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sin(5*x)=cos(4*x)

sin(5*x)=cos(4*x) equation

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Numerical solution:

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The solution

You have entered [src]
sin(5*x) = cos(4*x)
$$\sin{\left(5 x \right)} = \cos{\left(4 x \right)}$$
The graph
Rapid solution [src]
     -5*pi
x1 = -----
       6  
$$x_{1} = - \frac{5 \pi}{6}$$
     -pi 
x2 = ----
      6  
$$x_{2} = - \frac{\pi}{6}$$
     pi
x3 = --
     2 
$$x_{3} = \frac{\pi}{2}$$
Sum and product of roots [src]
sum
    5*pi   pi   pi
0 - ---- - -- + --
     6     6    2 
$$\left(\left(- \frac{5 \pi}{6} + 0\right) - \frac{\pi}{6}\right) + \frac{\pi}{2}$$
=
-pi 
----
 2  
$$- \frac{\pi}{2}$$
product
  -5*pi -pi  pi
1*-----*----*--
    6    6   2 
$$\frac{\pi}{2} - \frac{\pi}{6} \cdot 1 \left(- \frac{5 \pi}{6}\right)$$
=
    3
5*pi 
-----
  72 
$$\frac{5 \pi^{3}}{72}$$
5*pi^3/72
Numerical answer [src]
x1 = 23.2128790515246
x2 = -9.59931088596881
x3 = -91.9788515801012
x4 = 60.2138591938044
x5 = 65.1007810993885
x6 = 76.2708883121522
x7 = -34.0339204138894
x8 = 81.1578102177363
x9 = 12.0427718387609
x10 = 86.0447321233204
x11 = 16.2315620435473
x12 = -73.8274272827467
x13 = -39.6189740202713
x14 = 26.0054058547155
x15 = -27.7507351067098
x16 = 2.26892802759263
x17 = 34.3829862642883
x18 = 69.9877030049726
x19 = -11.693705988362
x20 = -45.9021593274509
x21 = 42.0624349730633
x22 = 67.8933079025794
x23 = -73.1292956585624
x24 = -43.8077642250577
x25 = 56.025068989018
x26 = 20.4203521882517
x27 = -87.7900613753148
x28 = 30.1941960595019
x29 = -64.7517152489896
x30 = 18.3259571459405
x31 = -104.54522219446
x32 = -6.10865238198015
x33 = -85.6956662729216
x34 = -83.6012711705284
x35 = -29.8451301093948
x36 = 51.1381470834339
x37 = -57.7703982410123
x38 = -66.1479786505851
x39 = 72.0820981073658
x40 = -89.884456477708
x41 = -69.6386371545737
x42 = -23.5619449540223
x43 = 74.176493209759
x44 = -55.6760031386191
x45 = 9.94837673636768
x46 = -78.0162175641465
x47 = 95.8185759914842
x48 = 51.8362788484534
x49 = 100.007366139275
x50 = -96.1676417848876
x51 = -94.0732466824944
x52 = 46.2512251778497
x53 = 7.8539817013759
x54 = 53.9306738866248
x55 = 64.4026493358639
x56 = 7.85398191123749
x57 = 44.1568300754565
x58 = -50.0909495322373
x59 = -75.9218224617533
x60 = 4.36332312998582
x61 = 21.8166156499291
x62 = 90.2335223281068
x63 = -47.9965544298441
x64 = -71.733032256967
x65 = 39.9680398706701
x66 = 28.0998009571087
x67 = 0.174532925199433
x68 = -53.5816080362259
x69 = 78.3652834145454
x70 = -15.8824961931484
x71 = -4.01425727958696
x72 = -17.9768912955416
x73 = 48.3456202802429
x74 = 37.873644768277
x75 = -61.9591884457987
x76 = -80.1106126008672
x77 = -67.5442420868592
x78 = 1075.29735215371
x79 = -64.0535835481919
x80 = -13.7881010907552
x81 = 23.9110107523223
x82 = -1.91986217719376
x83 = -59.8647933434055
x84 = 61.6101225953998
x85 = -36.12831520092
x86 = -20.0712863979348
x87 = 32.2885911618951
x88 = 88.1391272257137
x89 = 83.2522052880855
x90 = -22.165681500328
x91 = 97.9129710368819
x92 = -25.6563400043166
x93 = 94.4223125328932
x94 = -41.7133691226645
x95 = 62.3082542961976
x96 = 92.3279174305
x97 = -31.9395253114962
x98 = -99.6583002888762
x99 = 83.9503370209273
x100 = -36.1283154485727
x100 = -36.1283154485727
The graph
sin(5*x)=cos(4*x) equation