cos(2*x)=-0,2 (уравнение)

Найду корень уравнения: cos(2*x)=-0,2

Вы ввели

cos(2*x) = -1/5

$$\cos{\left(2 x \right)} = - \frac{1}{5}$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} = - \frac{1}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{1}{5} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{5} \right)}$$
Или
$$2 x = \pi n + \operatorname{acos}{\left(- \frac{1}{5} \right)}$$
$$2 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{5} \right)}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\operatorname{acos}{\left(- \frac{1}{5} \right)}}{2}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{2} + \frac{\operatorname{acos}{\left(- \frac{1}{5} \right)}}{2}$$

Быстрый ответ

          acos(-1/5)
x1 = pi - ----------
              2     

$$x_{1} = \pi - \frac{\operatorname{acos}{\left(- \frac{1}{5} \right)}}{2}$$

     acos(-1/5)
x2 = ----------
         2     

$$x_{2} = \frac{\operatorname{acos}{\left(- \frac{1}{5} \right)}}{2}$$

Численный ответ

x1 = -60.5763375419987

x2 = 98.2754493850762

x3 = -19.7356330453314

x4 = 19.7356330453314

x5 = -91.9922640778966

x6 = 85.709078770717

x7 = 26.018818352511

x8 = 96.503295137491

x9 = 46.2378126800543

x10 = 8.53870083697677

x11 = -24.2466641049257

x12 = 60.5763375419987

x13 = 83.9369245231318

x14 = -90.2201098303114

x15 = -33.6714420656951

x16 = 55.6625906408237

x17 = -63.7179301955885

x18 = 4.02766977738241

x19 = 90.2201098303114

x20 = -71.3705539087726

x21 = -82.5674861171272

x22 = -54.2931522348191

x23 = 68.2289612551828

x24 = -14.8218861441564

x25 = 82.5674861171272

x26 = -79.4258934635374

x27 = 11.6802934905666

x28 = 2.25551552979718

x29 = -17.9634787977461

x30 = -4.02766977738241

x31 = 41.7267816204599

x32 = -83.9369245231318

x33 = -76.2843008099477

x34 = 24.2466641049257

x35 = -120.266597960205

x36 = -526.901488679293

x37 = 39.9546273728747

x38 = 16.5940403917416

x39 = 38.5851889668701

x40 = 61.9457759480033

x41 = -57.4347448884089

x42 = -68.2289612551828

x43 = 48.0099669276395

x44 = 76.2843008099477

x45 = -2.25551552979718

x46 = -32.3020036596905

x47 = -10.310855084562

x48 = 30.5298494121053

x49 = 117.125005306615

x50 = 77.6537392159522

x51 = -61.9457759480033

x52 = -70.0011155027681

x53 = -77.6537392159522

x54 = -93.3617024839012

x55 = 10.310855084562

x56 = 17.9634787977461

x57 = -85.709078770717

x58 = -39.9546273728747

x59 = 63.7179301955885

x60 = 74.5121465623624

x61 = -5.39710818338697

x62 = -55.6625906408237

x63 = -27.3882567585155

x64 = -11.6802934905666

x65 = 99.6448877910808

x66 = 52.5209979872339

x67 = -99.6448877910808

x68 = -98.2754493850762

x69 = -38.5851889668701

x70 = 91.9922640778966

x71 = 70.0011155027681

x72 = 33.6714420656951

x73 = -13.4524477381518

x74 = -49.3794053336441

x75 = -41.7267816204599

x76 = 198.80641429995

x77 = -35.4435963132803

x78 = 32.3020036596905

x79 = -26.018818352511

x80 = -46.2378126800543

x81 = 54.2931522348191

x82 = -48.0099669276395

График