cos(x)+sin(2*x)=0 (уравнение)

Найду корень уравнения: cos(x)+sin(2*x)=0

Вы ввели

cos(x) + sin(2*x) = 0

$$\sin{\left(2 x \right)} + \cos{\left(x \right)} = 0$$

Быстрый ответ

     -5*pi
x1 = -----
       6  

$$x_{1} = - \frac{5 \pi}{6}$$

     -pi 
x2 = ----
      2  

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

     -pi 
x3 = ----
      6  

$$x_{3} = - \frac{\pi}{6}$$

     pi
x4 = --
     2 

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

Сумма и произведение корней

сумма

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

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

=

-pi

$$- \pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 28.7979326579064

x2 = -45.553093477052

x3 = -86.3937979737193

x4 = 86.3937979737193

x5 = 5.75958653158129

x6 = 72.7802298081635

x7 = 1.5707963267949

x8 = 36.1283155162826

x9 = 43.4586983746588

x10 = -7.85398163397448

x11 = 22.5147473507269

x12 = 95.8185759344887

x13 = -73.8274273593601

x14 = -23.5619449019235

x15 = -42.4115008234622

x16 = -36.1283155162826

x17 = 42.4115008234622

x18 = -58.1194640914112

x19 = -34.0339204138894

x20 = 37.1755130674792

x21 = 7.85398163397448

x22 = -14.1371669411541

x23 = -61.261056745001

x24 = -46.6002910282486

x25 = 20.4203522483337

x26 = -21.4675497995303

x27 = 26.7035375555132

x28 = -27.7507351067098

x29 = -51.8362787842316

x30 = -31.9395253114962

x31 = 53.9306738866248

x32 = -0.523598775598299

x33 = 62.3082542961976

x34 = 18.3259571459405

x35 = 14.1371669411541

x36 = -78.0162175641465

x37 = 218.340689424491

x38 = -94.7713783832921

x39 = -59.1666616426078

x40 = -69.6386371545737

x41 = -67.5442420521806

x42 = -80.1106126665397

x43 = 48.6946861306418

x44 = -1.5707963267949

x45 = -71.733032256967

x46 = -17.2787595947439

x47 = 80.1106126665397

x48 = 66.497044500984

x49 = 64.4026493985908

x50 = 89.5353906273091

x51 = -25.6563400043166

x52 = 58.1194640914112

x53 = -88.4881930761125

x54 = -40.317105721069

x55 = -63.3554518473942

x56 = -82.2050077689329

x57 = -65.4498469497874

x58 = -64.4026493985908

x59 = -44.5058959258554

x60 = 60.2138591938044

x61 = -15.1843644923507

x62 = 49.7418836818384

x63 = 100.007366139275

x64 = 97.9129710368819

x65 = 56.025068989018

x66 = 73.8274273593601

x67 = 9.94837673636768

x68 = -95.8185759344887

x69 = -50.789081233035

x70 = -89.5353906273091

x71 = 12.0427718387609

x72 = 29.845130209103

x73 = 45.553093477052

x74 = -38.2227106186758

x75 = 87.4409955249159

x76 = 93.7241808320955

x77 = -75.9218224617533

x78 = -29.845130209103

x79 = -84.2994028713261

x80 = 16.2315620435473

x81 = 70.6858347057703

x82 = 51.8362787842316

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