cos(3*x+pi/4)=1

$$cos{left (3 x + frac{pi}{4} right )} = 1$$

Дано уравнение
$$cos{left (3 x + frac{pi}{4} right )} = 1$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x + frac{pi}{4} = pi n + {acos}{left (1 right )}$$
$$3 x + frac{pi}{4} = pi n – pi + {acos}{left (1 right )}$$
Или
$$3 x + frac{pi}{4} = pi n$$
$$3 x + frac{pi}{4} = pi n – pi$$
, где n – любое целое число
Перенесём
$$frac{pi}{4}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = pi n – frac{pi}{4}$$
$$3 x = pi n – frac{5 pi}{4}$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} – frac{pi}{12}$$
$$x_{2} = frac{pi n}{3} – frac{5 pi}{12}$$

-pi
x1 = —-
12

$$x_{1} = – frac{pi}{12}$$

7*pi
x2 = —-
12

$$x_{2} = frac{7 pi}{12}$$

x1 = -8.63937976312000

x2 = -63.0936524530000

x3 = 24.8709417730000

x4 = -52.6216768809000

x5 = -31.6777259701000

x6 = 996.670269462000

x7 = 16.4933613073000

x8 = 29.0597318190000

x9 = 70.9476342622000

x10 = 93.9859802353000

x11 = 89.7971901413000

x12 = 6.02138631959000

x13 = -46.3384914779000

x14 = 64.6644486247000

x15 = -50.5272816961000

x16 = 22.7765465908000

x17 = 1.83259582655000

x18 = -25.3945407709000

x19 = -67.2824428253000

x20 = 8.11578143537000

x21 = -86.1319984903000

x22 = -77.7544181730000

x23 = -56.8104666996000

x24 = 54.1924733268000

x25 = 10.2101761577000

x26 = 98.1747705003000

x27 = -29.5833309149000

x28 = 91.8915852009000

x29 = -75.6600231301000

x30 = -84.0376034467000

x31 = 18.5877563829000

x32 = -88.2263935538000

x33 = 56.2868683516000

x34 = 35.3429173442000

x35 = -69.3768379241000

x36 = -90.3207886312000

x37 = 26.9653372189000

x38 = -48.4328865743000

x39 = -96.6039740063000

x40 = 85.6083999786000

x41 = -42.1497013316000

x42 = -60.9992570445000

x43 = -73.5656280728000

x44 = 43.7204979128000

x45 = -37.9609112985000

x46 = 47.9092880406000

x47 = 20.6821514738000

x48 = 33.2485219177000

x49 = 83.5140048699000

x50 = -92.4151837241000

x51 = -44.2440963978000

x52 = 12.3045711905000

x53 = 50.0036830651000

x54 = -65.1880476918000

x55 = 37.4373125853000

x56 = -54.7160723294000

x57 = -6.54498455422000

x58 = -98.6983693726000

x59 = -94.5095788398000

x60 = 66.7588437353000

x61 = 3.92699087937000

x62 = -17.0169598154000

x63 = 41.6261028271000

x64 = 39.5317077229000

x65 = 45.8148929842000

x66 = -33.7721210086000

x67 = 79.3252144374000

x68 = -0.261799242243000

x69 = 58.3812634020000

x70 = 62.5700535372000

x71 = 6.02138588892000

x72 = -19.1113553451000

x73 = -71.4712330047000

x74 = -35.8665159745000

x75 = 87.7027950673000

x76 = -2.35619432509000

x77 = -10.7337752934000

x78 = 14.3989662433000

x79 = -4.45058942523000

x80 = -79.8488131593000

x81 = 100.269165513000

x82 = -23.3001456762000

x83 = 68.8532388988000

x84 = -40.0553062829000

x85 = 75.1364243851000

x86 = -81.9432085119000

x87 = 81.4196097217000

x88 = 60.4756584640000

x89 = -27.4889358489000

x90 = 98.1747708343000

x91 = -21.2057505517000