Mister Exam

Other calculators

sinx+sin3x=2sin2x equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
sin(x) + sin(3*x) = 2*sin(2*x)
sin⁡(x)+sin⁡(3x)=2sin⁡(2x)\sin{\left(x \right)} + \sin{\left(3 x \right)} = 2 \sin{\left(2 x \right)}
Simplify
The graph
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
  pi   pi     
- -- + -- + pi
  2    2
(−π2+π2)+π\left(- \frac{\pi}{2} + \frac{\pi}{2}\right) + \pi 
=
pi
π\pi 
product
  -pi  pi   
0*----*--*pi
   2   2
ππ2⋅0(−π2)\pi \frac{\pi}{2} \cdot 0 \left(- \frac{\pi}{2}\right) 
=
0
00 
0
Rapid solution [src] 
x1 = 0
x1=0x_{1} = 0 
     -pi 
x2 = ----
      2
x2=−π2x_{2} = - \frac{\pi}{2} 
     pi
x3 = --
     2
x3=π2x_{3} = \frac{\pi}{2} 
x4 = pi
x4=πx_{4} = \pi 
x4 = pi
Numerical answer [src] 
x1 = 69.1150530230732
x2 = -62.8318074876145
x3 = 78.5398163397448
x4 = 50.2654784094319
x5 = -65.9734457253857
x6 = -15.707963267949
x7 = 86.3937979737193
x8 = 42.4115008234622
x9 = 73.8274273593601
x10 = 45.553093477052
x11 = 89.5353906273091
x12 = 103.672557568463
x13 = -81.6814264821145
x14 = -1.5707963267949
x15 = -58.1194640914112
x16 = -50.2654147146836
x17 = 81.6814859155387
x18 = -51.8362787842316
x19 = 15.707963267949
x20 = 7.85398163397448
x21 = -86.3937979737193
x22 = 6.28317668554181
x23 = -43.9823032301506
x24 = 58.1194640914112
x25 = -18.8495399461498
x26 = -67.5442420521806
x27 = -59.6902604182061
x28 = -6.2831143821254
x29 = -94.2477151718079
x30 = 21.9911485751286
x31 = 94.2477801894811
x32 = 12.5663019045638
x33 = -28.2743338823081
x34 = -9.42477796076938
x35 = -95.8185759344887
x36 = 59.6902604182061
x37 = 29.845130209103
x38 = 28.2743338823081
x39 = 80.1106126665397
x40 = -72.2566310325652
x41 = -80.1106126665397
x42 = 51.8362787842316
x43 = -29.845130209103
x44 = 37.699185827683
x45 = 25.1327215363518
x46 = -97.3893722612836
x47 = 56.5486021204051
x48 = 43.9823032517286
x49 = -40.8407044966673
x50 = 20.4203522483337
x51 = 69.1149752521823
x52 = 14.1371669411541
x53 = 4.71238898038469
x54 = -1269.20342490537
x55 = -37.699124949212
x56 = -23.5619449019235
x57 = -83.2522053201295
x58 = -36.1283155162826
x59 = -87.9646059559836
x60 = 1.5707963267949
x61 = -62.831811416058
x62 = 36.1283155162826
x63 = 95.8185759344887
x64 = -14.1371669411541
x65 = 100.530902429653
x66 = 0.0
x67 = -21.9911485751286
x68 = -39.2699081698724
x69 = -89.5353906273091
x70 = 34.5575191894877
x71 = 48.6946861306418
x72 = 65.9734457253857
x73 = 87.9646063022244
x74 = -45.553093477052
x75 = -53.4070751110265
x76 = -7.85398163397448
x77 = 64.4026493985908
x78 = 25.1327989510172
x79 = -73.8274273593601
x80 = -75.3982982373223
x81 = 92.6769832808989
x82 = 72.2566310325652
x83 = -42.4115008234622
x84 = -31.4159982155844
x84 = -31.4159982155844
    © Mister Exam – Calculator