sin(pi*x/3)=0.5 (уравнение)

Найду корень уравнения: sin(pi*x/3)=0.5

Вы ввели

   /pi*x\      
sin|----| = 1/2
   \ 3  /      

$$\sin{\left(\frac{\pi x}{3} \right)} = \frac{1}{2}$$

Подробное решение

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

Сумма и произведение корней

сумма

0 + 1/2 + 5/2

$$\left(0 + \frac{1}{2}\right) + \frac{5}{2}$$

=

3

$$3$$

произведение

1*1/2*5/2

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

=

5/4

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

Быстрый ответ

x1 = 1/2

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

x2 = 5/2

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

Численный ответ

x1 = 38.5

x2 = -17.5

x3 = 6.5

x4 = -75.5

x5 = 50.5

x6 = 8.5

x7 = 72.5

x8 = 54.5

x9 = -21.5

x10 = 32.5

x11 = 68.5

x12 = -47.5

x13 = 26.5

x14 = -83.5

x15 = 60.5

x16 = -101.5

x17 = 62.5

x18 = 84.5

x19 = 36.5

x20 = 98.5

x21 = -65.5

x22 = -39.5

x23 = 48.5

x24 = -77.5

x25 = 86.5

x26 = -45.5

x27 = 56.5

x28 = -59.5

x29 = -87.5

x30 = -15.5

x31 = 74.5

x32 = -95.5

x33 = -35.5

x34 = 18.5

x35 = -57.5

x36 = 92.5

x37 = -53.5

x38 = 80.5

x39 = -99.5

x40 = 78.5

x41 = -3.5

x42 = 14.5

x43 = -93.5

x44 = -9.5

x45 = -33.5

x46 = -51.5

x47 = -5.5

x48 = 0.5

x49 = 2.5

x50 = 66.5

x51 = -63.5

x52 = -89.5

x53 = -69.5

x54 = 44.5

x55 = 96.5

x56 = 90.5

x57 = -27.5

x58 = 42.5

x59 = 20.5

x60 = -41.5

x61 = -11.5

x62 = -29.5

x63 = -23.5

x64 = -81.5

x65 = 24.5

x66 = 12.5

x67 = 30.5

x68 = -71.5

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