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cos(x^2)=0

cos(x^2)=0 уравнение

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Численное решение:

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Решение

Вы ввели [src]
   / 2\    
cos\x / = 0
$$\cos{\left(x^{2} \right)} = 0$$
График
Сумма и произведение корней [src]
сумма
   ___   ____      ___   ____      ___   ____      ___   ____
-\/ 2 *\/ pi     \/ 2 *\/ pi    -\/ 6 *\/ pi     \/ 6 *\/ pi 
-------------- + ------------ + -------------- + ------------
      2               2               2               2      
$$\left(- \frac{\sqrt{2} \sqrt{\pi}}{2}\right) + \left(\frac{\sqrt{2} \sqrt{\pi}}{2}\right) + \left(- \frac{\sqrt{6} \sqrt{\pi}}{2}\right) + \left(\frac{\sqrt{6} \sqrt{\pi}}{2}\right)$$
=
0
$$0$$
произведение
   ___   ____      ___   ____      ___   ____      ___   ____
-\/ 2 *\/ pi     \/ 2 *\/ pi    -\/ 6 *\/ pi     \/ 6 *\/ pi 
-------------- * ------------ * -------------- * ------------
      2               2               2               2      
$$\left(- \frac{\sqrt{2} \sqrt{\pi}}{2}\right) * \left(\frac{\sqrt{2} \sqrt{\pi}}{2}\right) * \left(- \frac{\sqrt{6} \sqrt{\pi}}{2}\right) * \left(\frac{\sqrt{6} \sqrt{\pi}}{2}\right)$$
=
    2
3*pi 
-----
  4  
$$\frac{3 \pi^{2}}{4}$$
Быстрый ответ [src]
         ___   ____ 
      -\/ 2 *\/ pi  
x_1 = --------------
            2       
$$x_{1} = - \frac{\sqrt{2} \sqrt{\pi}}{2}$$
        ___   ____
      \/ 2 *\/ pi 
x_2 = ------------
           2      
$$x_{2} = \frac{\sqrt{2} \sqrt{\pi}}{2}$$
         ___   ____ 
      -\/ 6 *\/ pi  
x_3 = --------------
            2       
$$x_{3} = - \frac{\sqrt{6} \sqrt{\pi}}{2}$$
        ___   ____
      \/ 6 *\/ pi 
x_4 = ------------
           2      
$$x_{4} = \frac{\sqrt{6} \sqrt{\pi}}{2}$$
Численный ответ [src]
x1 = 46.0326432528734
x2 = -21.7441875995693
x3 = 13.5566651590649
x4 = 17.4115964538412
x5 = -75.8953893880049
x6 = -57.7477324384739
x7 = -53.6295447898027
x8 = -32.0270198644374
x9 = -93.7978156802077
x10 = -5.16754657023168
x11 = -42.0000508927152
x12 = 2.1708037636748
x13 = -74.2423350301113
x14 = -79.6323098451313
x15 = 27.9969170993996
x16 = -13.7864555104705
x17 = 31.3829459563694
x18 = 60.2503967723284
x19 = 16.0012437412711
x20 = -63.2520216621303
x21 = -81.792551958106
x22 = 36.042316272118
x23 = -7.82694427889971
x24 = -47.8726627710821
x25 = -92.1420324625326
x26 = 26.0797777885892
x27 = -43.9375543883695
x28 = -3.7599424119465
x29 = -68.2222069145618
x30 = -58.8524077721783
x31 = 68.1530977897007
x32 = 67.736962365963
x33 = 96.1791015163645
x34 = -29.8962056111858
x35 = 23.3466555505886
x36 = 62.2255007657586
x37 = 36.7757479512029
x38 = -17.8569777493103
x39 = 70.1296178457777
x40 = -67.8759576469418
x41 = -65.8556653468835
x42 = -69.7703218907394
x43 = 58.181320750246
x44 = 114.587462209783
x45 = 18.1189522958733
x46 = 57.4750787320006
x47 = -89.407955502065
x48 = 34.2088185043301
x49 = -33.7930307841704
x50 = 80.1827248574873
x51 = 63.9435910678085
x52 = 84.0842093790732
x53 = 4.15677273792348
x54 = 56.1199308198413
x55 = -2.1708037636748
x56 = 6.2665706865775
x57 = 20.2479095536667
x58 = 40.1647585280723
x59 = 22.3146238057912
x60 = -71.6803654074538
x61 = -76.1639733394572
x62 = 66.1412713071331
x63 = -97.7504683154682
x64 = 103.115082970798
x65 = 41.9626343588803
x66 = -46.338737344997
x67 = -3.31595752197827
x68 = 23.5476347720657
x69 = -85.7673550856064
x70 = 32.1249620498491
x71 = -37.7869535826396
x72 = -16.0012437412711
x73 = -8.7731989612085
x74 = -22.2441192889355
x75 = -50.6779241318116
x76 = -60.5883736018691
x77 = 10.2588183479024
x78 = 92.0738169932802
x79 = 89.4957567168811
x80 = 54.1251803643413
x81 = 82.2330723422884
x81 = 82.2330723422884
График
cos(x^2)=0 уравнение