sin(x)=sin(3*x) (уравнение)

Найду корень уравнения: sin(x)=sin(3*x)

Вы ввели

sin(x) = sin(3*x)

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     -3*pi
x2 = -----
       4  

$$x_{2} = - \frac{3 \pi}{4}$$

     -pi 
x3 = ----
      4  

$$x_{3} = - \frac{\pi}{4}$$

     pi
x4 = --
     4 

$$x_{4} = \frac{\pi}{4}$$

     3*pi
x5 = ----
      4  

$$x_{5} = \frac{3 \pi}{4}$$

Сумма и произведение корней

сумма

        3*pi   pi   pi   3*pi
0 + 0 - ---- - -- + -- + ----
         4     4    4     4  

$$\left(\left(\left(- \frac{3 \pi}{4} + \left(0 + 0\right)\right) - \frac{\pi}{4}\right) + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$

=

0

$$0$$

произведение

    -3*pi -pi  pi 3*pi
1*0*-----*----*--*----
      4    4   4   4  

$$\frac{3 \pi}{4} \frac{\pi}{4} - \frac{\pi}{4} 1 \cdot 0 \left(- \frac{3 \pi}{4}\right)$$

=

0

$$0$$

Численный ответ

x1 = -30.6305283725005

x2 = 69.9004365423729

x3 = -72.2566310325652

x4 = 96.6039740978861

x5 = 50.2654824574367

x6 = -46.3384916404494

x7 = -99.7455667514759

x8 = -84.037603483527

x9 = -65.9734457253857

x10 = 87.9645943005142

x11 = 60.4756585816035

x12 = -12.5663706143592

x13 = -37.6991118430775

x14 = -21.9911485751286

x15 = -41.6261026600648

x16 = 100.530964914873

x17 = 30.6305283725005

x18 = 101.316363078271

x19 = 76.1836218495525

x20 = -3.92699081698724

x21 = -280.387144332889

x22 = -47.9092879672443

x23 = 68.329640215578

x24 = -128.805298797182

x25 = -40.0553063332699

x26 = -33.7721210260903

x27 = 25.9181393921158

x28 = 28.2743338823081

x29 = 62.0464549083984

x30 = 74.6128255227576

x31 = -15.707963267949

x32 = -57.3340659280137

x33 = 78.5398163397448

x34 = -76.1836218495525

x35 = 172.002197784041

x36 = -77.7544181763474

x37 = 65.9734457253857

x38 = -51.0508806208341

x39 = -85.6083998103219

x40 = 32.2013246992954

x41 = 84.037603483527

x42 = 91.8915851175014

x43 = -69.9004365423729

x44 = -24.3473430653209

x45 = 40.0553063332699

x46 = 72.2566310325652

x47 = 90.3207887907066

x48 = -18.0641577581413

x49 = 19.6349540849362

x50 = 0.0

x51 = -55.7632696012188

x52 = 43.9822971502571

x53 = 46.3384916404494

x54 = -43.1968989868597

x55 = -91.8915851175014

x56 = 21.9911485751286

x57 = -32.2013246992954

x58 = -13.3517687777566

x59 = -35.3429173528852

x60 = -54.1924732744239

x61 = -43.9822971502571

x62 = 85.6083998103219

x63 = 10.2101761241668

x64 = -25.9181393921158

x65 = 3.92699081698724

x66 = 54.1924732744239

x67 = -63.6172512351933

x68 = 63.6172512351933

x69 = 18.0641577581413

x70 = 6.28318530717959

x71 = -11.7809724509617

x72 = 2.35619449019234

x73 = -90.3207887907066

x74 = 317.300858012569

x75 = -19.6349540849362

x76 = 98.174770424681

x77 = 47.9092879672443

x78 = -59.6902604182061

x79 = 52.621676947629

x80 = -68.329640215578

x81 = 8.63937979737193

x82 = -87.9645943005142

x83 = -62.0464549083984

x84 = 24.3473430653209

x85 = -98.174770424681

x86 = -79.3252145031423

x87 = 41.6261026600648

x88 = -2.35619449019234

x89 = 69.1150383789755

x90 = 94.2477796076938

x91 = -81.6814089933346

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