cos(x-pi/4)=1 (уравнение)

Найду корень уравнения: cos(x-pi/4)=1

Вы ввели

   /    pi\    
cos|x - --| = 1
   \    4 /    

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

Подробное решение

Дано уравнение
$$\cos{\left(x - \frac{\pi}{4} \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x + \frac{\pi}{4} = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$x + \frac{\pi}{4} = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{2}$$
$$x + \frac{\pi}{4} = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Перенесём
$$\frac{\pi}{4}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{\pi}{4}$$

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 = -87.179196419548

x2 = 0.78539789547023

x3 = -5.49778728507023

x4 = -5.49778700680011

x5 = -80.8960104115513

x6 = 101.316364217593

x7 = 13.3517691124798

x8 = 101.316362630045

x9 = -43.1968984966448

x10 = 76.1836219130226

x11 = 51.0508802520022

x12 = -68.3296406776765

x13 = 44.7676958096834

x14 = -36.9137135969066

x15 = 19.6349535809623

x16 = 57.3340662693301

x17 = 88.7499922107853

x18 = -30.6305280444586

x19 = -93.4623809277732

x20 = -74.6128259876378

x21 = -80.8960112165704

x22 = -62.0464553991111

x23 = -11.7809724257473

x24 = -99.7455662679839

x25 = -62.0464546173085

x26 = 82.466807184272

x27 = 69.900436761386

x28 = -18.0641582523216

x29 = -24.3473428556723

x30 = 32.2013247418065

x31 = 51.0508810545158

x32 = -49.4800837773799

x33 = -36.9137140604773

x34 = -55.7632691229967

x35 = 19.6349543026329

x36 = 13.3517698679338

x37 = 88.7499934333382

x38 = 25.9181388948737

x39 = 44.767695053091

x40 = -43.1968992620764

x41 = -55.7632699539578

x42 = 82.4668070327555

x43 = 32.2013251654123

x44 = -74.6128252014839

x45 = -24.3473436216976

x46 = 44.7676942601211

x47 = -18.0641577003401

x48 = 32.2013243173657

x49 = -5.49778662722657

x50 = 69.9004360424541

x51 = 25.9181396372431

x52 = 38.484511281858

x53 = 63.6172504667591

x54 = 25.9181394621816

x55 = -49.4800840940327

x56 = -68.3296400140743

x57 = 76.1836223087648

x58 = 69.9004366239102

x59 = 95.0331774083848

x60 = 76.1836214547509

x61 = -24.3473435707431

x62 = 7.0685830957142

x63 = -49.4800844438346

x64 = 19.6349534262936

x65 = -99.7455667547336

x66 = 88.7499929626081

x67 = -68.32964072224

x68 = -55.7632695910071

x69 = 95.0331782096424

x70 = 82.4668076723243

x71 = -11.7809728189029

x72 = 13.3517683209364

x73 = -36.9137132560831

x74 = 38.4845098737907

x75 = -62.0464548639416

x76 = 7.06858389927324

x77 = -93.4623811749839

x78 = 57.3340659463886

x79 = -30.630528833419

x80 = 38.4845105226779

x81 = 38.4845100861474

x82 = -93.4623816025082

x83 = 0.78539865659786

x84 = -18.0641574890547

x85 = -11.7809719785203

x86 = 63.6172507328697

x87 = 57.3340654754254

x88 = 63.617251460845

x89 = -87.1791956500412

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