Mister Exam

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

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#### Numerical solution:

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### The solution

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\/ 3
tan(x) = -----
3  
$$\tan{\left(x \right)} = \frac{\sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(x \right)} = \frac{\sqrt{3}}{3}$$
- 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
Sum and product of roots [src]
sum
pi
--
6 
$$\left(\frac{\pi}{6}\right)$$
=
pi
--
6 
$$\frac{\pi}{6}$$
product
pi
--
6 
$$\left(\frac{\pi}{6}\right)$$
=
pi
--
6 
$$\frac{\pi}{6}$$
Rapid solution [src]
      pi
x_1 = --
6 
$$x_{1} = \frac{\pi}{6}$$
x1 = 13.0899693899575
x2 = 57.0722665402146
x3 = -2.61799387799149
x4 = -84.2994028713261
x5 = -27.7507351067098
x6 = -21.4675497995303
x7 = 75.9218224617533
x8 = 94.7713783832921
x9 = -46.6002910282486
x10 = -71.733032256967
x11 = 38.2227106186758
x12 = 19.3731546971371
x13 = -93.7241808320955
x14 = -43.4586983746588
x15 = 25.6563400043166
x16 = -96.8657734856853
x17 = 53.9306738866248
x18 = -34.0339204138894
x19 = 44.5058959258554
x20 = 28.7979326579064
x21 = 97.9129710368819
x22 = 85.3466004225227
x23 = 82.2050077689329
x24 = -100.007366139275
x25 = -81.1578102177363
x26 = -37.1755130674792
x27 = -24.60914245312
x28 = -78.0162175641465
x29 = 47.6474885794452
x30 = -12.0427718387609
x31 = -90.5825881785057
x32 = 60.2138591938044
x33 = 3.66519142918809
x34 = 79.0634151153431
x35 = -62.3082542961976
x36 = 101.054563690472
x37 = 16.2315620435473
x38 = -52.8834763354282
x39 = 88.4881930761125
x40 = -18.3259571459405
x41 = -74.8746249105567
x42 = -5.75958653158129
x43 = 63.3554518473942
x44 = 41.3643032722656
x45 = -87.4409955249159
x46 = 31.9395253114962
x47 = 72.7802298081635
x48 = -68.5914396033772
x49 = 69.6386371545737
x50 = 66.497044500984
x51 = -65.4498469497874
x52 = -56.025068989018
x53 = 6.80678408277789
x54 = -15.1843644923507
x55 = -49.7418836818384
x56 = -59.1666616426078
x57 = 50.789081233035
x58 = -30.8923277602996
x59 = -40.317105721069
x60 = 22.5147473507269
x61 = 0.523598775598299
x62 = 9.94837673636768
x63 = 91.6297857297023
x64 = -8.90117918517108
x65 = 35.081117965086
x65 = 35.081117965086
The graph