cos(4*x)=sqrt(3)/2

$$cos{left (4 x right )} = frac{sqrt{3}}{2}$$

Дано уравнение
$$cos{left (4 x right )} = frac{sqrt{3}}{2}$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = pi n + {acos}{left (frac{sqrt{3}}{2} right )}$$
$$4 x = pi n – pi + {acos}{left (frac{sqrt{3}}{2} right )}$$
Или
$$4 x = pi n + frac{pi}{6}$$
$$4 x = pi n – frac{5 pi}{6}$$
, где n – любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = frac{pi n}{4} + frac{pi}{24}$$
$$x_{2} = frac{pi n}{4} – frac{5 pi}{24}$$

pi
x1 = —
24

$$x_{1} = frac{pi}{24}$$

11*pi
x2 = —–
24

$$x_{2} = frac{11 pi}{24}$$

x1 = -97.5202719552000

x2 = 12.4354709205000

x3 = -79.9797129726000

x4 = -56.6795674585000

x5 = -67.6751417461000

x6 = 55.1087711317000

x7 = 50.1345827635000

x8 = 28.1434341884000

x9 = -43.8513974564000

x10 = -81.8123086872000

x11 = -1.70169602069000

x12 = -28.1434341884000

x13 = 45.6839931710000

x14 = -75.5291233801000

x15 = 20.2894525544000

x16 = 80.2415123604000

x17 = -45.6839931710000

x18 = 72.1257313387000

x19 = -42.2806011296000

x20 = -65.8425460315000

x21 = 26.8344372494000

x22 = -29.7142305152000

x23 = -73.6965276655000

x24 = 18.7186562276000

x25 = -20.2894525544000

x26 = 1.70169602069000

x27 = -37.8300115370000

x28 = 64.2717497047000

x29 = 73.9583270533000

x30 = 56.4177680707000

x31 = -21.8602488812000

x32 = 100.400065221000

x33 = -50.1345827635000

x34 = -89.6662903212000

x35 = 59.8211601121000

x36 = -160.352125027000

x37 = 95.9494756284000

x38 = 15.8388629618000

x39 = 22.1220482690000

x40 = 88.0954939944000

x41 = -57.9885643975000

x42 = 0.130899693900000

x43 = 67.6751417461000

x44 = -95.6876762406000

x45 = 37.8300115370000

x46 = 4.58148928649000

x47 = 6.15228561328000

x48 = 44.1131968442000

x49 = 66.1043454193000

x50 = 23.6928445958000

x51 = -22.1220482690000

x52 = -100.661864609000

x53 = 36.2592152102000

x54 = 86.2628982798000

x55 = 94.1168799138000

x56 = -94.1168799138000

x57 = -84.9539013408000

x58 = -87.8336946066000

x59 = -7.72308194007000

x60 = 81.8123086872000

x61 = 48.5637864367000

x62 = -35.9974158224000

x63 = 7.98488132787000

x64 = -51.7053790903000

x65 = 29.9760299030000

x66 = -72.1257313387000

x67 = -86.2628982798000

x68 = 89.6662903212000

x69 = -78.6707160336000

x70 = 58.2503637853000

x71 = 102.232660936000

x72 = 14.2680666351000

x73 = -64.2717497047000

x74 = -39.4008078638000

x75 = -15.8388629618000

x76 = -83.1213056262000

x77 = 34.4266194956000

x78 = -53.5379748049000

x79 = -59.8211601121000

x80 = -17.4096592886000

x81 = -14.0062672473000

x82 = -31.5468262298000

x83 = 26.5726378616000

x84 = 42.2806011296000

x85 = -9.55567765467000

x86 = -6.15228561328000

x87 = 70.5549350119000

x88 = 51.9671784781000

x89 = -23.6928445958000

x90 = 92.5460835870000

x91 = 35.9974158224000

x92 = 78.4089166458000