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tanx/2=√3/2

tanx/2=√3/2 equation

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Numerical solution:

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The solution

You have entered [src]
           ___
tan(x)   \/ 3 
------ = -----
  2        2  
$$\frac{\tan{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\frac{\tan{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/2

The equation is transformed to
$$\tan{\left(x \right)} = \sqrt{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
The graph
Rapid solution [src]
     pi
x1 = --
     3 
$$x_{1} = \frac{\pi}{3}$$
Sum and product of roots [src]
sum
    pi
0 + --
    3 
$$0 + \frac{\pi}{3}$$
=
pi
--
3 
$$\frac{\pi}{3}$$
product
  pi
1*--
  3 
$$1 \frac{\pi}{3}$$
=
pi
--
3 
$$\frac{\pi}{3}$$
pi/3
Numerical answer [src]
x1 = 51.3126800086333
x2 = 4.18879020478639
x3 = 98.4365698124802
x4 = 48.1710873550435
x5 = -71.2094334813686
x6 = 67.0206432765823
x7 = 41.8879020478639
x8 = -49.2182849062401
x9 = 29.3215314335047
x10 = -61.7846555205993
x11 = 32.4631240870945
x12 = -27.2271363311115
x13 = -5.23598775598299
x14 = 16.7551608191456
x15 = 85.870199198121
x16 = -64.9262481741891
x17 = 70.162235930172
x18 = 79.5870138909414
x19 = -46.0766922526503
x20 = -90.0589894029074
x21 = 38.7463093942741
x22 = 73.3038285837618
x23 = 57.5958653158129
x24 = 82.7286065445312
x25 = -20.943951023932
x26 = 92.1533845053006
x27 = 7.33038285837618
x28 = -33.5103216382911
x29 = 76.4454212373516
x30 = -8.37758040957278
x31 = -39.7935069454707
x32 = -74.3510261349584
x33 = -99.4837673636768
x34 = -77.4926187885482
x35 = -55.5014702134197
x36 = 60.7374579694027
x37 = -96.342174710087
x38 = -86.9173967493176
x39 = -80.634211442138
x40 = 10.471975511966
x41 = -17.8023583703422
x42 = 26.1799387799149
x43 = -93.2005820564972
x44 = -14.6607657167524
x45 = -30.3687289847013
x46 = -2.0943951023932
x47 = -11.5191730631626
x48 = -68.0678408277789
x49 = -83.7758040957278
x50 = 23.0383461263252
x51 = 1.0471975511966
x52 = 13.6135681655558
x53 = 19.8967534727354
x54 = -42.9350995990605
x55 = -58.6430628670095
x56 = -24.0855436775217
x57 = -36.6519142918809
x58 = 54.4542726622231
x59 = 101.57816246607
x60 = -52.3598775598299
x61 = 45.0294947014537
x62 = 35.6047167406843
x63 = 95.2949771588904
x64 = 63.8790506229925
x64 = 63.8790506229925
The graph
tanx/2=√3/2 equation