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cos^2(x)=1/4

cos^2(x)=1/4 уравнение

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Численное решение:

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Решение

Вы ввели [src]
   2         
cos (x) = 1/4
$$\cos^{2}{\left(x \right)} = \frac{1}{4}$$
График
Быстрый ответ [src]
      pi
x_1 = --
      3 
$$x_{1} = \frac{\pi}{3}$$
      2*pi
x_2 = ----
       3  
$$x_{2} = \frac{2 \pi}{3}$$
      4*pi
x_3 = ----
       3  
$$x_{3} = \frac{4 \pi}{3}$$
      5*pi
x_4 = ----
       3  
$$x_{4} = \frac{5 \pi}{3}$$
Сумма и произведение корней [src]
сумма
pi   2*pi   4*pi   5*pi
-- + ---- + ---- + ----
3     3      3      3  
$$\left(\frac{\pi}{3}\right) + \left(\frac{2 \pi}{3}\right) + \left(\frac{4 \pi}{3}\right) + \left(\frac{5 \pi}{3}\right)$$
=
4*pi
$$4 \pi$$
произведение
pi   2*pi   4*pi   5*pi
-- * ---- * ---- * ----
3     3      3      3  
$$\left(\frac{\pi}{3}\right) * \left(\frac{2 \pi}{3}\right) * \left(\frac{4 \pi}{3}\right) * \left(\frac{5 \pi}{3}\right)$$
=
     4
40*pi 
------
  81  
$$\frac{40 \pi^{4}}{81}$$
Численный ответ [src]
x1 = -205.250720034533
x2 = -33.5103216382911
x3 = -2.0943951023932
x4 = -83.7758040957278
x5 = -4.18879020478639
x6 = -76.4454212373516
x7 = -55.5014702134197
x8 = -57.5958653158129
x9 = 39.7935069454707
x10 = -10.471975511966
x11 = 99.4837673636768
x12 = -96.342174710087
x13 = 4.18879020478639
x14 = -68.0678408277789
x15 = 63.8790506229925
x16 = -85.870199198121
x17 = -39.7935069454707
x18 = 83.7758040957278
x19 = 85.870199198121
x20 = -11.5191730631626
x21 = 46.0766922526503
x22 = -17.8023583703422
x23 = -61.7846555205993
x24 = -63.8790506229925
x25 = 52.3598775598299
x26 = 20.943951023932
x27 = -70.162235930172
x28 = 19.8967534727354
x29 = 16.7551608191456
x30 = -5.23598775598299
x31 = -77.4926187885482
x32 = 26.1799387799149
x33 = 1515.29485658148
x34 = 76.4454212373516
x35 = 41.8879020478639
x36 = -13.6135681655558
x37 = -378.038315981972
x38 = 38.7463093942741
x39 = -93.2005820564972
x40 = -49.2182849062401
x41 = 24.0855436775217
x42 = 92.1533845053006
x43 = 61.7846555205993
x44 = -26.1799387799149
x45 = -46.0766922526503
x46 = -30.3687289847013
x47 = -48.1710873550435
x48 = 10.471975511966
x49 = -322.536845768552
x50 = 96.342174710087
x51 = 98.4365698124802
x52 = 77.4926187885482
x53 = 2.0943951023932
x54 = -54.4542726622231
x55 = -24.0855436775217
x56 = -294.262511886244
x57 = -90.0589894029074
x58 = 11.5191730631626
x59 = 82.7286065445312
x60 = -41.8879020478639
x61 = -19.8967534727354
x62 = -35.6047167406843
x63 = -32.4631240870945
x64 = -79.5870138909414
x65 = 54.4542726622231
x66 = -98.4365698124802
x67 = 48.1710873550435
x68 = -60.7374579694027
x69 = -27.2271363311115
x70 = -71.2094334813686
x71 = 79.5870138909414
x72 = 30.3687289847013
x73 = 68.0678408277789
x74 = 55.5014702134197
x75 = -99.4837673636768
x76 = 60.7374579694027
x77 = 33.5103216382911
x78 = 8.37758040957278
x79 = -14.6607657167524
x80 = 17.8023583703422
x81 = 90.0589894029074
x82 = 74.3510261349584
x83 = 70.162235930172
x84 = -92.1533845053006
x85 = 32.4631240870945
x85 = 32.4631240870945
График
cos^2(x)=1/4 уравнение