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Реши любую задачу с помощью нейросети.
$$sin{left (3 x – frac{pi}{6} right )} = frac{1}{2}$$
– это простейшее тригонометрическое ур-ние
Разделим обе части ур-ния на -1
Ур-ние превратится в
$$cos{left (3 x + frac{pi}{3} right )} = – frac{1}{2}$$
Это ур-ние преобразуется в
$$3 x + frac{pi}{3} = pi n + {acos}{left (- frac{1}{2} right )}$$
$$3 x + frac{pi}{3} = pi n – pi + {acos}{left (- frac{1}{2} right )}$$
Или
$$3 x + frac{pi}{3} = pi n + frac{2 pi}{3}$$
$$3 x + frac{pi}{3} = pi n – frac{pi}{3}$$
, где n – любое целое число
Перенесём
$$frac{pi}{3}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$3 x = pi n + frac{pi}{3}$$
$$3 x = pi n – frac{2 pi}{3}$$
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} + frac{pi}{9}$$
$$x_{2} = frac{pi n}{3} – frac{2 pi}{9}$$
pi
x1 = —
9
pi
x2 = —
3
x1 = 794.124809657000
x2 = -52.0108117094000
x3 = 97.3893722613000
x4 = -1.74532925199000
x5 = -41.5388361975000
x6 = 48.5201532054000
x7 = -39.4444410951000
x8 = 63.8790506230000
x9 = 26.1799387799000
x10 = 68.0678408278000
x11 = -93.8987137573000
x12 = -8.02851455917000
x13 = -19.8967534727000
x14 = -95.9931088597000
x15 = 17.8023583703000
x16 = 77.8416846389000
x17 = 30.3687289847000
x18 = 2256.01259113000
x19 = -13.6135681656000
x20 = 6.63225115758000
x21 = 61.7846555206000
x22 = -61.7846555206000
x23 = -89.7099235525000
x24 = -100.181899064000
x25 = 13.6135681656000
x26 = 57.5958653158000
x27 = 46.4257581030000
x28 = 92.5024503557000
x29 = -10.1229096616000
x30 = 59.6902604182000
x31 = 4.53785605519000
x32 = -21.9911485751000
x33 = 88.3136601509000
x34 = -3.83972435439000
x35 = 21.9911485751000
x36 = 70.1622359302000
x37 = 19.8967534727000
x38 = 38.0481776935000
x39 = -87.6155284501000
x40 = -17.8023583703000
x41 = -83.4267382453000
x42 = -68.0678408278000
x43 = 15.7079632679000
x44 = -57.5958653158000
x45 = -63.8790506230000
x46 = -59.6902604182000
x47 = 28.2743338823000
x48 = -98.0875039621000
x49 = 94.5968454581000
x50 = -5.93411945678000
x51 = 33.8593874887000
x52 = -45.7276264023000
x53 = 72.2566310326000
x54 = -77.1435529381000
x55 = 82.0304748437000
x56 = -65.9734457254000
x57 = 0.349065850399000
x58 = 40.1425727959000
x59 = -72.2566310326000
x60 = -82.7286065445000
x61 = 50.6145483078000
x62 = 86.2192650485000
x63 = 3694.86202647000
x64 = -54.1052068118000
x65 = -37.3500459927000
x66 = 90.4080552533000
x67 = -24.0855436775000
x68 = 84.1248699461000
x69 = -43.6332312999000
x70 = -47.8220215046000
x71 = -91.8043186549000
x72 = -15.7079632679000
x73 = -70.1622359302000
x74 = 65.9734457254000
x75 = -30.3687289847000
x76 = 74.3510261350000
x77 = -85.5211333477000
x78 = 44.3313630007000
x79 = -33.1612557879000
x80 = -34.5575191895000
x81 = 2.44346095279000
x82 = -49.9164166070000
x83 = 42.2369678983000
x84 = -26.1799387799000
x85 = 79.9360797413000
x86 = 24.0855436775000
x87 = -129.503430498000
x88 = 53.4070751110000
x89 = 35.9537825911000
x90 = -74.3510261350000
x91 = -28.2743338823000
