cos(x)=√2/2 (уравнение)

Найду корень уравнения: cos(x)=√2/2

Вы ввели

           ___
         \/ 2 
cos(x) = -----
           2  

$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}$$
Или
$$x = \pi n + \frac{\pi}{4}$$
$$x = \pi n - \frac{3 \pi}{4}$$
, где n - любое целое число

Быстрый ответ

     pi
x1 = --
     4 

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

     7*pi
x2 = ----
      4  

$$x_{2} = \frac{7 \pi}{4}$$

Численный ответ

x1 = -7.06858347057703

x2 = 99.7455667514759

x3 = 76.1836218495525

x4 = 32.2013246992954

x5 = -5.49778714378214

x6 = -18.0641577581413

x7 = -182.997772071605

x8 = -19.6349540849362

x9 = 88.7499924639117

x10 = 7.06858347057703

x11 = -36.9137136796801

x12 = 25.9181393921158

x13 = -55.7632696012188

x14 = -0.785398163397448

x15 = 18.0641577581413

x16 = -351.072979038659

x17 = 57.3340659280137

x18 = -99.7455667514759

x19 = -80.8960108299372

x20 = -44.7676953136546

x21 = 30.6305283725005

x22 = 68.329640215578

x23 = 95.0331777710912

x24 = 0.785398163397448

x25 = 62.0464549083984

x26 = -25.9181393921158

x27 = -95.0331777710912

x28 = 5.49778714378214

x29 = 63.6172512351933

x30 = 87.1791961371168

x31 = 24.3473430653209

x32 = -101.316363078271

x33 = -30.6305283725005

x34 = -76.1836218495525

x35 = -93.4623814442964

x36 = 19.6349540849362

x37 = 80.8960108299372

x38 = 44.7676953136546

x39 = -51.0508806208341

x40 = -88.7499924639117

x41 = 13.3517687777566

x42 = 69.9004365423729

x43 = -87.1791961371168

x44 = -62.0464549083984

x45 = -68.329640215578

x46 = 82.4668071567321

x47 = -162.577419823272

x48 = -82.4668071567321

x49 = -32.2013246992954

x50 = -24.3473430653209

x51 = 36.9137136796801

x52 = -38.484510006475

x53 = 55.7632696012188

x54 = 49.4800842940392

x55 = 11.7809724509617

x56 = -13.3517687777566

x57 = 51.0508806208341

x58 = 93.4623814442964

x59 = -57.3340659280137

x60 = -74.6128255227576

x61 = -43.1968989868597

x62 = -69.9004365423729

x63 = -11.7809724509617

x64 = -63.6172512351933

x65 = -49.4800842940392

x66 = 43.1968989868597

x67 = 38.484510006475

x68 = 74.6128255227576

График