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-cos(x)=-(√3/2) equation

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Numerical solution:

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The solution

You have entered [src] 
             ___ 
          -\/ 3  
-cos(x) = -------
             2
−cos⁡(x)=−32- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}
Simplify
Detail solution
Given the equation
−cos⁡(x)=−32- \cos{\left(x \right)} = - \frac{\sqrt{3}}{2}
- this is the simplest trigonometric equation
Divide both parts of the equation by -1

The equation is transformed to
cos⁡(x)=32\cos{\left(x \right)} = \frac{\sqrt{3}}{2}
This equation is transformed to
x=πn+acos⁡(32)x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}
x=πn−π+acos⁡(32)x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}
Or
x=πn+π6x = \pi n + \frac{\pi}{6}
x=πn−5π6x = \pi n - \frac{5 \pi}{6}
, where n - is a integer
The graph
0-80-60-40-2020406080-1001002-2
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
pi   11*pi
-- + -----
6      6
π6+11π6\frac{\pi}{6} + \frac{11 \pi}{6} 
=
2*pi
2π2 \pi 
product
pi 11*pi
--*-----
6    6
π611π6\frac{\pi}{6} \frac{11 \pi}{6} 
=
     2
11*pi 
------
  36
11π236\frac{11 \pi^{2}}{36} 
11*pi^2/36
Rapid solution [src] 
     pi
x1 = --
     6
x1=π6x_{1} = \frac{\pi}{6} 
     11*pi
x2 = -----
       6
x2=11π6x_{2} = \frac{11 \pi}{6} 
x2 = 11*pi/6
Numerical answer [src] 
x1 = 62.3082542961976
x2 = -93.7241808320955
x3 = 69.6386371545737
x4 = -25.6563400043166
x5 = -94.7713783832921
x6 = 57.0722665402146
x7 = -30.8923277602996
x8 = -24.60914245312
x9 = 5.75958653158129
x10 = 100.007366139275
x11 = -74.8746249105567
x12 = 87.4409955249159
x13 = 63.3554518473942
x14 = -69.6386371545737
x15 = 24.60914245312
x16 = 194.255145746969
x17 = -31.9395253114962
x18 = -43.4586983746588
x19 = -37.1755130674792
x20 = 30.8923277602996
x21 = -75.9218224617533
x22 = 0.523598775598299
x23 = -82.2050077689329
x24 = 38.2227106186758
x25 = -68.5914396033772
x26 = 44.5058959258554
x27 = 43.4586983746588
x28 = 94.7713783832921
x29 = 37.1755130674792
x30 = 93.7241808320955
x31 = 68.5914396033772
x32 = 18.3259571459405
x33 = -0.523598775598299
x34 = 50.789081233035
x35 = -50.789081233035
x36 = 74.8746249105567
x37 = -87.4409955249159
x38 = -5.75958653158129
x39 = -56.025068989018
x40 = 19.3731546971371
x41 = 13.0899693899575
x42 = -57.0722665402146
x43 = -12.0427718387609
x44 = 6.80678408277789
x45 = -44.5058959258554
x46 = -81.1578102177363
x47 = -13.0899693899575
x48 = 88.4881930761125
x49 = -88.4881930761125
x50 = -18.3259571459405
x51 = 31.9395253114962
x52 = 82.2050077689329
x53 = -101.054563690472
x54 = 56.025068989018
x55 = 75.9218224617533
x56 = -38.2227106186758
x57 = 49.7418836818384
x58 = -6.80678408277789
x59 = 81.1578102177363
x60 = -100.007366139275
x61 = -62.3082542961976
x62 = 1168.1488683598
x63 = -49.7418836818384
x64 = 12.0427718387609
x65 = -19.3731546971371
x66 = 25.6563400043166
x67 = -63.3554518473942
x67 = -63.3554518473942
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