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cosx/5=-(√3/2) equation

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Numerical solution:

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The solution

You have entered [src] 
            ___ 
cos(x)   -\/ 3  
------ = -------
  5         2
cos⁡(x)5=−32\frac{\cos{\left(x \right)}}{5} = - \frac{\sqrt{3}}{2}
Simplify
Detail solution
Given the equation
cos⁡(x)5=−32\frac{\cos{\left(x \right)}}{5} = - \frac{\sqrt{3}}{2}
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/5

The equation is transformed to
cos⁡(x)=−532\cos{\left(x \right)} = - \frac{5 \sqrt{3}}{2}
As right part of the equation
modulo =
True

but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
The graph
0-80-60-40-2020406080-1001001-1
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
    /    /     ___\\              /    /     ___\\       /    /     ___\\     /    /     ___\\
    |    |-5*\/ 3 ||              |    |-5*\/ 3 ||       |    |-5*\/ 3 ||     |    |-5*\/ 3 ||
- re|acos|--------|| + 2*pi - I*im|acos|--------|| + I*im|acos|--------|| + re|acos|--------||
    \    \   2    //              \    \   2    //       \    \   2    //     \    \   2    //
(re⁡(acos⁡(−532))+iim⁡(acos⁡(−532)))+(−re⁡(acos⁡(−532))+2π−iim⁡(acos⁡(−532)))\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) 
=
2*pi
2π2 \pi 
product
/    /    /     ___\\              /    /     ___\\\ /    /    /     ___\\     /    /     ___\\\
|    |    |-5*\/ 3 ||              |    |-5*\/ 3 ||| |    |    |-5*\/ 3 ||     |    |-5*\/ 3 |||
|- re|acos|--------|| + 2*pi - I*im|acos|--------|||*|I*im|acos|--------|| + re|acos|--------|||
\    \    \   2    //              \    \   2    /// \    \    \   2    //     \    \   2    ///
(re⁡(acos⁡(−532))+iim⁡(acos⁡(−532)))(−re⁡(acos⁡(−532))+2π−iim⁡(acos⁡(−532)))\left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) 
=
 /    /    /     ___\\     /    /     ___\\\ /            /    /     ___\\     /    /     ___\\\
 |    |    |-5*\/ 3 ||     |    |-5*\/ 3 ||| |            |    |-5*\/ 3 ||     |    |-5*\/ 3 |||
-|I*im|acos|--------|| + re|acos|--------|||*|-2*pi + I*im|acos|--------|| + re|acos|--------|||
 \    \    \   2    //     \    \   2    /// \            \    \   2    //     \    \   2    ///
−(re⁡(acos⁡(−532))+iim⁡(acos⁡(−532)))(−2π+re⁡(acos⁡(−532))+iim⁡(acos⁡(−532)))- \left(\operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)}\right) 
-(i*im(acos(-5*sqrt(3)/2)) + re(acos(-5*sqrt(3)/2)))*(-2*pi + i*im(acos(-5*sqrt(3)/2)) + re(acos(-5*sqrt(3)/2)))
Rapid solution [src] 
         /    /     ___\\              /    /     ___\\
         |    |-5*\/ 3 ||              |    |-5*\/ 3 ||
x1 = - re|acos|--------|| + 2*pi - I*im|acos|--------||
         \    \   2    //              \    \   2    //
x1=−re⁡(acos⁡(−532))+2π−iim⁡(acos⁡(−532))x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} 
         /    /     ___\\     /    /     ___\\
         |    |-5*\/ 3 ||     |    |-5*\/ 3 ||
x2 = I*im|acos|--------|| + re|acos|--------||
         \    \   2    //     \    \   2    //
x2=re⁡(acos⁡(−532))+iim⁡(acos⁡(−532))x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(- \frac{5 \sqrt{3}}{2} \right)}\right)} 
x2 = re(acos(-5*sqrt(3)/2)) + i*im(acos(-5*sqrt(3)/2))
Numerical answer [src] 
x1 = 3.14159265358979 + 2.14513586791928*i
x2 = 3.14159265358979 - 2.14513586791928*i
x2 = 3.14159265358979 - 2.14513586791928*i
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