sin(3x)=0 (уравнение)

Найду корень уравнения: sin(3x)=0

Вы ввели

sin(3*x) = 0

$$\sin{\left(3 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(3 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(3 x \right)} = 0$$
Это ур-ние преобразуется в
$$3 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$3 x = 2 \pi n$$
$$3 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{3}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{3}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     3 

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

Сумма и произведение корней

сумма

pi
--
3 

$$\frac{\pi}{3}$$

=

pi
--
3 

$$\frac{\pi}{3}$$

произведение

  pi
0*--
  3 

$$0 \frac{\pi}{3}$$

=

0

$$0$$

Численный ответ

x1 = -17.8023583703422

x2 = -8.37758040957278

x3 = -43.9822971502571

x4 = 74.3510261349584

x5 = 72.2566310325652

x6 = -79.5870138909414

x7 = 96.342174710087

x8 = 30.3687289847013

x9 = -26.1799387799149

x10 = 24.0855436775217

x11 = 569.675467850949

x12 = -15.707963267949

x13 = 98.4365698124802

x14 = 92.1533845053006

x15 = 19.8967534727354

x16 = -77.4926187885482

x17 = -29.3215314335047

x18 = 21.9911485751286

x19 = -54.4542726622231

x20 = 109.955742875643

x21 = 39.7935069454707

x22 = 80.634211442138

x23 = 17.8023583703422

x24 = -68.0678408277789

x25 = 85.870199198121

x26 = 15.707963267949

x27 = -98.4365698124802

x28 = 50.2654824574367

x29 = 26.1799387799149

x30 = 2.0943951023932

x31 = -50.2654824574367

x32 = -65.9734457253857

x33 = -24.0855436775217

x34 = 0.0

x35 = 46.0766922526503

x36 = -63.8790506229925

x37 = 65.9734457253857

x38 = -31.4159265358979

x39 = 54.4542726622231

x40 = -85.870199198121

x41 = 81.6814089933346

x42 = -59.6902604182061

x43 = -6.28318530717959

x44 = 68.0678408277789

x45 = -4.18879020478639

x46 = -33.5103216382911

x47 = -28.2743338823081

x48 = -35.6047167406843

x49 = -46.0766922526503

x50 = -2.0943951023932

x51 = -90.0589894029074

x52 = -21.9911485751286

x53 = 83.7758040957278

x54 = 52.3598775598299

x55 = 6.28318530717959

x56 = -19.8967534727354

x57 = 32.4631240870945

x58 = -94.2477796076938

x59 = 41.8879020478639

x60 = -92.1533845053006

x61 = 76.4454212373516

x62 = -48.1710873550435

x63 = -81.6814089933346

x64 = 8.37758040957278

x65 = -99.4837673636768

x66 = -39.7935069454707

x67 = -57.5958653158129

x68 = 48.1710873550435

x69 = 87.9645943005142

x70 = 37.6991118430775

x71 = -13.6135681655558

x72 = 78.5398163397448

x73 = 34.5575191894877

x74 = -72.2566310325652

x75 = 43.9822971502571

x76 = 746.651854003174

x77 = -61.7846555205993

x78 = 100.530964914873

x79 = -11.5191730631626

x80 = -37.6991118430775

x81 = -41.8879020478639

x82 = 56.5486677646163

x83 = -87.9645943005142

x84 = -10.471975511966

x85 = 61.7846555205993

x86 = -83.7758040957278

x87 = 63.8790506229925

x88 = -70.162235930172

x89 = 28.2743338823081

x90 = 90.0589894029074

x91 = 4.18879020478639

x92 = 59.6902604182061

x93 = -55.5014702134197

x94 = 10.471975511966

x95 = 70.162235930172

x96 = 94.2477796076938

График