cos2x=3/4 (уравнение)

Найду корень уравнения: cos2x=3/4

Вы ввели

cos(2*x) = 3/4

$$\cos{\left(2 x \right)} = \frac{3}{4}$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} = \frac{3}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
Или
$$2 x = \pi n + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{4} \right)}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\operatorname{acos}{\left(\frac{3}{4} \right)}}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2} + \frac{\operatorname{acos}{\left(\frac{3}{4} \right)}}{2}$$

Быстрый ответ

          acos(3/4)
x1 = pi - ---------
              2    

$$x_{1} = \pi - \frac{\operatorname{acos}{\left(\frac{3}{4} \right)}}{2}$$

     acos(3/4)
x2 = ---------
         2    

$$x_{2} = \frac{\operatorname{acos}{\left(\frac{3}{4} \right)}}{2}$$

Численный ответ

x1 = 27.9129667584014

x2 = 100.169597790967

x3 = -100.169597790967

x4 = 3.5029597774965

x5 = -103.311190444556

x6 = -25.4941083526251

x7 = -62.4704859478892

x8 = -53.7684422349332

x9 = 34.196152065581

x10 = -44.3436642741638

x11 = 18.4881887976321

x12 = 84.4616345230177

x13 = -65.612078601479

x14 = -40.4793373727606

x15 = 53.7684422349332

x16 = -87.6032271766075

x17 = 31.7772936598046

x18 = -71.8952639086585

x19 = 62.4704859478892

x20 = -5.92181818327288

x21 = -97.7507393851903

x22 = 22.3525156990353

x23 = 25.4941083526251

x24 = -93.8864124837871

x25 = -9.78614508467609

x26 = 0.361367123906708

x27 = -34.196152065581

x28 = -75.7595908100618

x29 = -678.945380299302

x30 = -82.0427761172413

x31 = -21.6297814512218

x32 = -3.5029597774965

x33 = -38.0604789669842

x34 = -43.6209300263504

x35 = -41.202071620574

x36 = -16.0693303918557

x37 = 5.92181818327288

x38 = 16.0693303918557

x39 = 2.78022552968309

x40 = 56.1873006407096

x41 = -12.2050034904525

x42 = 82.0427761172413

x43 = -56.1873006407096

x44 = 90.7448198301973

x45 = -31.7772936598046

x46 = -49.90411533353

x47 = -46.7625226799402

x48 = 46.7625226799402

x49 = 66.3348128492924

x50 = -90.7448198301973

x51 = 88.3259614244209

x52 = -84.4616345230177

x53 = 38.0604789669842

x54 = 24.7713741048116

x55 = -63.1932201957026

x56 = 71.8952639086585

x57 = -18.4881887976321

x58 = -60.0516275421128

x59 = 9.78614508467609

x60 = -28.6357010062148

x61 = 40.4793373727606

x62 = 47.4852569277536

x63 = -91.4675540780107

x64 = 97.7507393851903

x65 = 60.0516275421128

x66 = 49.90411533353

x67 = -27.9129667584014

x68 = -47.4852569277536

x69 = -69.4764055028822

x70 = 68.7536712550687

x71 = 12.2050034904525

x72 = 69.4764055028822

x73 = 91.4675540780107

x74 = 110.317109999549

x75 = 44.3436642741638

x76 = 78.1784492158381

x77 = -19.2109230454455

x78 = -68.7536712550687

x79 = -78.1784492158381

x80 = 93.8864124837871

x81 = -85.1843687708311

x82 = 75.7595908100618

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