.3207886690967

x25 = -57.3340660035604

x26 = 0.785398118063847

x27 = -24.3473429491357

x28 = 63.6172513369298

x29 = 52.6216768417318

x30 = -40.0553062838236

x31 = 55.7632697213615

x32 = 69.9004366179912

x33 = -99.7455667547305

x34 = 41.6261027663993

x35 = -93.4623815613976

x36 = 38.4845098973237

x37 = -41.6261027314388

x38 = -19.6349541522704

x39 = -82.4668071752083

x40 = 60.4756584745212

x41 = -10.210176008893

x42 = 71.4712325592813

x43 = -0.785398166130751

x44 = -60.4756586297418

x45 = 46.3384915861013

x46 = 98.1747704999445

x47 = -46.3384915220366

x48 = -62.0464548652478

x49 = -465.741111003319

x50 = -32.2013245860493

x51 = 84.0376034192262

x52 = -19.6349539733882

x53 = -49.4800844094223

x54 = -55.763269590985

x55 = 33.7721211448164

x56 = -71.4712329855388

x57 = -35.3429174368834

x58 = 54.1924733267788

x59 = 88.7499926302988

x60 = -98.1747705479865

x61 = 30.6305282706443

x62 = 44.7676955973049

x63 = -54.1924731634027

x64 = 82.4668070519044

x65 = -2.35619437671896

x66 = 85.6083999066255

x67 = 16.4933613203203

x68 = -76.1836217409515

x69 = -85.608399889346

x70 = 40.055306209136

x71 = -98.1747703186947

x72 = -33.7721211587531

x73 = 2.35619442704144

x74 = 93.462381626966

x75 = 11.7809725680634

x76 = 96.6039739860399

x77 = 5.49778696422816

x78 = -27.4889358330644

x79 = 47.9092880382216

x80 = 10.2101761577675

x81 = 22.7765470504813

x82 = 3.92699087784889

x83 = 25.918139458182

x84 = -79.325214568582

x85 = 68.3296401658547

x86 = 74.6128254135616

x87 = 99.7455668738049

x88 = 76.1836219127145

x89 = -18.0641577028072

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