sin(2*x)=cos(x) (уравнение)

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

Вы ввели

sin(2*x) = cos(x)

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

Быстрый ответ

     -pi 
x1 = ----
      2  

$$x_{1} = - \frac{\pi}{2}$$

     pi
x2 = --
     6 

$$x_{2} = \frac{\pi}{6}$$

     pi
x3 = --
     2 

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

     5*pi
x4 = ----
      6  

$$x_{4} = \frac{5 \pi}{6}$$

Сумма и произведение корней

сумма

    pi   pi   pi   5*pi
0 - -- + -- + -- + ----
    2    6    2     6  

$$\left(\left(\left(- \frac{\pi}{2} + 0\right) + \frac{\pi}{6}\right) + \frac{\pi}{2}\right) + \frac{5 \pi}{6}$$

=

pi

$$\pi$$

произведение

  -pi  pi pi 5*pi
1*----*--*--*----
   2   6  2   6  

$$\frac{5 \pi}{6} \frac{\pi}{2} \frac{\pi}{6} \cdot 1 \left(- \frac{\pi}{2}\right)$$

=

     4
-5*pi 
------
 144  

$$- \frac{5 \pi^{4}}{144}$$

Численный ответ

x1 = -45.553093477052

x2 = 86.3937979737193

x3 = 40.317105721069

x4 = -22.5147473507269

x5 = -72.7802298081635

x6 = -3.66519142918809

x7 = 36.1283155162826

x8 = 4.71238898038469

x9 = -7.85398163397448

x10 = 95.8185759344887

x11 = -73.8274273593601

x12 = 88.4881930761125

x13 = -23.5619449019235

x14 = 84.2994028713261

x15 = -93.7241808320955

x16 = -42.4115008234622

x17 = 82.2050077689329

x18 = 50.789081233035

x19 = -2937.91272988205

x20 = 0.523598775598299

x21 = -36.1283155162826

x22 = 6.80678408277789

x23 = 42.4115008234622

x24 = -58.1194640914112

x25 = -53.9306738866248

x26 = -81.1578102177363

x27 = 7.85398163397448

x28 = -14.1371669411541

x29 = 20.4203522483337

x30 = -12.0427718387609

x31 = -56.025068989018

x32 = -51.8362787842316

x33 = -60.2138591938044

x34 = 27.7507351067098

x35 = 14.1371669411541

x36 = -16.2315620435473

x37 = 65.4498469497874

x38 = 44.5058959258554

x39 = -43.4586983746588

x40 = -20.4203522483337

x41 = -87.4409955249159

x42 = -83.2522053201295

x43 = -67.5442420521806

x44 = -80.1106126665397

x45 = 48.6946861306418

x46 = 34.0339204138894

x47 = -1.5707963267949

x48 = 23.5619449019235

x49 = -66.497044500984

x50 = -17.2787595947439

x51 = 80.1106126665397

x52 = 78.0162175641465

x53 = 64.4026493985908

x54 = -91.6297857297023

x55 = 58.1194640914112

x56 = -97.9129710368819

x57 = -64.4026493985908

x58 = 94.7713783832921

x59 = -47.6474885794452

x60 = 67.5442420521806

x61 = 92.6769832808989

x62 = -5.75958653158129

x63 = -100.007366139275

x64 = 73.8274273593601

x65 = -95.8185759344887

x66 = 31.9395253114962

x67 = 75.9218224617533

x68 = -89.5353906273091

x69 = 21.4675497995303

x70 = 71.733032256967

x71 = -49.7418836818384

x72 = -37.1755130674792

x73 = 29.845130209103

x74 = -4.71238898038469

x75 = 38.2227106186758

x76 = -29.845130209103

x77 = -39.2699081698724

x78 = 102.101761241668

x79 = 57.0722665402146

x80 = -9.94837673636768

x81 = 51.8362787842316

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