sin(3*x)-cos(3*x)=0

$$sin{left (3 x right )} – cos{left (3 x right )} = 0$$

Дано уравнение
$$sin{left (3 x right )} – cos{left (3 x right )} = 0$$
преобразуем:
$$frac{sin{left (3 x right )}}{cos{left (3 x right )}} = 1$$
или
$$tan{left (3 x right )} = 1$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = pi n + {atan}{left (-1 right )}$$
Или
$$3 x = pi n – frac{pi}{4}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = frac{pi n}{3} – frac{pi}{12}$$

-pi
x1 = —-
4

$$x_{1} = – frac{pi}{4}$$

pi
x2 = —
12

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

x1 = 2287.34125120000

x2 = 15.9697626557000

x3 = 90.3207887907000

x4 = 77.7544181763000

x5 = 6.54498469498000

x6 = -1.83259571459000

x7 = -45.8148928649000

x8 = 33.7721210261000

x9 = -47.9092879672000

x10 = -30.1069295969000

x11 = 13.8753675534000

x12 = -25.9181393921000

x13 = -67.8060414400000

x14 = 30.6305283725000

x15 = 215.984494934000

x16 = 84.0376034835000

x17 = -50.0036830696000

x18 = 20.1585528605000

x19 = -56.2868683768000

x20 = 64.1408500108000

x21 = 48.4328867428000

x22 = 86.1319985859000

x23 = 49.4800842940000

x24 = 50.5272818452000

x25 = -6.02138591938000

x26 = -100.269165527000

x27 = 70.4240353180000

x28 = -54.1924732744000

x29 = -39.5317075577000

x30 = 72.5184304204000

x31 = -28.0125344945000

x32 = 40.0553063333000

x33 = 57.8576647036000

x34 = 28.5361332701000

x35 = -32.2013246993000

x36 = -3.92699081699000

x37 = 35.8665161285000

x38 = 0.261799387799000

x39 = 46.3384916404000

x40 = -23.8237442897000

x41 = 42.1497014357000

x42 = -52.0980781720000

x43 = -17.5405589825000

x44 = -69.9004365424000

x45 = 92.4151838931000

x46 = -61.5228561328000

x47 = -96.0803753223000

x48 = 101.839961854000

x49 = -63.6172512352000

x50 = -76.1836218496000

x51 = 18.0641577581000

x52 = -65.7116463376000

x53 = -15.4461638801000

x54 = -93.9859802199000

x55 = 4.45058959259000

x56 = -12.3045712266000

x57 = -8.11578102177000

x58 = 71.4712328692000

x59 = 66.2352451132000

x60 = -43.7204977625000

x61 = -34.2957198017000

x62 = 59.9520598060000

x63 = 11.7809724510000

x64 = -19.6349540849000

x65 = -80.3724120543000

x66 = 24.3473430653000

x67 = 62.0464549084000

x68 = -78.2780169519000

x69 = 2.35619449019000

x70 = -41.6261026601000

x71 = -91.8915851175000

x72 = 10.7337748998000

x73 = 22.2529479629000

x74 = -87.7027949127000

x75 = -71.9948316448000

x76 = 79.8488132787000

x77 = -89.7971900151000

x78 = 26.4417381677000

x79 = -83.5140047079000

x80 = 94.5095789955000

x81 = -74.0892267472000

x82 = -58.3812634792000

x83 = -10.2101761242000

x84 = -1053.21893712000

x85 = -85.6083998103000

x86 = -98.1747704247000

x87 = 37.9609112309000

x88 = 75.6600230740000

x89 = 68.3296402156000

x90 = -21.7293491873000

x91 = 99.7455667515000

x92 = 52.6216769476000

x93 = 81.9432083811000

x94 = 88.2263936883000

x95 = 55.7632696012000

x96 = 44.2440965381000