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Equation:
Equation 4-x=1
Equation x^2+x-72=0
Equation 3/8*x+15=1/6*x+10
Equation sin(3*x)=-1
Express {x} in terms of y where:
-10*x+15*y=-19
-3*x-13*y=7
-16*x-3*y=-16
5*x+13*y=-1
Identical expressions
sin3x+sin9x= zero
sinus of 3x plus sinus of 9x equally 0
sinus of 3x plus sinus of 9x equally zero
sin3x+sin9x=O
Similar expressions
sin3x-sin9x=0

sin3x+sin9x=0 equation

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

The solution

You have entered [src]

sin(3*x) + sin(9*x) = 0

$$\sin{\left(3 x \right)} + \sin{\left(9 x \right)} = 0$$

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

  5*pi   2*pi   pi   pi   pi   pi   pi   pi   2*pi   5*pi     
- ---- - ---- - -- - -- - -- + -- + -- + -- + ---- + ---- + pi
   6      3     2    3    6    6    3    2     3      6

$$\left(\left(\left(\left(\left(\left(\left(\left(\left(- \frac{5 \pi}{6} - \frac{2 \pi}{3}\right) - \frac{\pi}{2}\right) - \frac{\pi}{3}\right) - \frac{\pi}{6}\right) + \frac{\pi}{6}\right) + \frac{\pi}{3}\right) + \frac{\pi}{2}\right) + \frac{2 \pi}{3}\right) + \frac{5 \pi}{6}\right) + \pi$$

pi

$$\pi$$

product

  -5*pi -2*pi -pi  -pi  -pi  pi pi pi 2*pi 5*pi   
0*-----*-----*----*----*----*--*--*--*----*----*pi
    6     3    2    3    6   6  3  2   3    6

$$\pi \frac{5 \pi}{6} \frac{2 \pi}{3} \frac{\pi}{2} \frac{\pi}{3} \frac{\pi}{6} \cdot - \frac{\pi}{6} \cdot - \frac{\pi}{3} \cdot - \frac{\pi}{2} \cdot - \frac{2 \pi}{3} \cdot 0 \left(- \frac{5 \pi}{6}\right)$$

$$0$$

Rapid solution [src]

x1 = 0

$$x_{1} = 0$$

     -5*pi
x2 = -----
       6

$$x_{2} = - \frac{5 \pi}{6}$$

     -2*pi
x3 = -----
       3

$$x_{3} = - \frac{2 \pi}{3}$$

     -pi 
x4 = ----
      2

$$x_{4} = - \frac{\pi}{2}$$

     -pi 
x5 = ----
      3

$$x_{5} = - \frac{\pi}{3}$$

     -pi 
x6 = ----
      6

$$x_{6} = - \frac{\pi}{6}$$

     pi
x7 = --
     6

$$x_{7} = \frac{\pi}{6}$$

     pi
x8 = --
     3

$$x_{8} = \frac{\pi}{3}$$

     pi
x9 = --
     2

$$x_{9} = \frac{\pi}{2}$$

      2*pi
x10 = ----
       3

$$x_{10} = \frac{2 \pi}{3}$$

      5*pi
x11 = ----
       6

$$x_{11} = \frac{5 \pi}{6}$$

x12 = pi

$$x_{12} = \pi$$

x12 = pi

Numerical answer [src]

x1 = -80.1106126488474

x2 = -21.9911485751286

x3 = -95.8185758710707

x4 = 70.162235930172

x5 = 38.2227106411424

x6 = 50.2654824574367

x7 = 54.4542726622231

x8 = -39.7935069454707

x9 = -14.1371670288058

x10 = -51.8362787064342

x11 = 48.1710873550435

x12 = -41.8879020478639

x13 = -73.8274272874554

x14 = 23.0383461263252

x15 = -100.007366131088

x16 = -5.75958652418445

x17 = 41.3643031809126

x18 = -78.0162175477172

x19 = -19.8967534727354

x20 = -25.6563400360841

x21 = 97.9129710722574

x22 = 18.3259571113714

x23 = 0.0

x24 = -3.66519146333868

x25 = -36.1283155471544

x26 = 43.9822971502571

x27 = -43.9822971502571

x28 = 16.2315620582544

x29 = 9.94837677192715

x30 = -12.0427718061402

x31 = -27.7507351061622

x32 = 75.9218224991565

x33 = 53.9306739246208

x34 = 34.0339203536073

x35 = -65.9734457253857

x36 = -87.9645943005142

x37 = -90.0589894029074

x38 = 26.1799387799149

x39 = 82.2050078081952

x40 = 7.85398156323863

x41 = -69.6386371711468

x42 = -56.0250689658707

x43 = 24.0855436775217

x44 = 87.9645943005142

x45 = -68.5914396168299

x46 = -63.8790506229925

x47 = 92.1533845053006

x48 = 56.0250689490422

x49 = 31.9395253488514

x50 = 14.6607657167524

x51 = -47.6474886059294

x52 = 72.2566310325652

x53 = -17.8023583703422

x54 = 40.3171056875068

x55 = 2.0943951023932

x56 = -60.7374579694027

x57 = -85.870199198121

x58 = 46.0766922526503

x59 = 62.3082542647397

x60 = 78.0162175408331

x61 = 73.8274272238026

x62 = -34.0339203853826

x63 = -42.4115008967313

x64 = 28.2743338823081

x65 = -71.733032268673

x66 = 94.2477796076938

x67 = 21.9911485751286

x68 = -15.707963267949

x69 = 12.0427717539012

x70 = -61.7846555205993

x71 = 65.9734457253857

x72 = -31.9395254400222

x73 = -81.157810257599

x74 = 4.18879020478639

x75 = -9.94837684908959

x76 = 60.2138592244649

x77 = -7.85398169885663

x78 = 100.007366129686

x79 = 6.28318530717959

x80 = 68.0678408277789

x81 = 86.3937980770007

x82 = -96.8657736141804

x83 = -28.2743338823081

x84 = -29.8451301356856

x85 = -93.7241808491601

x86 = 84.2994028428616

x87 = 80.1106127345707

x88 = 90.0589894029074

x89 = -58.1194640908306

x90 = -49.7418836876647

x91 = -83.7758040957278

x92 = -37.6991118430775

x93 = -91.6297857283069

x93 = -91.6297857283069

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Identical expressions

Similar expressions

sin3x+sin9x=0 equation

Numerical solution:

The solution