2*sin(x-(pi/4))=1

$$2 sin{left (x – frac{pi}{4} right )} = 1$$

Дано уравнение
$$2 sin{left (x – frac{pi}{4} right )} = 1$$
– это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -2

Ур-ние превратится в
$$cos{left (x + frac{pi}{4} right )} = – frac{1}{2}$$
Это ур-ние преобразуется в
$$x + frac{pi}{4} = pi n + {acos}{left (- frac{1}{2} right )}$$
$$x + frac{pi}{4} = pi n – pi + {acos}{left (- frac{1}{2} right )}$$
Или
$$x + frac{pi}{4} = pi n + frac{2 pi}{3}$$
$$x + frac{pi}{4} = pi n – frac{pi}{3}$$
, где n – любое целое число
Перенесём
$$frac{pi}{4}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$x = pi n + frac{5 pi}{12}$$
$$x = pi n – frac{7 pi}{12}$$

5*pi
x1 = —-
12

$$x_{1} = frac{5 pi}{12}$$

13*pi
x2 = —–
12

$$x_{2} = frac{13 pi}{12}$$

x1 = -17.5405589825000

x2 = -71.9948316448000

x3 = -15.4461638801000

x4 = 15.9697626557000

x5 = -28.0125344945000

x6 = -97.1275728735000

x7 = 53.6688744988000

x8 = -61.5228561328000

x9 = -4.97418836818000

x10 = 26.4417381677000

x11 = 3.40339204139000

x12 = 13.8753675534000

x13 = -86.6555973615000

x14 = -42.6733002113000

x15 = 110.217542263000

x16 = 82.9904059323000

x17 = 34.8193185773000

x18 = -74.0892267472000

x19 = -90.8443875663000

x20 = 51.5744793964000

x21 = -2.87979326579000

x22 = 66.2352451132000

x23 = -65.7116463376000

x24 = 89.2735912395000

x25 = 70.4240353180000

x26 = 76.7072206252000

x27 = 85.0848010347000

x28 = -21.7293491873000

x29 = -30.1069295969000

x30 = 97.6511716491000

x31 = 32.7249234749000

x32 = 59.9520598060000

x33 = 39.0081087821000

x34 = -40.5789051089000

x35 = -23.8237442897000

x36 = -46.8620904160000

x37 = -11.2573736754000

x38 = 57.8576647036000

x39 = 47.3856891916000

x40 = 1.30899693900000

x41 = -36.3901149041000

x42 = -99.2219679759000

x43 = -59.4284610304000

x44 = 28.5361332701000

x45 = -53.1452757232000

x46 = -67.8060414400000

x47 = -80.3724120543000

x48 = 95.5567765467000

x49 = -34.2957198017000

x50 = -48.9564855184000

x51 = 78.8016157275000

x52 = 342.695398629000

x53 = -9.16297857297000

x54 = -78.2780169519000

x55 = -92.9387826687000

x56 = 64.1408500108000

x57 = -84.5612022591000

x58 = -306.567083113000

x59 = 72.5184304204000

x60 = 103.934356956000

x61 = 7.59218224618000

x62 = -55.2396708256000

x63 = 9.68657734857000

x64 = 91.3679863419000

x65 = 41.1025038845000

x66 = 45.2912940893000

x67 = 20.1585528605000

x68 = 22.2529479629000