Дано

$$cos{left (2 x right )} = frac{sqrt{2}}{2}$$
Подробное решение
Дано уравнение
$$cos{left (2 x right )} = frac{sqrt{2}}{2}$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = pi n + {acos}{left (frac{sqrt{2}}{2} right )}$$
$$2 x = pi n – pi + {acos}{left (frac{sqrt{2}}{2} right )}$$
Или
$$2 x = pi n + frac{pi}{4}$$
$$2 x = pi n – frac{3 pi}{4}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = frac{pi n}{2} + frac{pi}{8}$$
$$x_{2} = frac{pi n}{2} – frac{3 pi}{8}$$
Ответ

pi
x1 = —
8

$$x_{1} = frac{pi}{8}$$

7*pi
x2 = —-
8

$$x_{2} = frac{7 pi}{8}$$
Численный ответ

x1 = -100.138265833000

x2 = 93.8550805260000

x3 = -82.0741080750000

x4 = -103.279858487000

x5 = -84.4303025652000

x6 = -47.5165888855000

x7 = 68.7223392973000

x8 = -40.4480054150000

x9 = -91.4988860358000

x10 = 100.138265833000

x11 = -5.89048622548000

x12 = 109.563043794000

x13 = 88.3572933822000

x14 = 27.8816348006000

x15 = 62.4391539901000

x16 = 25.5254403104000

x17 = 71.8639319509000

x18 = -426.863901807000

x19 = -25.5254403104000

x20 = 96.9966731796000

x21 = -3.53429173529000

x22 = -41.2334035784000

x23 = -24.7400421470000

x24 = -27.8816348006000

x25 = 60.0829594999000

x26 = 97.7820713430000

x27 = -1105.44791498000

x28 = 56.1559686829000

x29 = -75.7909227679000

x30 = 82.0741080750000

x31 = 53.7997741927000

x32 = -71.8639319509000

x33 = -31.8086256176000

x34 = -109.563043794000

x35 = -62.4391539901000

x36 = -2.74889357189000

x37 = -53.7997741927000

x38 = -90.7134878724000

x39 = -65.5807466437000

x40 = 34.1648201078000

x41 = 5.89048622548000

x42 = -97.7820713430000

x43 = -16.1006623496000

x44 = -9.81747704247000

x45 = 49.8727833757000

x46 = 24.7400421470000

x47 = 31.8086256176000

x48 = 91.4988860358000

x49 = 16.1006623496000

x50 = 22.3838476568000

x51 = 47.5165888855000

x52 = 40.4480054150000

x53 = -56.1559686829000

x54 = 2.74889357189000

x55 = 0.392699081699000

x56 = 78.1471172580000

x57 = 21230.4904539000

x58 = -46.7311907221000

x59 = -49.8727833757000

x60 = 90.7134878724000

x61 = 66.3661448071000

x62 = -21.5984494934000

x63 = -43.5895980686000

x64 = 84.4303025652000

x65 = -93.8550805260000

x66 = 138.622775840000

x67 = -63.2245521535000

x68 = 9.81747704247000

x69 = -38.0918109248000

x70 = -19.2422550032000

x71 = -34.1648201078000

x72 = -69.5077374607000

x73 = -60.0829594999000

x74 = 69.5077374607000

x75 = -87.5718952188000

x76 = -12.1736715327000

x77 = 46.7311907221000

x78 = 38.0918109248000

x79 = 75.7909227679000

x80 = -78.1471172580000

x81 = -68.7223392973000

x82 = 44.3749962320000

x83 = 3.53429173529000

x84 = -18.4568568398000

x85 = -85.2157007286000

x86 = 12.1736715327000

x87 = 18.4568568398000

   
4.97
Elena2008
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