cos(x)=cos(3*x) (уравнение)

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

Вы ввели

cos(x) = cos(3*x)

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     -pi 
x2 = ----
      2  

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

     pi
x3 = --
     2 

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

x4 = pi

$$x_{4} = \pi$$

Сумма и произведение корней

сумма

        pi   pi     
0 + 0 - -- + -- + pi
        2    2      

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

=

pi

$$\pi$$

произведение

    -pi  pi   
1*0*----*--*pi
     2   2    

$$\pi \frac{\pi}{2} 1 \cdot 0 \left(- \frac{\pi}{2}\right)$$

=

0

$$0$$

Численный ответ

x1 = -45.553093477052

x2 = 75.3982236793524

x3 = 86.3937979737193

x4 = -91.1061867632284

x5 = -81.6814090375457

x6 = 31.4159265728873

x7 = 37.6991119937168

x8 = 84.8230015887783

x9 = 36.1283155162826

x10 = 72.2566310277219

x11 = -7.85398163397448

x12 = 95.8185759344887

x13 = -73.8274273593601

x14 = -23.5619449019235

x15 = 97.38937222667

x16 = 65.9734457527245

x17 = 43.9822971693493

x18 = -53.407075257786

x19 = 9.42477806710815

x20 = 94.2477792514877

x21 = -47.1238897080294

x22 = 56.5486676266806

x23 = -36.1283155162826

x24 = -58.1194640914112

x25 = 42.4115008234622

x26 = 2.89784959789169e-7

x27 = -21.9911485864718

x28 = -37.6991118769198

x29 = -25.1327411700478

x30 = 62.8318530302311

x31 = 7.85398163397448

x32 = -14.1371669411541

x33 = 20.4203522483337

x34 = -87.9645943590963

x35 = -51.8362787842316

x36 = -50.2654823143599

x37 = -9.42477810445402

x38 = -207.34511550934

x39 = 14.1371669411541

x40 = -43.9822971746609

x41 = 53.4070751278617

x42 = -28.2743337371269

x43 = -65.9734457652028

x44 = 59.6902605703693

x45 = -97.389372410446

x46 = -67.5442420521806

x47 = -80.1106126665397

x48 = -21.9911486312213

x49 = -15.7079632963762

x50 = -1.5707963267949

x51 = 0.0

x52 = 50.2654824463642

x53 = 80.1106126665397

x54 = 64.4026493985908

x55 = -72.2566308917313

x56 = -94.2477794692392

x57 = -6.28318516003462

x58 = 78.5398162040055

x59 = -12.5663705453118

x60 = 87.964594335453

x61 = 18.8495559220487

x62 = -69.1150382393654

x63 = 58.1194640914112

x64 = -78.5398162373076

x65 = 100.530964781462

x66 = -56.5486676717583

x67 = 94.2477796093527

x68 = -75.398223834204

x69 = 81.6814091468681

x70 = -43.982296876345

x71 = -28.2743341715057

x72 = 12.5663704724455

x73 = 28.2743338652459

x74 = -65.9734453602046

x75 = 34.5575190494922

x76 = 73.8274273593601

x77 = -95.8185759344887

x78 = 6.28318528433976

x79 = -89.5353906273091

x80 = -34.5575191076725

x81 = 29.845130209103

x82 = -906.349480560655

x83 = -3.14159262638665

x84 = 50.2654819973737

x85 = 9.42477801500462

x86 = 43.9822971001043

x87 = 40.8407044744738

x88 = -31.4159266812001

x89 = 15.7079634169143

x90 = -29.845130209103

x91 = -100.530964804106

x92 = -59.6902604573056

x93 = 21.9911485851767

x94 = 51.8362787842316

График