cos(2*x-pi/4)=0

Дано

$$\cos{\left (2 x — \frac{\pi}{4} \right )} = 0$$
Подробное решение
Дано уравнение
$$\cos{\left (2 x — \frac{\pi}{4} \right )} = 0$$
— это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left (2 x — \frac{\pi}{4} \right )} = 0$$
Это ур-ние преобразуется в
$$2 x + \frac{\pi}{4} = 2 \pi n + {asin}{\left (0 \right )}$$
$$2 x + \frac{\pi}{4} = 2 \pi n — {asin}{\left (0 \right )} + \pi$$
Или
$$2 x + \frac{\pi}{4} = 2 \pi n$$
$$2 x + \frac{\pi}{4} = 2 \pi n + \pi$$
, где n — любое целое число
Перенесём
$$\frac{\pi}{4}$$
в правую часть ур-ния
с противоположным знаком, итого:
$$2 x = 2 \pi n — \frac{\pi}{4}$$
$$2 x = 2 \pi n + \frac{3 \pi}{4}$$
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \pi n — \frac{\pi}{8}$$
$$x_{2} = \pi n + \frac{3 \pi}{8}$$

Ответ
Читайте также  5*x=-140

-pi
x1 = —-
8

$$x_{1} = — \frac{\pi}{8}$$

3*pi
x2 = —-
8

$$x_{2} = \frac{3 \pi}{8}$$
Численный ответ

x1 = 93.8550805260000

x2 = -82.0741080750000

x3 = 84.4303025652000

x4 = -52.2289778659000

x5 = 32.5940237810000

x6 = -47.5165888855000

x7 = 68.7223392973000

x8 = -58.5121631731000

x9 = -61.6537558267000

x10 = -91.4988860358000

x11 = 100.138265833000

x12 = -55.3705705195000

x13 = 27.8816348006000

x14 = -0.392699081699000

x15 = 26.3108384738000

x16 = 71.8639319509000

x17 = 42.0188017418000

x18 = -44.3749962320000

x19 = 87.5718952188000

x20 = 4.31968989869000

x21 = -25.5254403104000

x22 = 76.5763209313000

x23 = -3.53429173529000

x24 = -41.2334035784000

x25 = -45.9457925588000

x26 = 56.1559686829000

x27 = 65.5807466437000

x28 = -75.7909227679000

x29 = 9.03207887907000

x30 = -74.2201264411000

x31 = -17.6714586764000

x32 = -31.8086256176000

x33 = -83.6449044018000

x34 = -11.3882733693000

x35 = -53.7997741927000

x36 = 34.1648201078000

x37 = -184.175869317000

x38 = 5.89048622548000

x39 = 98.5674695064000

x40 = -97.7820713430000

x41 = 35.7356164346000

x42 = -88.3572933822000

x43 = -16.1006623496000

x44 = -9.81747704247000

x45 = 49.8727833757000

x46 = 70.2931356241000

x47 = 24.7400421470000

x48 = 92.2842841992000

x49 = -33.3794219444000

x50 = -67.9369411339000

x51 = -99.3528676698000

x52 = 40.4480054150000

x53 = -89.9280897090000

x54 = 2.74889357189000

x55 = 78.1471172580000

x56 = -1.96349540849000

x57 = -77.3617190946000

x58 = -5389.79489631000

x59 = 86.0010988920000

x60 = 90.7134878724000

x61 = -30.2378292908000

x62 = 62.4391539901000

x63 = -80.5033117482000

x64 = 57.7267650097000

x65 = -38.0918109248000

x66 = 21.5984494934000

x67 = -19.2422550032000

x68 = -36.5210145980000

x69 = -69.5077374607000

x70 = -23.9546439836000

x71 = -60.0829594999000

x72 = 43.5895980686000

x73 = -96.2112750162000

x74 = -39.6626072516000

x75 = 46.7311907221000

x76 = -66.3661448071000

x77 = 79.7179135848000

x78 = 10.6028752059000

x79 = -8.24668071567000

x80 = 54.5851723561000

x81 = 20.0276531666000

x82 = -22.3838476568000

x83 = 13.7444678595000

x84 = 64.0099503169000

x85 = 48.3019870489000

x86 = 12.1736715327000

x87 = 18.4568568398000

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