cos(2*x-1)=0 (уравнение)

Найду корень уравнения: cos(2*x-1)=0

Вы ввели

cos(2*x - 1) = 0

$$\cos{\left(2 x - 1 \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x - 1 \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(2 x - 1 \right)} = 0$$
Это ур-ние преобразуется в
$$2 x - 1 = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x - 1 = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$2 x - 1 = \pi n + \frac{\pi}{2}$$
$$2 x - 1 = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Перенесём
$$-1$$
в правую часть ур-ния
с противоположным знаком, итого:
$$2 x = \pi n + 1 + \frac{\pi}{2}$$
$$2 x = \pi n - \frac{\pi}{2} + 1$$
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{1}{2} + \frac{\pi}{4}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{4} + \frac{1}{2}$$

Быстрый ответ

     1   pi
x1 = - + --
     2   4 

$$x_{1} = \frac{1}{2} + \frac{\pi}{4}$$

     1   3*pi
x2 = - + ----
     2    4  

$$x_{2} = \frac{1}{2} + \frac{3 \pi}{4}$$

Численный ответ

x1 = 71.9712328691678

x2 = 70.4004365423729

x3 = -25.4181393921158

x4 = -0.285398163397448

x5 = -1.85619449019234

x6 = -97.674770424681

x7 = -52.121676947629

x8 = 20.1349540849362

x9 = 27.9889357189107

x10 = 26.4181393921158

x11 = 21.7057504117311

x12 = 7.56858347057703

x13 = -23.8473430653209

x14 = -88.2499924639117

x15 = -9.71017612416683

x16 = 92.3915851175014

x17 = 4.42699081698724

x18 = 95.5331777710912

x19 = -36.4137136796801

x20 = -74.1128255227576

x21 = 79.8252145031423

x22 = -55.2632696012188

x23 = 73.5420291959627

x24 = 49.9800842940392

x25 = 106.528752058656

x26 = -67.829640215578

x27 = 56.2632696012188

x28 = -58.4048622548086

x29 = 5.99778714378214

x30 = 76.6836218495525

x31 = 62.5464549083984

x32 = -45.8384916404494

x33 = 51.5508806208341

x34 = 43.6968989868597

x35 = 12.2809724509617

x36 = 29.5597320457056

x37 = -53.6924732744239

x38 = -47.4092879672443

x39 = -14.4225651045515

x40 = -37.984510006475

x41 = -33.2721210260903

x42 = -15.9933614313464

x43 = -89.8207887907066

x44 = 18.5641577581413

x45 = 98.674770424681

x46 = -19.1349540849362

x47 = -8.13937979737193

x48 = 10.7101761241668

x49 = 87.6791961371168

x50 = 40.5553063332699

x51 = -31.7013246992954

x52 = -69.4004365423729

x53 = 64.1172512351933

x54 = 54.6924732744239

x55 = 78.2544181763474

x56 = 32.7013246992954

x57 = -39.5553063332699

x58 = 48.4092879672443

x59 = 100.245566751476

x60 = 93.9623814442964

x61 = -17.5641577581413

x62 = -66.2588438887831

x63 = -44.2676953136546

x64 = -61.5464549083984

x65 = 42.1261026600648

x66 = -22.276546738526

x67 = -80.3960108299372

x68 = 35.8429173528852

x69 = 86.1083998103219

x70 = 13.8517687777566

x71 = 34.2721210260903

x72 = 84.537603483527

x73 = -30.1305283725005

x74 = -3.42699081698724

x75 = 65.6880475619882

x76 = -99.2455667514759

x77 = -81.9668071567321

x78 = 57.8340659280137

x79 = -11.2809724509617

x80 = -91.3915851175014

x81 = -59.9756585816035

x82 = -96.1039740978861

x83 = -77.2544181763474

x84 = -83.537603483527

x85 = -75.6836218495525

x86 = 148.940252882118

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