sin(x)-sqrt(2)/2=0

$$sin{left (x right )} – frac{sqrt{2}}{2} = 0$$

Дано уравнение
$$sin{left (x right )} – frac{sqrt{2}}{2} = 0$$
– это простейшее тригонометрическое ур-ние

Перенесём -sqrt(2)/2 в правую часть ур-ния

с изменением знака при -sqrt(2)/2

Получим:
$$sin{left (x right )} – frac{sqrt{2}}{2} + frac{sqrt{2}}{2} = frac{sqrt{2}}{2}$$
Это ур-ние преобразуется в
$$x = 2 pi n + {asin}{left (frac{sqrt{2}}{2} right )}$$
$$x = 2 pi n – {asin}{left (frac{sqrt{2}}{2} right )} + pi$$
Или
$$x = 2 pi n + frac{pi}{4}$$
$$x = 2 pi n + frac{3 pi}{4}$$
, где n – любое целое число

pi
x1 = —
4

$$x_{1} = frac{pi}{4}$$

3*pi
x2 = —-
4

$$x_{2} = frac{3 pi}{4}$$

x1 = -80.8960108299000

x2 = 58.9048622548000

x3 = 21.2057504117000

x4 = 82.4668071567000

x5 = 0.785398163397000

x6 = -73.0420291960000

x7 = 96.6039740979000

x8 = 32.2013246993000

x9 = 51.0508806208000

x10 = 25.9181393921000

x11 = -5.49778714378000

x12 = 77.7544181763000

x13 = 57.3340659280000

x14 = -43.1968989869000

x15 = 33.7721210261000

x16 = 76.1836218496000

x17 = -29.0597320457000

x18 = 46.3384916404000

x19 = -99.7455667515000

x20 = -60.4756585816000

x21 = -5043.04160718000

x22 = -85.6083998103000

x23 = 101.316363078000

x24 = 71.4712328692000

x25 = -74.6128255228000

x26 = 88.7499924639000

x27 = -10.2101761242000

x28 = 90.3207887907000

x29 = -55.7632696012000

x30 = -54.1924732744000

x31 = 7.06858347058000

x32 = -47.9092879672000

x33 = 18963.4386552000

x34 = 14.9225651046000

x35 = 95.0331777711000

x36 = -98.1747704247000

x37 = 40.0553063333000

x38 = -18.0641577581000

x39 = 65.1880475620000

x40 = -36.9137136797000

x41 = 69.9004365424000

x42 = -501.869426411000

x43 = -1160.03308734000

x44 = 13.3517687778000

x45 = -22.7765467385000

x46 = -30.6305283725000

x47 = 63.6172512352000

x48 = -66.7588438888000

x49 = -1010.80743629000

x50 = 19.6349540849000

x51 = 38.4845100065000

x52 = 2.35619449019000

x53 = -79.3252145031000

x54 = -3.92699081699000

x55 = -91.8915851175000

x56 = -62.0464549084000

x57 = -49.4800842940000

x58 = -186.139364725000

x59 = 52.6216769476000

x60 = -68.3296402156000

x61 = -93.4623814443000

x62 = -35.3429173529000

x63 = 44.7676953137000

x64 = -41.6261026601000

x65 = 84.0376034835000

x66 = -87.1791961371000

x67 = -24.3473430653000

x68 = -16.4933614313000

x69 = -11.7809724510000

x70 = 27.4889357189000

x71 = 128.019900634000

x72 = 8.63937979737000

x73 = -2347.55511039000

x74 = -237.975643509000

x75 = 1213.44016245000