cos(2pi*x)=-1 (уравнение)

Найду корень уравнения: cos(2pi*x)=-1

Вы ввели

cos(2*pi*x) = -1

$$\cos{\left(2 \pi x \right)} = -1$$

Подробное решение

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

Сумма и произведение корней

сумма

0 + 1/2

$$0 + \frac{1}{2}$$

=

1/2

$$\frac{1}{2}$$

произведение

1*1/2

$$1 \cdot \frac{1}{2}$$

=

1/2

$$\frac{1}{2}$$

Быстрый ответ

x1 = 1/2

$$x_{1} = \frac{1}{2}$$

Численный ответ

x1 = -41.5

x2 = 4.5

x3 = -91.5

x4 = 12.5

x5 = -15.5

x6 = -1.5

x7 = -61.5

x8 = -55.5

x9 = -71.5

x10 = -17.5

x11 = 18.5

x12 = 92.5

x13 = 52.5

x14 = 54.5

x15 = 2.5

x16 = 56.5

x17 = 60.5

x18 = 10.5

x19 = 86.5

x20 = -35.5

x21 = 50.5

x22 = -49.5

x23 = -25.5

x24 = 0.5

x25 = -43.5

x26 = -77.5

x27 = 96.5

x28 = 34.5

x29 = -63.5

x30 = 38.5

x31 = 78.5

x32 = 20.5

x33 = 26.5

x34 = 82.5

x35 = -11.5

x36 = -23.5

x37 = -47.5

x38 = 100.5

x39 = -27.5

x40 = 70.5

x41 = -65.5

x42 = 84.5

x43 = -99.5

x44 = -29.5

x45 = 48.5

x46 = -97.5

x47 = 94.5

x48 = -89.5

x49 = -51.5

x50 = -75.5

x51 = -59.5

x52 = 44.5

x53 = 76.5

x54 = -93.5

x55 = 90.5

x56 = -9.5

x57 = -57.5

x58 = 66.5

x59 = 42.5

x60 = 22.5

x61 = -3.5

x62 = -33.5

x63 = -83.5

x64 = 30.5

x65 = -85.5

x66 = 24.5

x67 = -53.5

x68 = 6.5

x69 = -87.5

x70 = 16.5

x71 = 14.5

x72 = -79.5

x73 = 98.5

x74 = 74.5

x75 = -37.5

x76 = -81.5

x77 = -7.5

x78 = 80.5

x79 = -13.5

x80 = -31.5

x81 = 28.5

x82 = 64.5

x83 = -5.5

x84 = -45.5

x85 = -67.5

x86 = 88.5

x87 = -69.5

x88 = 8.5

x89 = -19.5

x90 = 40.5

x91 = -73.5

x92 = 32.5

x93 = -21.5

x94 = 58.5

x95 = 36.5

x96 = 68.5

x97 = 72.5

x98 = 62.5

x99 = 46.5

x100 = -95.5

x101 = -39.5

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