3sin5x=0 (уравнение)

Найду корень уравнения: 3sin5x=0

Вы ввели

3*sin(5*x) = 0

$$3 \sin{\left(5 x \right)} = 0$$

Подробное решение

Дано уравнение
$$3 \sin{\left(5 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$3 \sin{\left(5 x \right)} = 0$$

Разделим обе части ур-ния на 3

Ур-ние превратится в
$$\sin{\left(5 x \right)} = 0$$
Это ур-ние преобразуется в
$$5 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$5 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$5 x = 2 \pi n$$
$$5 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$5$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{5}$$
$$x_{2} = \frac{2 \pi n}{5} + \frac{\pi}{5}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     5 

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

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        5 

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

=

pi
--
5 

$$\frac{\pi}{5}$$

произведение

    pi
1*0*--
    5 

$$1 \cdot 0 \frac{\pi}{5}$$

=

0

$$0$$

Численный ответ

x1 = 42.0973415581032

x2 = -91.734505484822

x3 = 84.1946831162065

x4 = -96.1327351998477

x5 = 26.3893782901543

x6 = 11.3097335529233

x7 = 45.867252742411

x8 = -11.9380520836412

x9 = 21.9911485751286

x10 = 48.3805268652828

x11 = -20.1061929829747

x12 = 5.65486677646163

x13 = -98.0176907920015

x14 = -76.026542216873

x15 = -21.9911485751286

x16 = 99.9026463841554

x17 = -37.6991118430775

x18 = 11.9380520836412

x19 = 50.2654824574367

x20 = -32.0442450666159

x21 = -35.8141562509236

x22 = -49.6371639267187

x23 = 18.2212373908208

x24 = -69.7433569096934

x25 = -13.8230076757951

x26 = 72.2566310325652

x27 = -74.1415866247191

x28 = 0.0

x29 = 82.3097275240526

x30 = -1.88495559215388

x31 = -89.8495498926681

x32 = 52.1504380495906

x33 = -3.76991118430775

x34 = -16962.7153737927

x35 = 89.2212313619501

x36 = 96.1327351998477

x37 = 74.1415866247191

x38 = 94.2477796076938

x39 = 101.159283445591

x40 = -59.6902604182061

x41 = 87.9645943005142

x42 = -93.6194610769758

x43 = 54.0353936417444

x44 = 62.2035345410779

x45 = 65.9734457253857

x46 = 38.3274303737955

x47 = 20.1061929829747

x48 = -86.0796387083603

x49 = -33.9292006587698

x50 = 55.9203492338983

x51 = 67.8584013175395

x52 = 5.02654824574367

x53 = -42.0973415581032

x54 = -81.6814089933346

x55 = 40.2123859659494

x56 = -64.0884901332318

x57 = 98.0176907920015

x58 = -25.7610597594363

x59 = 76.026542216873

x60 = -43.9822971502571

x61 = 32.0442450666159

x62 = 64.0884901332318

x63 = 189.752196276824

x64 = 43.9822971502571

x65 = 33.9292006587698

x66 = 77.9114978090269

x67 = -87.9645943005142

x68 = -23.8761041672824

x69 = 28.2743338823081

x70 = -67.8584013175395

x71 = -77.9114978090269

x72 = -27.6460153515902

x73 = 16.3362817986669

x74 = 30.159289474462

x75 = -10.0530964914873

x76 = -55.9203492338983

x77 = -57.8053048260522

x78 = 1.88495559215388

x79 = 408.407044966673

x80 = -45.867252742411

x81 = 10.0530964914873

x82 = 60.318578948924

x83 = -47.7522083345649

x84 = -79.7964534011807

x85 = 86.0796387083603

x86 = -71.6283125018473

x87 = -5.65486677646163

x88 = -15.707963267949

x89 = -52.7787565803085

x90 = 6.28318530717959

x91 = -99.9026463841554

x92 = -54.0353936417444

x93 = 8.16814089933346

x94 = 23.8761041672824

x95 = 70.3716754404114

x96 = -65.9734457253857

x97 = 92.3628240155399

График