(cos(x)-sin(x))^2-sin(4*x)=1 (уравнение)

Найду корень уравнения: (cos(x)-sin(x))^2-sin(4*x)=1

Вы ввели

                 2               
(cos(x) - sin(x))  - sin(4*x) = 1

$$\left(- \sin{\left(x \right)} + \cos{\left(x \right)}\right)^{2} - \sin{\left(4 x \right)} = 1$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

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

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

     -3*pi
x3 = -----
       2  

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

     -4*pi
x4 = -----
       3  

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

x5 = -pi

$$x_{5} = - \pi$$

     -2*pi
x6 = -----
       3  

$$x_{6} = - \frac{2 \pi}{3}$$

     -pi 
x7 = ----
      2  

$$x_{7} = - \frac{\pi}{2}$$

     -pi 
x8 = ----
      3  

$$x_{8} = - \frac{\pi}{3}$$

     pi
x9 = --
     3 

$$x_{9} = \frac{\pi}{3}$$

      pi
x10 = --
      2 

$$x_{10} = \frac{\pi}{2}$$

      2*pi
x11 = ----
       3  

$$x_{11} = \frac{2 \pi}{3}$$

x12 = pi

$$x_{12} = \pi$$

      4*pi
x13 = ----
       3  

$$x_{13} = \frac{4 \pi}{3}$$

      3*pi
x14 = ----
       2  

$$x_{14} = \frac{3 \pi}{2}$$

      5*pi
x15 = ----
       3  

$$x_{15} = \frac{5 \pi}{3}$$

x16 = 2*pi

$$x_{16} = 2 \pi$$

Сумма и произведение корней

сумма

        5*pi   3*pi   4*pi        2*pi   pi   pi   pi   pi   2*pi        4*pi   3*pi   5*pi       
0 + 0 - ---- - ---- - ---- - pi - ---- - -- - -- + -- + -- + ---- + pi + ---- + ---- + ---- + 2*pi
         3      2      3           3     2    3    3    2     3           3      2      3         

$$\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{5 \pi}{3} + \left(0 + 0\right)\right) - \frac{3 \pi}{2}\right) - \frac{4 \pi}{3}\right) - \pi\right) - \frac{2 \pi}{3}\right) - \frac{\pi}{2}\right) - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \frac{\pi}{2}\right) + \frac{2 \pi}{3}\right) + \pi\right) + \frac{4 \pi}{3}\right) + \frac{3 \pi}{2}\right) + \frac{5 \pi}{3}\right) + 2 \pi$$

=

2*pi

$$2 \pi$$

произведение

    -5*pi -3*pi -4*pi     -2*pi -pi  -pi  pi pi 2*pi    4*pi 3*pi 5*pi     
1*0*-----*-----*-----*-pi*-----*----*----*--*--*----*pi*----*----*----*2*pi
      3     2     3         3    2    3   3  2   3       3    2    3       

$$2 \pi \frac{5 \pi}{3} \frac{3 \pi}{2} \frac{4 \pi}{3} \pi \frac{2 \pi}{3} \frac{\pi}{2} \frac{\pi}{3} - \frac{\pi}{3} - \frac{\pi}{2} - \frac{2 \pi}{3} - \pi - \frac{4 \pi}{3} - \frac{3 \pi}{2} 1 \cdot 0 \left(- \frac{5 \pi}{3}\right)$$

=

0

$$0$$

Численный ответ

x1 = -92.1533845053006

x2 = -99.4837673636768

x3 = -72.2566310325652

x4 = 333.008821280518

x5 = 86.3937979737193

x6 = 48.1710873550435

x7 = 57.5958653158129

x8 = 50.2654824574367

x9 = -29.3215314335047

x10 = 90.0589894029074

x11 = 26.1799387799149

x12 = 36.1283155162826

x13 = -7.85398163397448

x14 = -73.8274273593601

x15 = -65.9734457253857

x16 = 87.9645943005142

x17 = -7.33038285837618

x18 = -37.6991118430775

x19 = -36.6519142918809

x20 = -21.9911485751286

x21 = -83.7758040957278

x22 = 92.1533845053006

x23 = 101.57816246607

x24 = -77.4926187885482

x25 = -46.0766922526503

x26 = 2.0943951023932

x27 = -58.1194640914112

x28 = 83.7758040957278

x29 = -4.18879020478639

x30 = 28.2743338823081

x31 = -14.1371669411541

x32 = -17.8023583703422

x33 = 10.471975511966

x34 = -15.707963267949

x35 = -51.8362787842316

x36 = 65.9734457253857

x37 = -94.2477796076938

x38 = 98.4365698124802

x39 = 14.1371669411541

x40 = -61.7846555205993

x41 = -98.9601685880785

x42 = 68.0678408277789

x43 = 72.2566310325652

x44 = -80.1106126665397

x45 = -19.8967534727354

x46 = 4.18879020478639

x47 = 0.0

x48 = 43.9822971502571

x49 = -85.870199198121

x50 = 80.1106126665397

x51 = 21.9911485751286

x52 = 32.4631240870945

x53 = -70.162235930172

x54 = 17.8023583703422

x55 = -23.0383461263252

x56 = -43.9822971502571

x57 = 46.0766922526503

x58 = -105.243353895258

x59 = 58.1194640914112

x60 = -33.5103216382911

x61 = 61.7846555205993

x62 = -55.5014702134197

x63 = -39.7935069454707

x64 = 54.4542726622231

x65 = 75.398223686155

x66 = -26.1799387799149

x67 = 6.28318530717959

x68 = -9.42477796076938

x69 = 96.342174710087

x70 = -95.8185759344887

x71 = -90.0589894029074

x72 = -49.2182849062401

x73 = -59.6902604182061

x74 = 76.4454212373516

x75 = -63.8790506229925

x76 = -48.1710873550435

x77 = 39.7935069454707

x78 = 24.0855436775217

x79 = 70.162235930172

x80 = -68.0678408277789

x81 = -87.9645943005142

x82 = -24.0855436775217

x83 = -11.5191730631626

x84 = 20.943951023932

x85 = -29.845130209103

x86 = -5.23598775598299

x87 = -41.8879020478639

x88 = -2.0943951023932

x89 = 94.2477796076938

x90 = -81.6814089933346

График