sin(3x+pi)=0 (уравнение)

Найду корень уравнения: sin(3x+pi)=0

Вы ввели

sin(3*x + pi) = 0

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

Подробное решение

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

с изменением знака при 0

Получим:
$$\sin{\left(3 x + \pi \right)} = 0$$

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\sin{\left(3 x \right)} = 0$$
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 = 59.6902604182061

x2 = 74.3510261349584

x3 = 21.9911485751286

x4 = -55.5014702134197

x5 = -87.9645943005142

x6 = 83.7758040957278

x7 = 56.5486677646163

x8 = -99.4837673636768

x9 = 26.1799387799149

x10 = -33.5103216382911

x11 = -43.9822971502571

x12 = -85.870199198121

x13 = 48.1710873550435

x14 = -90.0589894029074

x15 = 39.7935069454707

x16 = 6.28318530717959

x17 = 68.0678408277789

x18 = 746.651854003174

x19 = 72.2566310325652

x20 = 10.471975511966

x21 = 2.0943951023932

x22 = -72.2566310325652

x23 = -79.5870138909414

x24 = -26.1799387799149

x25 = -21.9911485751286

x26 = 54.4542726622231

x27 = -31.4159265358979

x28 = -48.1710873550435

x29 = 98.4365698124802

x30 = -92.1533845053006

x31 = -4.18879020478639

x32 = -98.4365698124802

x33 = -39.7935069454707

x34 = 34.5575191894877

x35 = -10.471975511966

x36 = -63.8790506229925

x37 = -94.2477796076938

x38 = -24.0855436775217

x39 = 80.634211442138

x40 = 90.0589894029074

x41 = -50.2654824574367

x42 = 15.707963267949

x43 = -35.6047167406843

x44 = 96.342174710087

x45 = 63.8790506229925

x46 = 8.37758040957278

x47 = 24.0855436775217

x48 = 0.0

x49 = -13.6135681655558

x50 = -8.37758040957278

x51 = 19.8967534727354

x52 = -37.6991118430775

x53 = 61.7846555205993

x54 = 65.9734457253857

x55 = 85.870199198121

x56 = -61.7846555205993

x57 = 81.6814089933346

x58 = 17.8023583703422

x59 = 109.955742875643

x60 = -19.8967534727354

x61 = -41.8879020478639

x62 = 41.8879020478639

x63 = -81.6814089933346

x64 = -54.4542726622231

x65 = 28.2743338823081

x66 = -46.0766922526503

x67 = 100.530964914873

x68 = -29.3215314335047

x69 = 52.3598775598299

x70 = -77.4926187885482

x71 = 70.162235930172

x72 = -2.0943951023932

x73 = 4.18879020478639

x74 = 76.4454212373516

x75 = -70.162235930172

x76 = -57.5958653158129

x77 = 87.9645943005142

x78 = 569.675467850949

x79 = -11.5191730631626

x80 = 32.4631240870945

x81 = 37.6991118430775

x82 = -28.2743338823081

x83 = -6.28318530717959

x84 = 43.9822971502571

x85 = -17.8023583703422

x86 = 94.2477796076938

x87 = -68.0678408277789

x88 = -59.6902604182061

x89 = -15.707963267949

x90 = 30.3687289847013

x91 = 78.5398163397448

x92 = 92.1533845053006

x93 = -65.9734457253857

x94 = 50.2654824574367

x95 = 46.0766922526503

x96 = -83.7758040957278

График