sin(2*x)=sin(x) (уравнение)

Найду корень уравнения: sin(2*x)=sin(x)

Вы ввели

sin(2*x) = sin(x)

$$\sin{\left(2 x \right)} = \sin{\left(x \right)}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     -5*pi
x2 = -----
       3  

$$x_{2} = - \frac{5 \pi}{3}$$

x3 = -pi

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

     -pi 
x4 = ----
      3  

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

     pi
x5 = --
     3 

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

x6 = pi

$$x_{6} = \pi$$

     5*pi
x7 = ----
      3  

$$x_{7} = \frac{5 \pi}{3}$$

Сумма и произведение корней

сумма

        5*pi        pi   pi        5*pi
0 + 0 - ---- - pi - -- + -- + pi + ----
         3          3    3          3  

$$\left(\left(\left(\left(\left(- \frac{5 \pi}{3} + \left(0 + 0\right)\right) - \pi\right) - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \pi\right) + \frac{5 \pi}{3}$$

=

0

$$0$$

произведение

    -5*pi     -pi  pi    5*pi
1*0*-----*-pi*----*--*pi*----
      3        3   3      3  

$$\frac{5 \pi}{3} \pi \frac{\pi}{3} - \frac{\pi}{3} - \pi 1 \cdot 0 \left(- \frac{5 \pi}{3}\right)$$

=

0

$$0$$

Численный ответ

x1 = -45.0294947014537

x2 = -99.4837673636768

x3 = -97.3893722612836

x4 = -72.2566310325652

x5 = -1.0471975511966

x6 = -51.3126800086333

x7 = 57.5958653158129

x8 = -34.5575191894877

x9 = 50.2654824574367

x10 = 26.1799387799149

x11 = 36.6519142918809

x12 = -28.2743338823081

x13 = -65.9734457253857

x14 = 87.9645943005142

x15 = -7.33038285837618

x16 = 80.634211442138

x17 = -37.6991118430775

x18 = -36.6519142918809

x19 = -21.9911485751286

x20 = 42.9350995990605

x21 = 100.530964914873

x22 = 59.6902604182061

x23 = -6.28318530717959

x24 = 28.2743338823081

x25 = -17.8023583703422

x26 = 30.3687289847013

x27 = -15.707963267949

x28 = 78.5398163397448

x29 = 65.9734457253857

x30 = -94.2477796076938

x31 = 13.6135681655558

x32 = -50.2654824574367

x33 = -61.7846555205993

x34 = 68.0678408277789

x35 = -31.4159265358979

x36 = -57.5958653158129

x37 = -78.5398163397448

x38 = 95.2949771588904

x39 = 72.2566310325652

x40 = -19.8967534727354

x41 = 0.0

x42 = 43.9822971502571

x43 = 74.3510261349584

x44 = 53.4070751110265

x45 = -75.398223686155

x46 = 56.5486677646163

x47 = 32.4631240870945

x48 = -70.162235930172

x49 = 21.9911485751286

x50 = 17.8023583703422

x51 = 86.9173967493176

x52 = -43.9822971502571

x53 = -74.3510261349584

x54 = 40.8407044966673

x55 = 61.7846555205993

x56 = 12.5663706143592

x57 = -55.5014702134197

x58 = 11.5191730631626

x59 = -3.14159265358979

x60 = 84.8230016469244

x61 = -26.1799387799149

x62 = -89.0117918517108

x63 = 6.28318530717959

x64 = 34.5575191894877

x65 = -47.1238898038469

x66 = -13.6135681655558

x67 = 63.8790506229925

x68 = -9.42477796076938

x69 = 81.6814089933346

x70 = 51.3126800086333

x71 = 19.8967534727354

x72 = -30.3687289847013

x73 = 7.33038285837618

x74 = -59.6902604182061

x75 = 37.6991118430775

x76 = 76.4454212373516

x77 = 9.42477796076938

x78 = -63.8790506229925

x79 = -80.634211442138

x80 = -53.4070751110265

x81 = 70.162235930172

x82 = 24.0855436775217

x83 = -95.2949771588904

x84 = -68.0678408277789

x85 = 1.0471975511966

x86 = -87.9645943005142

x87 = -879.645943005142

x88 = -24.0855436775217

x89 = 97.3893722612836

x90 = 15.707963267949

x91 = -11.5191730631626

x92 = 94.2477796076938

x93 = -81.6814089933346

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