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Реши любую задачу с помощью нейросети.
$$7 cos{left (2 x + 1 right )} = 2$$
– это простейшее тригонометрическое ур-ние
Разделим обе части ур-ния на 7
Ур-ние превратится в
$$cos{left (2 x + 1 right )} = frac{2}{7}$$
Это ур-ние преобразуется в
$$2 x + 1 = pi n + {acos}{left (frac{2}{7} right )}$$
$$2 x + 1 = pi n – pi + {acos}{left (frac{2}{7} right )}$$
Или
$$2 x + 1 = pi n + {acos}{left (frac{2}{7} right )}$$
$$2 x + 1 = pi n – pi + {acos}{left (frac{2}{7} right )}$$
, где n – любое целое число
Перенесём
$$1$$
в правую часть ур-ния
с противоположным знаком, итого:
$$2 x = pi n – 1 + {acos}{left (frac{2}{7} right )}$$
$$2 x = pi n – pi – 1 + {acos}{left (frac{2}{7} right )}$$
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = frac{pi n}{2} – frac{1}{2} + frac{1}{2} {acos}{left (frac{2}{7} right )}$$
$$x_{2} = frac{pi n}{2} – frac{pi}{2} – frac{1}{2} + frac{1}{2} {acos}{left (frac{2}{7} right )}$$
1 acos(2/7)
x1 = – – + ———
2 2
1 acos(2/7)
x2 = – – + pi – ———
2 2
x1 = -65.8329234127000
x2 = 100.671487228000
x3 = 64.8329234127000
x4 = 15.8484855806000
x5 = 94.3883019204000
x6 = 23.9922189160000
x7 = 89.9656646414000
x8 = -85.9635239596000
x9 = -6.14266299450000
x10 = -43.8417748376000
x11 = 52.2665527983000
x12 = 81.8219313060000
x13 = -57.6891900773000
x14 = 61.6913307591000
x15 = -48.2644121165000
x16 = -4.28211496627000
x17 = -51.4060047701000
x18 = 20.8506262624000
x19 = -73.3971533452000
x20 = 96.2488499486000
x21 = -28.1338115696000
x22 = -1.14052231268000
x23 = 42.8417748376000
x24 = -13.7068929270000
x25 = 67.9745160663000
x26 = 74.2577013735000
x27 = 59.8307827309000
x28 = -50.1249601448000
x29 = 88.1051166132000
x30 = -87.8240719878000
x31 = 0.140522312679000
x32 = 28.4148561950000
x33 = 83.6824793342000
x34 = -94.1072572950000
x35 = -100.390442602000
x36 = 53.5475974237000
x37 = -79.6803386524000
x38 = -12.4258483017000
x39 = -21.8506262624000
x40 = 97.5298945740000
x41 = 2.00107034091000
x42 = -15.5674409553000
x43 = 80.5408866807000
x44 = 22.1316708878000
x45 = 58.5497381055000
x46 = -19.9900782342000
x47 = -92.2467092668000
x48 = 31.5564488486000
x49 = -7.42370761986000
x50 = -63.9723753845000
x51 = 72.3971533452000
x52 = -95.3883019204000
x53 = -70.2555606917000
x54 = 30.2754042232000
x55 = 45.9833674912000
x56 = 3.28211496627000
x57 = 17.7090336089000
x58 = 39.7001821840000
x59 = -59.5497381055000
x60 = 86.8240719878000
x61 = 9.56530027345000
x62 = 44.1228194629000
x63 = 8.28425564809000
x64 = -81.5408866807000
x65 = -37.5585895304000
x66 = 36.5585895304000
x67 = 37.8396341558000
x68 = 66.1139680381000
x69 = 50.4060047701000
x70 = 75.5387459988000
x71 = -26.2732635414000
x72 = -34.4169968768000
x73 = -72.1161087199000
x74 = -29.4148561950000
x75 = -56.4081454519000
x76 = -35.6980415022000
x77 = -90.9656646414000
x78 = 6.42370761986000
x79 = 14.5674409553000
x80 = 159.080703020000
x81 = -41.9812268093000
x82 = -78.3992940271000