sin(pi*x)=-1 (уравнение)

Найду корень уравнения: sin(pi*x)=-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
$$\pi x = 2 \pi n - \frac{\pi}{2}$$
$$\pi x = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\pi$$
получим ответ:
$$x_{1} = \frac{2 \pi n - \frac{\pi}{2}}{\pi}$$
$$x_{2} = \frac{2 \pi n + \frac{3 \pi}{2}}{\pi}$$

Сумма и произведение корней

сумма

0 - 1/2 + 3/2

$$\left(- \frac{1}{2} + 0\right) + \frac{3}{2}$$

=

1

$$1$$

произведение

1*-1/2*3/2

$$1 \left(- \frac{1}{2}\right) \frac{3}{2}$$

=

-3/4

$$- \frac{3}{4}$$

Быстрый ответ

x1 = -1/2

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

x2 = 3/2

$$x_{2} = \frac{3}{2}$$

Численный ответ

x1 = 49.5000001413479

x2 = -50.4999998586521

x3 = 25.5000001413479

x4 = -10.4999998586521

x5 = -90.4999998586521

x6 = 79.5000001413479

x7 = 67.5000001413479

x8 = 59.5000001413479

x9 = 3.50000014134786

x10 = -38.4999998586521

x11 = 75.5000001413479

x12 = 83.5000001413479

x13 = -48.4999998586521

x14 = -56.4999998586521

x15 = -62.4999998586521

x16 = -18.4999998586521

x17 = 51.5000001413479

x18 = 97.5000001413479

x19 = -68.4999998586521

x20 = 21.5000001413479

x21 = 89.5000001413479

x22 = 99.5000001413479

x23 = 7.50000014134786

x24 = -36.4999998586521

x25 = -82.4999998586521

x26 = 39.5000001413479

x27 = -70.4999998586521

x28 = 15.5000001413479

x29 = 23.5000001413479

x30 = 13.5000001413479

x31 = 17.5000001413479

x32 = 61.5000001413479

x33 = 91.5000001413479

x34 = -22.4999998586521

x35 = -2.49999985865214

x36 = -92.4999998586521

x37 = 35.5000001413479

x38 = -80.4999998586521

x39 = -4.49999985865214

x40 = -88.4999998586521

x41 = -14.4999998586521

x42 = 45.5000001413479

x43 = -8.49999985865214

x44 = -76.4999998586521

x45 = -66.4999998586521

x46 = -0.499999858652136

x47 = -12.4999998586521

x48 = -28.4999998586521

x49 = 1.50000014134786

x50 = -84.4999998586521

x51 = 95.5000001413479

x52 = 71.5000001413479

x53 = -74.4999998586521

x54 = 57.5000001413479

x55 = -60.4999998586521

x56 = -34.4999998586521

x57 = -98.4999998586521

x58 = 5.50000014134786

x59 = 31.5000001413479

x60 = -64.4999998586521

x61 = -16.4999998586521

x62 = -20.4999998586521

x63 = 73.5000001413479

x64 = 41.5000001413479

x65 = 77.5000001413479

x66 = 55.5000001413479

x67 = -30.4999998586521

x68 = -40.4999998586521

x69 = 33.5000001413479

x70 = -6.49999985865214

x71 = -24.4999998586521

x72 = 85.5000001413479

x73 = 11.5000001413479

x74 = -26.4999998586521

x75 = -86.4999998586521

x76 = 93.5000001413479

x77 = -72.4999998586521

x78 = 65.5000001413479

x79 = 47.5000001413479

x80 = -96.4999998586521

x81 = 69.5000001413479

x82 = -54.4999998586521

x83 = -94.4999998586521

x84 = -58.4999998586521

x85 = -52.4999998586521

x86 = -32.4999998586521

x87 = 53.5000001413479

x88 = 43.5000001413479

x89 = -100.499999858652

x90 = -46.4999998586521

x91 = -78.4999998586521

x92 = 63.5000001413479

x93 = 87.5000001413479

x94 = -44.4999998586521

x95 = 81.5000001413479

x96 = 29.5000001413479

x97 = 37.5000001413479

x98 = -42.4999998586521

x99 = 27.5000001413479

x100 = 19.5000001413479

x101 = 9.50000014134786

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