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Реши любую задачу с помощью нейросети.
$$- cos{left (2 x right )} + frac{sqrt{3}}{2} = 0$$
– это простейшее тригонометрическое ур-ние
Перенесём sqrt(3)/2 в правую часть ур-ния
с изменением знака при sqrt(3)/2
Получим:
$$- cos{left (2 x right )} – frac{sqrt{3}}{2} + frac{sqrt{3}}{2} = – frac{sqrt{3}}{2}$$
Разделим обе части ур-ния на -1
Ур-ние превратится в
$$cos{left (2 x right )} = frac{sqrt{3}}{2}$$
Это ур-ние преобразуется в
$$2 x = pi n + {acos}{left (frac{sqrt{3}}{2} right )}$$
$$2 x = pi n – pi + {acos}{left (frac{sqrt{3}}{2} right )}$$
Или
$$2 x = pi n + frac{pi}{6}$$
$$2 x = pi n – frac{5 pi}{6}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = frac{pi n}{2} + frac{pi}{12}$$
$$x_{2} = frac{pi n}{2} – frac{5 pi}{12}$$
pi
x1 = —
12
11*pi
x2 = —–
12
x1 = -15.9697626557000
x2 = 30272.1250106000
x3 = -40.5789051089000
x4 = -56.2868683768000
x5 = 15.9697626557000
x6 = -87.7027949127000
x7 = -97.6511716491000
x8 = 53.6688744988000
x9 = -62.5700536840000
x10 = 93.9859802199000
x11 = -9.68657734857000
x12 = -71.9948316448000
x13 = 3.40339204139000
x14 = 100.269165527000
x15 = 132.208690839000
x16 = 138.491876146000
x17 = -63.0936524596000
x18 = 90.8443875663000
x19 = 78.2780169519000
x20 = 46.8620904160000
x21 = -59.9520598060000
x22 = 37.9609112309000
x23 = 6.02138591938000
x24 = -75.6600230740000
x25 = 69.3768377668000
x26 = 31.6777259237000
x27 = -53.6688744988000
x28 = 66.2352451132000
x29 = -65.7116463376000
x30 = -91.3679863419000
x31 = -232.739655753000
x32 = -43.7204977625000
x33 = -515.482994577000
x34 = 18.5877565337000
x35 = 97.6511716491000
x36 = -37.9609112309000
x37 = 25.3945406165000
x38 = 59.9520598060000
x39 = 40.5789051089000
x40 = -41.1025038845000
x41 = -78.2780169519000
x42 = 28.0125344945000
x43 = -100.269165527000
x44 = -28.0125344945000
x45 = -19.1113553093000
x46 = 2.87979326579000
x47 = 12.3045712266000
x48 = -25.3945406165000
x49 = 47.3856891916000
x50 = -47.3856891916000
x51 = 34.2957198017000
x52 = -21.7293491873000
x53 = -103.934356956000
x54 = 75.6600230740000
x55 = 24.8709418409000
x56 = 56.2868683768000
x57 = 68.8532389912000
x58 = 62.5700536840000
x59 = -81.9432083811000
x60 = -69.3768377668000
x61 = -3.40339204139000
x62 = -12.3045712266000
x63 = 5397.51797826000
x64 = -34.2957198017000
x65 = 25430.9307314000
x66 = -93.9859802199000
x67 = -18.5877565337000
x68 = 81.9432083811000
x69 = -31.6777259237000
x70 = 50.0036830696000
x71 = 88.2263936883000
x72 = -84.5612022591000
x73 = 0.261799387799000
x74 = -50.0036830696000
x75 = -85.0848010347000
x76 = -6.02138591938000
x77 = 84.5612022591000
x78 = 44.2440965381000
x79 = 9.68657734857000
x80 = 91.3679863419000
x81 = 71.9948316448000
x82 = 22.2529479629000
