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tan(x)=-sqrt(3)/3

tan(x)=-sqrt(3)/3 equation

A equation with variable:

Numerical solution:

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The solution

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            ___ 
         -\/ 3  
tan(x) = -------
            3   
$$\tan{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
The graph
Rapid solution [src]
     -pi 
x1 = ----
      6  
$$x_{1} = - \frac{\pi}{6}$$
x1 = -pi/6
Sum and product of roots [src]
sum
-pi 
----
 6  
$$- \frac{\pi}{6}$$
=
-pi 
----
 6  
$$- \frac{\pi}{6}$$
product
-pi 
----
 6  
$$- \frac{\pi}{6}$$
=
-pi 
----
 6  
$$- \frac{\pi}{6}$$
-pi/6
Numerical answer [src]
x1 = -79.0634151153431
x2 = 87.4409955249159
x3 = 93.7241808320955
x4 = -41.3643032722656
x5 = 30.8923277602996
x6 = -9.94837673636768
x7 = -28.7979326579064
x8 = -38.2227106186758
x9 = -88.4881930761125
x10 = 15.1843644923507
x11 = -97.9129710368819
x12 = -35.081117965086
x13 = 2.61799387799149
x14 = 43.4586983746588
x15 = -47.6474885794452
x16 = -101.054563690472
x17 = -19.3731546971371
x18 = 56.025068989018
x19 = 62.3082542961976
x20 = -53.9306738866248
x21 = 59.1666616426078
x22 = -25.6563400043166
x23 = -0.523598775598299
x24 = 46.6002910282486
x25 = -13.0899693899575
x26 = 27.7507351067098
x27 = -57.0722665402146
x28 = 96.8657734856853
x29 = -16.2315620435473
x30 = -50.789081233035
x31 = 78.0162175641465
x32 = 84.2994028713261
x33 = 34.0339204138894
x34 = -31.9395253114962
x35 = 49.7418836818384
x36 = 18.3259571459405
x37 = 81.1578102177363
x38 = 24.60914245312
x39 = 68.5914396033772
x40 = -22.5147473507269
x41 = -69.6386371545737
x42 = -66.497044500984
x43 = 40.317105721069
x44 = 74.8746249105567
x45 = -63.3554518473942
x46 = -3.66519142918809
x47 = -6.80678408277789
x48 = 21.4675497995303
x49 = -75.9218224617533
x50 = -91.6297857297023
x51 = 8.90117918517108
x52 = 52.8834763354282
x53 = 12.0427718387609
x54 = -82.2050077689329
x55 = -72.7802298081635
x56 = 5.75958653158129
x57 = -44.5058959258554
x58 = -60.2138591938044
x59 = 90.5825881785057
x60 = 65.4498469497874
x61 = 37.1755130674792
x62 = 100.007366139275
x63 = -85.3466004225227
x64 = 71.733032256967
x65 = -94.7713783832921
x65 = -94.7713783832921
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