cos(4*x)=-1

$$cos{left (4 x right )} = -1$$

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

pi
x1 = —
4

$$x_{1} = frac{pi}{4}$$

x1 = 32.2013247419000

x2 = -62.0464548652000

x3 = -63.6172513105000

x4 = -0.785398166131000

x5 = 38.4845098973000

x6 = 19.6349541952000

x7 = 71.4712325593000

x8 = 18.0641575853000

x9 = -40.0553062838000

x10 = -35.3429174369000

x11 = -90.3207886691000

x12 = 16.4933613203000

x13 = 2.35619442704000

x14 = -38.4845100907000

x15 = -85.6083998893000

x16 = -77.7544181730000

x17 = 54.1924733268000

x18 = -82.4668071752000

x19 = -33.7721211588000

x20 = 69.9004366180000

x21 = 82.4668070519000

x22 = -3.92699105527000

x23 = 63.6172513369000

x24 = 49.4800839996000

x25 = 44.7676955973000

x26 = 77.7544182977000

x27 = -2.35619437672000

x28 = 62.0464548186000

x29 = 0.785398118064000

x30 = 33.7721211448000

x31 = -99.7455667547000

x32 = 60.4756584745000

x33 = 22.7765470505000

x34 = 85.6083999066000

x35 = -32.2013245860000

x36 = -71.4712329855000

x37 = 11.7809725681000

x38 = -5.49778725648000

x39 = 96.6039739860000

x40 = 55.7632697214000

x41 = -68.3296400954000

x42 = 68.3296401659000

x43 = -465.741111003000

x44 = 88.7499926303000

x45 = 41.6261027664000

x46 = -57.3340660036000

x47 = 24.3473430065000

x48 = 98.1747704999000

x49 = 93.4623816270000

x50 = 25.9181394582000

x51 = -33.7721210086000

x52 = -49.4800844094000

x53 = 40.0553062091000

x54 = 52.6216768417000

x55 = 99.7455668738000

x56 = -60.4756586297000

x57 = -19.6349539734000

x58 = -46.3384915220000

x59 = -98.1747703187000

x60 = 74.6128254136000

x61 = -27.4889358331000

x62 = -93.4623815614000

x63 = 5.49778696423000

x64 = -54.1924731634000

x65 = 3.92699087785000

x66 = -16.4933615591000

x67 = 66.7588441131000

x68 = 27.4889354809000

x69 = -98.1747705480000

x70 = -11.7809724257000

x71 = 10.2101761578000

x72 = 76.1836219127000

x73 = 90.3207887458000

x74 = -84.0376034471000

x75 = 91.8915851975000

x76 = 30.6305282706000

x77 = -79.3252145686000

x78 = 47.9092880382000

x79 = -18.0641577028000

x80 = -24.3473429491000

x81 = -76.1836217410000

x82 = 8.63937970041000

x83 = 46.3384915861000

x84 = 84.0376034192000

x85 = -41.6261027314000

x86 = -55.7632695910000

x87 = -19.6349541523000

x88 = -10.2101760089000

x89 = -13.3517688688000