cos(pi-x)=-√2/2 (уравнение)

Найду корень уравнения: cos(pi-x)=-√2/2

Вы ввели

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

$$\cos{\left(\pi - x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(\pi - x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\cos{\left(x \right)} = \frac{\sqrt{2}}{2}$$
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  

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

Сумма и произведение корней

сумма

    pi   7*pi
0 + -- + ----
    4     4  

$$\left(0 + \frac{\pi}{4}\right) + \frac{7 \pi}{4}$$

=

2*pi

$$2 \pi$$

произведение

  pi 7*pi
1*--*----
  4   4  

$$\frac{7 \pi}{4} \cdot 1 \frac{\pi}{4}$$

=

    2
7*pi 
-----
  16 

$$\frac{7 \pi^{2}}{16}$$

Численный ответ

x1 = -11.7809724509617

x2 = 69.9004365423729

x3 = -30.6305283725005

x4 = 95.0331777710912

x5 = -95.0331777710912

x6 = 51.0508806208341

x7 = -44.7676953136546

x8 = 25.9181393921158

x9 = 0.785398163397448

x10 = -93.4623814442964

x11 = 99.7455667514759

x12 = -82.4668071567321

x13 = 87.1791961371168

x14 = -18.0641577581413

x15 = -162.577419823272

x16 = 19.6349540849362

x17 = 55.7632696012188

x18 = -55.7632696012188

x19 = 43.1968989868597

x20 = 7.06858347057703

x21 = -19.6349540849362

x22 = -43.1968989868597

x23 = 62.0464549083984

x24 = 57.3340659280137

x25 = -32.2013246992954

x26 = -13.3517687777566

x27 = 74.6128255227576

x28 = -101.316363078271

x29 = -57.3340659280137

x30 = -74.6128255227576

x31 = -88.7499924639117

x32 = -182.997772071605

x33 = 93.4623814442964

x34 = 5.49778714378214

x35 = -76.1836218495525

x36 = -68.329640215578

x37 = -99.7455667514759

x38 = 80.8960108299372

x39 = -51.0508806208341

x40 = 13.3517687777566

x41 = 36.9137136796801

x42 = -25.9181393921158

x43 = -0.785398163397448

x44 = -36.9137136796801

x45 = 11.7809724509617

x46 = 32.2013246992954

x47 = 88.7499924639117

x48 = -62.0464549083984

x49 = 24.3473430653209

x50 = -38.484510006475

x51 = 30.6305283725005

x52 = -80.8960108299372

x53 = -5.49778714378214

x54 = -49.4800842940392

x55 = 82.4668071567321

x56 = 76.1836218495525

x57 = -7.06858347057703

x58 = -69.9004365423729

x59 = -63.6172512351933

x60 = 68.329640215578

x61 = -24.3473430653209

x62 = 63.6172512351933

x63 = -87.1791961371168

x64 = -351.072979038659

x65 = 38.484510006475

x66 = 44.7676953136546

x67 = 18.0641577581413

x68 = 49.4800842940392

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