sin(pi*(5*x+15)/6)=1/2 (уравнение)

Найду корень уравнения: sin(pi*(5*x+15)/6)=1/2

Вы ввели

   /pi*(5*x + 15)\      
sin|-------------| = 1/2
   \      6      /      

$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(\frac{\pi \left(5 x + 15\right)}{6} \right)} = \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{5 \pi x}{6} = \pi n + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
$$\frac{5 \pi x}{6} = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{2} \right)}$$
Или
$$\frac{5 \pi x}{6} = \pi n + \frac{\pi}{3}$$
$$\frac{5 \pi x}{6} = \pi n - \frac{2 \pi}{3}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{5 \pi}{6}$$
получим ответ:
$$x_{1} = \frac{6 \left(\pi n + \frac{\pi}{3}\right)}{5 \pi}$$
$$x_{2} = \frac{6 \left(\pi n - \frac{2 \pi}{3}\right)}{5 \pi}$$

Быстрый ответ

x1 = 2/5

$$x_{1} = \frac{2}{5}$$

x2 = 2

$$x_{2} = 2$$

Сумма и произведение корней

сумма

0 + 2/5 + 2

$$\left(0 + \frac{2}{5}\right) + 2$$

=

12/5

$$\frac{12}{5}$$

произведение

1*2/5*2

$$1 \cdot \frac{2}{5} \cdot 2$$

=

4/5

$$\frac{4}{5}$$

Численный ответ

x1 = 82.0

x2 = 46.0

x3 = 50.8

x4 = 2.0

x5 = 50.0

x6 = 0.4

x7 = 70.0

x8 = 91.6

x9 = -23.6

x10 = -2.0

x11 = 100.4

x12 = -19.6

x13 = -34.0

x14 = 67.6

x15 = 52.4

x16 = 86.8

x17 = 12.4

x18 = -16.4

x19 = 31.6

x20 = 218.8

x21 = 55.6

x22 = 88.4

x23 = -70.0

x24 = -95.6

x25 = 24.4

x26 = 36.4

x27 = 72.4

x28 = 84.4

x29 = -46.0

x30 = 170.8

x31 = -76.4

x32 = 76.4

x33 = 40.4

x34 = 60.4

x35 = 38.0

x36 = -64.4

x37 = -59.6

x38 = -71.6

x39 = -38.0

x40 = -74.0

x41 = 94.0

x42 = -43.6

x43 = -28.4

x44 = -31.6

x45 = 74.8

x46 = 58.0

x47 = 194.8

x48 = 28.4

x49 = 48.4

x50 = -91.6

x51 = 79.6

x52 = -62.0

x53 = 122.8

x54 = 22.0

x55 = 158.8

x56 = 98.8

x57 = -7.6

x58 = 146.8

x59 = -14.0

x60 = -52.4

x61 = -79.6

x62 = 14.0

x63 = 62.0

x64 = 98.0

x65 = -26.0

x66 = 10.0

x67 = -82.0

x68 = -10.0

x69 = 110.8

x70 = -35.6

x71 = -86.0

x72 = 182.8

x73 = -100.4

x74 = -88.4

x75 = -67.6

x76 = 134.8

x77 = 74.0

x78 = -58.0

x79 = -11.6

x80 = 43.6

x81 = 86.0

x82 = 62.8

x83 = -50.0

x84 = 26.0

x85 = -55.6

x86 = -83.6

x87 = 16.4

x88 = -47.6

x89 = 34.0

x90 = -94.0

x91 = 4.4

x92 = -4.4

x93 = -40.4

x94 = -22.0

x95 = 96.4

x96 = 7.6

x97 = 64.4

x98 = 38.8

x99 = 206.8

x100 = 19.6

x101 = -98.0

График