cos6x=-√2/2 (уравнение)

Найду корень уравнения: cos6x=-√2/2

Вы ввели

              ___ 
           -\/ 2  
cos(6*x) = -------
              2   

$$\cos{\left(6 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(6 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$6 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$6 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Или
$$6 x = \pi n + \frac{3 \pi}{4}$$
$$6 x = \pi n - \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$6$$
получим ответ:
$$x_{1} = \frac{\pi n}{6} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{6} - \frac{\pi}{24}$$

Быстрый ответ

     pi
x1 = --
     8 

$$x_{1} = \frac{\pi}{8}$$

     5*pi
x2 = ----
      24 

$$x_{2} = \frac{5 \pi}{24}$$

Сумма и произведение корней

сумма

    pi   5*pi
0 + -- + ----
    8     24 

$$\left(0 + \frac{\pi}{8}\right) + \frac{5 \pi}{24}$$

=

pi
--
3 

$$\frac{\pi}{3}$$

произведение

  pi 5*pi
1*--*----
  8   24 

$$\frac{5 \pi}{24} \cdot 1 \frac{\pi}{8}$$

=

    2
5*pi 
-----
 192 

$$\frac{5 \pi^{2}}{192}$$

Численный ответ

x1 = 84.1685031774265

x2 = -18.45685683984

x3 = -33.9030207199899

x4 = 71.8639319508665

x5 = 56.1559686829176

x6 = -91.7606854236019

x7 = -47.7783882733448

x8 = -35.997415822383

x9 = -7.72308194007491

x10 = -65.5807466436869

x11 = -1.70169602069447

x12 = 62.177354602298

x13 = 12.1736715326604

x14 = -31.8086256175967

x15 = -21.5984494934298

x16 = 40.1862060271694

x17 = -40.4480054149686

x18 = 64.2717497046912

x19 = -16.1006623496477

x20 = 38.0918109247762

x21 = 100.138265833175

x22 = -14.0062672472545

x23 = 98.0438707307815

x24 = -77.885317870247

x25 = 82.0741080750334

x26 = 34.164820107789

x27 = 60.0829594999048

x28 = -5.89048622548086

x29 = 18.1950574520409

x30 = 49.872783375738

x31 = 66.3661448070844

x32 = 73.9583270532597

x33 = -89.6662903212087

x34 = -73.6965276654606

x35 = -29.7142305152035

x36 = 58.2503637853107

x37 = -27.8816348006094

x38 = -82.0741080750334

x39 = -55.8941692951184

x40 = -49.872783375738

x41 = -11.9118721448613

x42 = 81.0269105238367

x43 = 22.3838476568273

x44 = 95.9494756283883

x45 = -51.705379090332

x46 = -45.6839931709516

x47 = 27.8816348006094

x48 = 0.392699081698724

x49 = -38.0918109247762

x50 = 7.98488132787406

x51 = 5.89048622548086

x52 = -69.7695368484733

x53 = -84.1685031774265

x54 = 78.1471172580461

x55 = -43.5895980685584

x56 = 16.1006623496477

x57 = -994.444974555069

x58 = -3.79609112308767

x59 = -57.9885643975116

x60 = 93.8550805259951

x61 = -53.0143760293278

x62 = 14.2680666350536

x63 = -95.6876762405891

x64 = 36.2592152101822

x65 = 10.0792764302673

x66 = 88.3572933822129

x67 = -60.0829594999048

x68 = 43.5895980685584

x69 = -75.7909227678538

x70 = 23.692844595823

x71 = 51.9671784781312

x72 = 131.292392981273

x73 = -9.8174770424681

x74 = -99.8764664453755

x75 = 86.2628982798197

x76 = 29.9760299030026

x77 = -25.7872396982162

x78 = 90.7134878724053

x79 = -79.9797129726402

x80 = -71.8639319508665

x81 = 32.0704250053958

x82 = 44.3749962319558

x83 = -93.8550805259951

x84 = 42.2806011295626

x85 = 80.2415123604393

x86 = -97.7820713429823

x87 = 76.0527221556529

x88 = -23.692844595823

x89 = 54.0615735805244

x90 = -67.6751417460801

x91 = 20.2894525544341

x92 = 3.53429173528852

x93 = 19.5040543910366

x94 = -53.7997741927252

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