tan(pi*(x+6)/3)=sqrt(3) (уравнение)

Найду корень уравнения: tan(pi*(x+6)/3)=sqrt(3)

Вы ввели

   /pi*(x + 6)\     ___
tan|----------| = \/ 3 
   \    3     /        

$$\tan{\left(\frac{\pi \left(x + 6\right)}{3} \right)} = \sqrt{3}$$

Подробное решение

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

Быстрый ответ

x1 = 1

$$x_{1} = 1$$

Сумма и произведение корней

сумма

1

$$1$$

=

1

$$1$$

произведение

1

$$1$$

=

1

$$1$$

Численный ответ

x1 = -77.0

x2 = 40.0

x3 = 94.0

x4 = -83.0

x5 = -59.0

x6 = 97.0

x7 = -98.0

x8 = 31.0

x9 = -11.0

x10 = 79.0

x11 = 58.0

x12 = 34.0

x13 = 52.0

x14 = -71.0

x15 = 100.0

x16 = -47.0

x17 = 25.0

x18 = -62.0

x19 = 16.0

x20 = 67.0

x21 = -44.0

x22 = -80.0

x23 = -20.0

x24 = 88.0

x25 = 61.0

x26 = 10.0

x27 = 76.0

x28 = -2.0

x29 = -53.0

x30 = -92.0

x31 = 13.0

x32 = 55.0

x33 = -32.0

x34 = 73.0

x35 = -29.0

x36 = -23.0

x37 = -65.0

x38 = 49.0

x39 = 85.0

x40 = -26.0

x41 = -86.0

x42 = 19.0

x43 = -17.0

x44 = 82.0

x45 = -95.0

x46 = 1.0

x47 = 37.0

x48 = -35.0

x49 = 22.0

x50 = 46.0

x51 = 64.0

x52 = -68.0

x53 = 91.0

x54 = 28.0

x55 = -56.0

x56 = -38.0

x57 = 70.0

x58 = 4.0

x59 = 7.0

x60 = 43.0

x61 = -41.0

x62 = -74.0

x63 = -50.0

x64 = -5.0

x65 = -8.0

x66 = -89.0

x67 = -14.0

График