Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation e^x=0
-
Equation 1-5*x=-6*x+8
-
Equation 10*(x-9)=7
-
Equation cos(x)=3
- Express {x} in terms of y where:
- -11*x+10*y=-9
- -9*x-4*y=-20
- -9*x-15*y=-4
- 18*x-11*y=2
-
Identical expressions
- sin(4x)+sin(3x)+sin(2x)= zero
- sinus of (4x) plus sinus of (3x) plus sinus of (2x) equally 0
- sinus of (4x) plus sinus of (3x) plus sinus of (2x) equally zero
- sin4x+sin3x+sin2x=0
- sin(4x)+sin(3x)+sin(2x)=O
-
Similar expressions
- sin(4x)+sin(3x)-sin(2x)=0
- sin(4x)-sin(3x)+sin(2x)=0
sin(4x)+sin(3x)+sin(2x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(4*x) + sin(3*x) + sin(2*x) = 0
$$\left(\sin{\left(3 x \right)} + \sin{\left(4 x \right)}\right) + \sin{\left(2 x \right)} = 0$$
Rapid solution
[src]
x1 = 0
$$x_{1} = 0$$
-2*pi
x2 = -----
3
$$x_{2} = - \frac{2 \pi}{3}$$
-pi
x3 = ----
3
$$x_{3} = - \frac{\pi}{3}$$
pi
x4 = --
3
$$x_{4} = \frac{\pi}{3}$$
2*pi
x5 = ----
3
$$x_{5} = \frac{2 \pi}{3}$$
x6 = pi
$$x_{6} = \pi$$
x6 = pi
Sum and product of roots
[src]
sum
2*pi pi pi 2*pi - ---- - -- + -- + ---- + pi 3 3 3 3
$$\left(\left(\left(- \frac{2 \pi}{3} - \frac{\pi}{3}\right) + \frac{\pi}{3}\right) + \frac{2 \pi}{3}\right) + \pi$$
=
pi
$$\pi$$
product
-2*pi -pi pi 2*pi
0*-----*----*--*----*pi
3 3 3 3
$$\pi \frac{2 \pi}{3} \frac{\pi}{3} \cdot - \frac{\pi}{3} \cdot 0 \left(- \frac{2 \pi}{3}\right)$$
=
0
$$0$$
0
Numerical answer
[src]
x1 = 90.0589892465429
x2 = -4.1887901139423
x3 = -17.8023583703422
x4 = -35.6047168238723
x5 = -26.1799387799149
x6 = 43.9822971502571
x7 = 98.4365697297568
x8 = 85.8701992908153
x9 = -48.1710872662315
x10 = 41.8879021323064
x11 = -15.707963267949
x12 = 64.9262481866418
x13 = -21.9911485751286
x14 = -27.2271365746161
x15 = -13.6135681655558
x16 = 0.0
x17 = -39.7935069072804
x18 = -55.5014702134197
x19 = -50.2654824574367
x20 = -10.4719756110445
x21 = 10.4719754256716
x22 = 36.6519142918809
x23 = -96.3421746084435
x24 = 17.8023583703422
x25 = -79.5870139813601
x26 = 63.8790506229925
x27 = 57.5958653158129
x28 = 70.162235930172
x29 = -73.3038283826811
x30 = 19.8967534727354
x31 = -94.2477796076938
x32 = -57.5958653158129
x33 = -59.6902604182061
x34 = -33.5103217241494
x35 = 4.18879026358866
x36 = 35.6047167744284
x37 = 83.7758041869106
x38 = 96.342174652375
x39 = 58.6430628283586
x40 = -77.4926188719937
x41 = -83.7758040747184
x42 = -68.0678408277789
x43 = -70.162235930172
x44 = -27.2271362031096
x45 = -99.4837673636768
x46 = 21.9911485751286
x47 = 79.5870138734005
x48 = 68.0678408277789
x49 = 74.3510261349584
x50 = -90.058989349726
x51 = -81.6814089933346
x52 = -46.0766921878318
x53 = 50.2654824574367
x54 = 8.37758033426669
x55 = -87.9645943005142
x56 = -41.8879016525879
x57 = -29.3215313465118
x58 = 24.0855436775217
x59 = 61.7846555205993
x60 = -8.37758034328977
x61 = 92.1533846238229
x62 = 48.1710874397708
x63 = 54.4542725770633
x64 = 32.4631240870945
x65 = 28.2743338823081
x66 = -61.7846555205993
x67 = -65.9734457253857
x68 = 72.2566310325652
x69 = 39.7935070371482
x70 = 30.3687289847013
x71 = 6.28318530717959
x72 = 94.2477796076938
x73 = -37.6991118430775
x74 = 65.9734457253857
x75 = -43.9822971502571
x76 = 87.9645943005142
x77 = -92.1533844196459
x78 = -11.5191730631626
x79 = -24.0855436775217
x80 = -52.3598774723247
x81 = 14.6607657264679
x82 = -53.4070751110265
x83 = 76.4454212373516
x84 = -1.0471975511966
x85 = -2.09439502720987
x86 = -19.8967534727354
x87 = 26.1799387799149
x88 = -63.8790506229925
x89 = -67.0206430091552
x90 = 52.3598774930226
x90 = 52.3598774930226