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Реши любую задачу с помощью нейросети.
$$cos^{2}{left (x right )} = frac{1}{10}$$
преобразуем
$$cos^{2}{left (x right )} – frac{1}{10} = 0$$
$$cos^{2}{left (x right )} – frac{1}{10} = 0$$
Сделаем замену
$$w = cos{left (x right )}$$
Это уравнение вида
a*w^2 + b*w + c = 0
Квадратное уравнение можно решить
с помощью дискриминанта.
Корни квадратного уравнения:
$$w_{1} = frac{sqrt{D} – b}{2 a}$$
$$w_{2} = frac{- sqrt{D} – b}{2 a}$$
где D = b^2 – 4*a*c – это дискриминант.
Т.к.
$$a = 1$$
$$b = 0$$
$$c = – frac{1}{10}$$
, то
D = b^2 – 4 * a * c =
(0)^2 – 4 * (1) * (-1/10) = 2/5
Т.к. D > 0, то уравнение имеет два корня.
w1 = (-b + sqrt(D)) / (2*a)
w2 = (-b – sqrt(D)) / (2*a)
или
$$w_{1} = frac{sqrt{10}}{10}$$
$$w_{2} = – frac{sqrt{10}}{10}$$
делаем обратную замену
$$cos{left (x right )} = w$$
Дано уравнение
$$cos{left (x right )} = w$$
– это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = pi n + {acos}{left (w right )}$$
$$x = pi n + {acos}{left (w right )} – pi$$
Или
$$x = pi n + {acos}{left (w right )}$$
$$x = pi n + {acos}{left (w right )} – pi$$
, где n – любое целое число
подставляем w:
$$x_{1} = pi n + {acos}{left (w_{1} right )}$$
$$x_{1} = pi n + {acos}{left (frac{sqrt{10}}{10} right )}$$
$$x_{1} = pi n + {acos}{left (frac{sqrt{10}}{10} right )}$$
$$x_{2} = pi n + {acos}{left (w_{2} right )}$$
$$x_{2} = pi n + {acos}{left (- frac{sqrt{10}}{10} right )}$$
$$x_{2} = pi n + {acos}{left (- frac{sqrt{10}}{10} right )}$$
$$x_{3} = pi n + {acos}{left (w_{1} right )} – pi$$
$$x_{3} = pi n – pi + {acos}{left (frac{sqrt{10}}{10} right )}$$
$$x_{3} = pi n – pi + {acos}{left (frac{sqrt{10}}{10} right )}$$
$$x_{4} = pi n + {acos}{left (w_{2} right )} – pi$$
$$x_{4} = pi n – pi + {acos}{left (- frac{sqrt{10}}{10} right )}$$
$$x_{4} = pi n – pi + {acos}{left (- frac{sqrt{10}}{10} right )}$$
/ ____
|/ 10 |
x2 = – acos|——| + 2*pi
10 /
/ ____
|-/ 10 |
x3 = acos|——–|
10 /
/ ____
|/ 10 |
x4 = acos|——|
10 /
x1 = -89.8571411817000
x2 = -8.17573218837000
x3 = 86.0720474193000
x4 = 77.2907705673000
x5 = -30.1668807635000
x6 = -20.0986016939000
x7 = -23.8836954563000
x8 = -76.6472694586000
x9 = -99.2819191425000
x10 = 13.8154163868000
x11 = 1.89254688119000
x12 = 96.1403264889000
x13 = -32.6649723083000
x14 = -70.3640841514000
x15 = 67.8659926066000
x16 = 76.6472694586000
x17 = -10.6738237332000
x18 = 38.9481576155000
x19 = -67.2224914978000
x20 = 42.0897502691000
x21 = 1619.81276348000
x22 = -33.3084734171000
x23 = -26.3817870011000
x24 = 17.6005101491000
x25 = -92.3552327265000
x26 = -39.5916587243000
x27 = 82.9304547657000
x28 = 45.8748440314000
x29 = 162.113772214000
x30 = -71.0075852602000
x31 = 32.6649723083000
x32 = 7.53223107958000
x33 = 30.1668807635000
x34 = -35.8065649619000
x35 = 60.9393061906000
x36 = -11.3173248420000
x37 = -27.0252881099000
x38 = 92.3552327265000
x39 = -55.2996219922000
x40 = -79.7888621121000
x41 = -49.0164366850000
x42 = 11.3173248420000
x43 = -98.6384180337000
x44 = -337.399459707000
x45 = -83.5739558745000
x46 = -82.9304547657000
x47 = 52.1580293386000
x48 = -52.1580293386000
x49 = -985.211047455000
x50 = -67.8659926066000
x51 = 61.5828072994000
x52 = -61.5828072994000
x53 = 89.8571411817000
x54 = 98.6384180337000
x55 = -57.7977135370000
x56 = -74.1491779138000
x57 = -42.0897502691000
x58 = -13.8154163868000
x59 = 64.0808988442000
x60 = 55.2996219922000
x61 = 83.5739558745000
x62 = 23.2401943475000
x63 = -17.6005101491000
x64 = 23.8836954563000
x65 = 26.3817870011000
x66 = 4.39063842599000
x67 = 48.3729355762000
x68 = -48.3729355762000
x69 = 33.3084734171000
x70 = -4.39063842599000
x71 = 10.6738237332000
x72 = -77.2907705673000
x73 = -466.848259612000
x74 = 8.17573218837000
x75 = 16.9570090403000
x76 = 74.1491779138000
x77 = 54.6561208834000
x78 = 99.2819191425000
x79 = -92.9987338353000
x80 = 39.5916587243000
x81 = 20.0986016939000
x82 = -64.0808988442000
x83 = -45.8748440314000
x84 = -5.03413953478000
x85 = -96.1403264889000
x86 = 14.4589174956000
x87 = -86.0720474193000
x88 = -54.6561208834000
x89 = 70.3640841514000
x90 = -1.89254688119000
