sqrt(2)*sin(3*x)=1

Разделим обе части ур-ния на sqrt(2)

Ур-ние превратится в
$$sin{left (3 x right )} = frac{sqrt{2}}{2}$$
Это ур-ние преобразуется в
$$3 x = 2 pi n + {asin}{left (frac{sqrt{2}}{2} right )}$$
$$3 x = 2 pi n – {asin}{left (frac{sqrt{2}}{2} right )} + pi$$
Или
$$3 x = 2 pi n + frac{pi}{4}$$
$$3 x = 2 pi n + frac{3 pi}{4}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{2 pi}{3} n + frac{pi}{12}$$
$$x_{2} = frac{2 pi}{3} n + frac{pi}{4}$$

pi
x1 = —
12

pi
x2 = —
4

x1 = 90.3207887907000

x2 = -32.7249234749000

x3 = 98.6983692003000

x4 = 6.54498469498000

x5 = 17.5405589825000

x6 = -1.83259571459000

x7 = -45.8148928649000

x8 = -26.4417381677000

x9 = -47.9092879672000

x10 = -13.8753675534000

x11 = 21.7293491873000

x12 = 92.4151838931000

x13 = 69.9004365424000

x14 = 63.6172512352000

x15 = 74.0892267472000

x16 = 30.1069295969000

x17 = 84.0376034835000

x18 = -50.0036830696000

x19 = -70.4240353180000

x20 = 67.8060414400000

x21 = -273.580360250000

x22 = 104.981554507000

x23 = 60.9992573572000

x24 = 48.4328867428000

x25 = -73.0420291960000

x26 = 86.1319985859000

x27 = -1371.56699268000

x28 = 76.1836218496000

x29 = 50.5272818452000

x30 = -6.02138591938000

x31 = -55.7632696012000

x32 = -39.5317075577000

x33 = -22.2529479629000

x34 = 40.0553063333000

x35 = 4.45058959259000

x36 = -79.3252145031000

x37 = -18.0641577581000

x38 = -57.8576647036000

x39 = -62.0464549084000

x40 = 0.261799387799000

x41 = 46.3384916404000

x42 = -11.7809724510000

x43 = -20.1585528605000

x44 = 71.9948316448000

x45 = 42.1497014357000

x46 = -52.0980781720000

x47 = -97.6511716491000

x48 = -66.2352451132000

x49 = -96.0803753223000

x50 = -9.68657734857000

x51 = 32.2013246993000

x52 = -99.7455667515000

x53 = -8.11578102177000

x54 = -43.7204977625000

x55 = 34.2957198017000

x56 = -76.7072206252000

x57 = -1206.10977959000

x58 = -89.7971900151000

x59 = 81.9432083811000

x60 = -35.3429173529000

x61 = -41.6261026601000

x62 = -30.6305283725000

x63 = -91.8915851175000

x64 = -15.9697626557000

x65 = -87.7027949127000

x66 = 96.6039740979000

x67 = -93.9859802199000

x68 = 25.9181393921000

x69 = 78.2780169519000

x70 = -29.0597320457000

x71 = -59.9520598060000

x72 = -83.5140047079000

x73 = 94.5095789955000

x74 = -53.6688744988000

x75 = 719.162918284000

x76 = 23.8237442897000

x77 = -85.6083998103000

x78 = -81.4196096055000

x79 = -64.1408500108000

x80 = 28.0125344945000

x81 = 100.792764303000

x82 = -37.4373124553000

x83 = 37.9609112309000

x84 = -3.92699081699000

x85 = 19.6349540849000

x86 = 52.6216769476000

x87 = -497.680636206000

x88 = -68.3296402156000

x89 = 88.2263936883000

x90 = -24.3473430653000

x91 = 44.2440965381000

x92 = 11.2573736754000

x93 = 8.63937979737000

x94 = 65.7116463376000

x95 = 2.35619449019000