sin3x=0 (уравнение)

Найду корень уравнения: sin3x=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
0 + 0 + --
        3 

$$\left(0 + 0\right) + \frac{\pi}{3}$$

=

pi
--
3 

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

произведение

    pi
1*0*--
    3 

$$1 \cdot 0 \frac{\pi}{3}$$

=

0

$$0$$

Численный ответ

x1 = 83.7758040957278

x2 = 8.37758040957278

x3 = 63.8790506229925

x4 = -54.4542726622231

x5 = -79.5870138909414

x6 = -83.7758040957278

x7 = 70.162235930172

x8 = 56.5486677646163

x9 = 81.6814089933346

x10 = 98.4365698124802

x11 = 10.471975511966

x12 = -6.28318530717959

x13 = -13.6135681655558

x14 = -59.6902604182061

x15 = 87.9645943005142

x16 = 100.530964914873

x17 = -37.6991118430775

x18 = 85.870199198121

x19 = 65.9734457253857

x20 = 109.955742875643

x21 = 30.3687289847013

x22 = -50.2654824574367

x23 = 46.0766922526503

x24 = 15.707963267949

x25 = 746.651854003174

x26 = 59.6902604182061

x27 = -63.8790506229925

x28 = -29.3215314335047

x29 = 74.3510261349584

x30 = -17.8023583703422

x31 = 52.3598775598299

x32 = -68.0678408277789

x33 = 96.342174710087

x34 = 24.0855436775217

x35 = -31.4159265358979

x36 = 41.8879020478639

x37 = 17.8023583703422

x38 = 68.0678408277789

x39 = -39.7935069454707

x40 = 21.9911485751286

x41 = 50.2654824574367

x42 = -57.5958653158129

x43 = 90.0589894029074

x44 = -70.162235930172

x45 = -15.707963267949

x46 = -48.1710873550435

x47 = 569.675467850949

x48 = 32.4631240870945

x49 = 80.634211442138

x50 = -11.5191730631626

x51 = -61.7846555205993

x52 = -92.1533845053006

x53 = -2.0943951023932

x54 = 28.2743338823081

x55 = 43.9822971502571

x56 = -4.18879020478639

x57 = 92.1533845053006

x58 = -35.6047167406843

x59 = -21.9911485751286

x60 = 94.2477796076938

x61 = 76.4454212373516

x62 = -87.9645943005142

x63 = -55.5014702134197

x64 = -90.0589894029074

x65 = 48.1710873550435

x66 = 4.18879020478639

x67 = 37.6991118430775

x68 = -28.2743338823081

x69 = 2.0943951023932

x70 = -98.4365698124802

x71 = -26.1799387799149

x72 = 39.7935069454707

x73 = -46.0766922526503

x74 = -24.0855436775217

x75 = -33.5103216382911

x76 = -41.8879020478639

x77 = -65.9734457253857

x78 = -94.2477796076938

x79 = 6.28318530717959

x80 = 61.7846555205993

x81 = 78.5398163397448

x82 = 19.8967534727354

x83 = 0.0

x84 = 72.2566310325652

x85 = -10.471975511966

x86 = -99.4837673636768

x87 = -19.8967534727354

x88 = -77.4926187885482

x89 = -8.37758040957278

x90 = -43.9822971502571

x91 = 26.1799387799149

x92 = -85.870199198121

x93 = -81.6814089933346

x94 = 54.4542726622231

x95 = -72.2566310325652

x96 = 34.5575191894877

График