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Дано

$$sin{left (x right )} = – frac{1}{4}$$
Подробное решение
Дано уравнение
$$sin{left (x right )} = – frac{1}{4}$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 pi n + {asin}{left (- frac{1}{4} right )}$$
$$x = 2 pi n – {asin}{left (- frac{1}{4} right )} + pi$$
Или
$$x = 2 pi n – {asin}{left (frac{1}{4} right )}$$
$$x = 2 pi n + {asin}{left (frac{1}{4} right )} + pi$$
, где n – любое целое число
Ответ
$$x_{1} = {asin}{left (frac{1}{4} right )} + pi$$

x2 = -asin(1/4)

$$x_{2} = – {asin}{left (frac{1}{4} right )}$$
Численный ответ

x1 = -46.8712095487000

x2 = -94.5004598628000

x3 = 68.8623581238000

x4 = 37.4464315879000

x5 = -25.3854214839000

x6 = -81.9340892485000

x7 = 100.278284660000

x8 = -63.0845333269000

x9 = 91.3588672092000

x10 = 28.5270141375000

x11 = -31.6686067910000

x12 = -100.783645170000

x13 = 31.1632462808000

x14 = -56.8013480198000

x15 = -0.252680255142000

x16 = -75.6509039413000

x17 = -28.0216536272000

x18 = 22.2438288303000

x19 = -90.8535066990000

x20 = 56.2959875095000

x21 = -19.1022361767000

x22 = 53.6597553662000

x23 = 75.1455434310000

x24 = -78.2871360846000

x25 = -37.9517920982000

x26 = 3.39427290873000

x27 = 85.0756819021000

x28 = -9.17209770563000

x29 = 97.6420525164000

x30 = 66.2261259805000

x31 = 50.0128022023000

x32 = 12.3136903592000

x33 = -6.53586556232000

x34 = -59.4375801631000

x35 = 15.9606435231000

x36 = -65.7207654702000

x37 = 190160.350642000

x38 = -15.4552830128000

x39 = -84.5703213918000

x40 = 18.5968756664000

x41 = 34.8101994446000

x42 = -21.7384683200000

x43 = -270.429648464000

x44 = 41.0933847518000

x45 = 59.9429406733000

x46 = 47.3765700590000

x47 = -50.5181627126000

x48 = -44.2349774054000

x49 = -97.1366920061000

x50 = -2.88891239845000

x51 = 87.7119140454000

x52 = 43.7296168951000

x53 = 6.03050505204000

x54 = -72.0039507774000

x55 = 72.5093112877000

x56 = -69.3677186341000

x57 = -88.2172745557000

x58 = -34.3048389343000

x59 = -53.1543948559000

x60 = 62.5791728167000

x61 = 9.67745821591000

x62 = 93.9950993526000

x63 = 78.7924965949000

x64 = 81.4287287382000

x65 = 24.8800609736000

x66 = -12.8190508695000

x67 = -40.5880242415000

   
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