sin(7*x)=0 (уравнение)

Найду корень уравнения: sin(7*x)=0

Вы ввели

sin(7*x) = 0

$$\sin{\left(7 x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(7 x \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\sin{\left(7 x \right)} = 0$$
Это ур-ние преобразуется в
$$7 x = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$7 x = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
Или
$$7 x = 2 \pi n$$
$$7 x = 2 \pi n + \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$7$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{7}$$
$$x_{2} = \frac{2 \pi n}{7} + \frac{\pi}{7}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     7 

$$x_{2} = \frac{\pi}{7}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        7 

$$\left(0 + 0\right) + \frac{\pi}{7}$$

=

pi
--
7 

$$\frac{\pi}{7}$$

произведение

    pi
1*0*--
    7 

$$1 \cdot 0 \frac{\pi}{7}$$

=

0

$$0$$

Численный ответ

x1 = -83.9254037458988

x2 = -75.8470226366679

x3 = 50.2654824574367

x4 = 46.2262919028212

x5 = 52.060678259488

x6 = -35.9039160410262

x7 = 39.9431065956417

x8 = 2.24399475256414

x9 = -41.738302397693

x10 = 78.091017389232

x11 = 83.4766047953859

x12 = -9.87357691128221

x13 = 86.1693984984629

x14 = -65.9734457253857

x15 = 87.9645943005142

x16 = -31.8647254864108

x17 = -37.6991118430775

x18 = -21.9911485751286

x19 = -8.97597901025655

x20 = 34.1087202389749

x21 = 100.082165964361

x22 = 26.030339129744

x23 = 17.9519580205131

x24 = -30.0695296843594

x25 = -101.877361766412

x26 = 20.1959527730772

x27 = 28.2743338823081

x28 = -96.0429754097451

x29 = 30.0695296843594

x30 = -15.707963267949

x31 = 96.0429754097451

x32 = -70.0126362800011

x33 = -92.0037848551297

x34 = -13.9127674658977

x35 = 65.9734457253857

x36 = 76.2958215871807

x37 = -71.8078320820524

x38 = 48.0214877048726

x39 = -17.9519580205131

x40 = -45.7774929523084

x41 = -74.0518268346165

x42 = 38.1479107935903

x43 = -89.7597901025655

x44 = 60.1390593687189

x45 = 68.2174404779498

x46 = -19.7471538225644

x47 = -63.7294509728215

x48 = 32.3135244369236

x49 = 72.2566310325652

x50 = 0.0

x51 = 56.0998688141035

x52 = 43.9822971502571

x53 = 21.9911485751286

x54 = -85.7205995479501

x55 = 24.2351433276927

x56 = 90.2085890530783

x57 = -43.9822971502571

x58 = 92.0037848551297

x59 = -72.7054299830781

x60 = -79.8862131912833

x61 = -53.8558740615393

x62 = 61.9342551707702

x63 = -48.0214877048726

x64 = -32.3135244369236

x65 = 98.2869701623092

x66 = -61.9342551707702

x67 = 6.28318530717959

x68 = -23.7863443771799

x69 = -57.8950646161548

x70 = -93.798980657181

x71 = 12.1175716638463

x72 = -27.8255349317953

x73 = 70.0126362800011

x74 = -1.79519580205131

x75 = 63.2806520223087

x76 = -4.03919055461545

x77 = -59.6902604182061

x78 = 64.1782499233343

x79 = 8.0783811092309

x80 = 16.1567622184618

x81 = -26.030339129744

x82 = 82.1302079438475

x83 = -87.9645943005142

x84 = 54.3046730120521

x85 = -81.6814089933346

x86 = 74.0518268346165

x87 = -39.9431065956417

x88 = -49.8166835069239

x89 = -52.060678259488

x90 = 42.1871013482058

x91 = -5.83438635666676

x92 = -97.8381712117964

x93 = 94.2477796076938

x94 = -67.768641527437

x95 = 4.03919055461545

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