Решите уравнение sin(5*x)=sin(x) (синус от (5 умножить на х) равно синус от (х)) - Найдите корень уравнения подробно по-шагам. [Есть ОТВЕТ!]

sin(5*x)=sin(x) (уравнение)

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    Найду корень уравнения: sin(5*x)=sin(x)

    Решение

    Вы ввели [src]
    sin(5*x) = sin(x)
    $$\sin{\left(5 x \right)} = \sin{\left(x \right)}$$
    График
    Быстрый ответ [src]
    x1 = 0
    $$x_{1} = 0$$
         -5*pi
    x2 = -----
           6  
    $$x_{2} = - \frac{5 \pi}{6}$$
         -pi 
    x3 = ----
          2  
    $$x_{3} = - \frac{\pi}{2}$$
         -pi 
    x4 = ----
          6  
    $$x_{4} = - \frac{\pi}{6}$$
         pi
    x5 = --
         6 
    $$x_{5} = \frac{\pi}{6}$$
         pi
    x6 = --
         2 
    $$x_{6} = \frac{\pi}{2}$$
         5*pi
    x7 = ----
          6  
    $$x_{7} = \frac{5 \pi}{6}$$
    Сумма и произведение корней [src]
    сумма
      5*pi   pi   pi   pi   pi   5*pi
    - ---- - -- - -- + -- + -- + ----
       6     2    6    6    2     6  
    $$\left(\left(\left(\left(- \frac{5 \pi}{6} - \frac{\pi}{2}\right) - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{\pi}{2}\right) + \frac{5 \pi}{6}$$
    =
    0
    $$0$$
    произведение
      -5*pi -pi  -pi  pi pi 5*pi
    0*-----*----*----*--*--*----
        6    2    6   6  2   6  
    $$\frac{5 \pi}{6} \frac{\pi}{2} \frac{\pi}{6} \cdot - \frac{\pi}{6} \cdot - \frac{\pi}{2} \cdot 0 \left(- \frac{5 \pi}{6}\right)$$
    =
    0
    $$0$$
    Численный ответ [src]
    x1 = 71.733032256967
    x2 = 34.0339204138894
    x3 = -43.9822971502571
    x4 = 73.8274274507798
    x5 = 57.0722665402146
    x6 = 78.0162175641465
    x7 = 72.2566310325652
    x8 = -62.3082542961976
    x9 = 31.9395253114962
    x10 = 6.80678408277789
    x11 = -15.707963267949
    x12 = -12.0427718387609
    x13 = -100.007366139275
    x14 = 64.402649321335
    x15 = 9.94837673636768
    x16 = -56.025068989018
    x17 = 21.9911485751286
    x18 = -51.8362786930768
    x19 = 40.317105721069
    x20 = -3.66519142918809
    x21 = -93.7241808320955
    x22 = 86.3937978991244
    x23 = 50.2654824574367
    x24 = -36.1283154345693
    x25 = -25.6563400043166
    x26 = 53.9306738866248
    x27 = 38.2227106186758
    x28 = -65.9734457253857
    x29 = -47.6474885794452
    x30 = -27.7507351067098
    x31 = 49.7418836818384
    x32 = -49.7418836818384
    x33 = 0.0
    x34 = 65.9734457253857
    x35 = -69.6386371545737
    x36 = -59.6902604182061
    x37 = -1.57079641043406
    x38 = -87.4409955249159
    x39 = 62.3082542961976
    x40 = 18.3259571459405
    x41 = -14.1371668568862
    x42 = 12.0427718387609
    x43 = 20.4203521665398
    x44 = -21.9911485751286
    x45 = -89.5353907149608
    x46 = 75.9218224617533
    x47 = 41.3643032722656
    x48 = 42.4115007438019
    x49 = -95.8185758687429
    x50 = -5.75958653158129
    x51 = 6.28318530717959
    x52 = -75.9218224617533
    x53 = 97.9129710368819
    x54 = -7.85398151509217
    x55 = -29.8451301034425
    x56 = -78.0162175641465
    x57 = -45.5530935634293
    x58 = -34.0339204138894
    x59 = 51.836278874331
    x60 = -81.6814089933346
    x61 = 29.8451302975665
    x62 = 82.2050077689329
    x63 = 87.9645943005142
    x64 = 95.8185760269036
    x65 = 80.1106128189844
    x66 = 56.025068989018
    x67 = -72.7802298081635
    x68 = 43.9822971502571
    x69 = 84.2994028713261
    x70 = -37.6991118430775
    x71 = -58.1194640125579
    x72 = 14.1371670414222
    x73 = -9.94837673636768
    x74 = 37.1755130674792
    x75 = 100.007366139275
    x76 = 22.5147473507269
    x77 = -87.9645943005142
    x78 = -80.1106125908558
    x79 = -91.6297857297023
    x80 = -31.9395253114962
    x81 = 66.497044500984
    x82 = -73.827427281571
    x83 = 7.85398172049285
    x84 = 60.2138591938044
    x85 = 28.2743338823081
    x86 = -71.733032256967
    x87 = 16.2315620435473
    x88 = -97.9129710368819
    x89 = -23.5619449870988
    x90 = -67.5442421393955
    x91 = 28.7979326579064
    x92 = -53.9306738866248
    x93 = 94.2477796076938
    График
    sin(5*x)=sin(x) (уравнение) /media/krcore-image-pods/hash/equation/0/79/9855e1abad2cad8194b80b1ebd5e5.png
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