sin(pix)=1 (уравнение)

Найду корень уравнения: sin(pix)=1

Вы ввели

sin(pi*x) = 1

$$\sin{\left(\pi x \right)} = 1$$

Подробное решение

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

Быстрый ответ

x1 = 1/2

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

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

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

Численный ответ

x1 = -43.5000001246852

x2 = 56.4999998753148

x3 = -71.5000001246852

x4 = -73.5000001246852

x5 = -83.5000001246852

x6 = -81.5000001246852

x7 = 50.4999998753148

x8 = -37.5000001246852

x9 = 48.4999998753148

x10 = 100.499999875315

x11 = -69.5000001246852

x12 = -63.5000001246852

x13 = 4.49999987531484

x14 = 64.4999998753148

x15 = -27.5000001246852

x16 = 8.49999987531485

x17 = -7.50000012468516

x18 = -19.5000001246852

x19 = -95.5000001246852

x20 = -49.5000001246852

x21 = 90.4999998753148

x22 = 46.4999998753148

x23 = 6.49999987531484

x24 = -67.5000001246852

x25 = -53.5000001246852

x26 = -93.5000001246852

x27 = 0.499999875314845

x28 = 86.4999998753148

x29 = 82.4999998753148

x30 = 76.4999998753148

x31 = -99.5000001246852

x32 = 22.4999998753148

x33 = -21.5000001246852

x34 = -87.5000001246852

x35 = 54.4999998753148

x36 = -85.5000001246852

x37 = -25.5000001246852

x38 = 74.4999998753148

x39 = -89.5000001246852

x40 = 42.4999998753148

x41 = -29.5000001246852

x42 = 32.4999998753148

x43 = -97.5000001246852

x44 = 52.4999998753148

x45 = 72.4999998753148

x46 = 12.4999998753148

x47 = 58.4999998753148

x48 = -13.5000001246852

x49 = -15.5000001246852

x50 = 44.4999998753148

x51 = 88.4999998753148

x52 = -55.5000001246852

x53 = 10.4999998753148

x54 = -41.5000001246852

x55 = 14.4999998753148

x56 = 62.4999998753148

x57 = -91.5000001246852

x58 = 66.4999998753148

x59 = 92.4999998753148

x60 = 38.4999998753148

x61 = -61.5000001246852

x62 = 26.4999998753148

x63 = -45.5000001246852

x64 = -11.5000001246852

x65 = -23.5000001246852

x66 = 2.49999987531484

x67 = -47.5000001246852

x68 = 36.4999998753148

x69 = -9.50000012468515

x70 = -3.50000012468516

x71 = -5.50000012468516

x72 = 96.4999998753148

x73 = -35.5000001246852

x74 = -33.5000001246852

x75 = -17.5000001246852

x76 = -57.5000001246852

x77 = 60.4999998753148

x78 = 34.4999998753148

x79 = 84.4999998753148

x80 = 94.4999998753148

x81 = 30.4999998753148

x82 = 20.4999998753148

x83 = 16.4999998753148

x84 = -65.5000001246852

x85 = -39.5000001246852

x86 = 24.4999998753148

x87 = -77.5000001246852

x88 = -51.5000001246852

x89 = 18.4999998753148

x90 = 28.4999998753148

x91 = -79.5000001246852

x92 = -75.5000001246852

x93 = 40.4999998753148

x94 = 78.4999998753148

x95 = 70.4999998753148

x96 = -1.50000012468516

x97 = -59.5000001246852

x98 = 98.4999998753148

x99 = -31.5000001246852

x100 = 80.4999998753148

x101 = 68.4999998753148

График