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2*cos(x+pi/3)=5 equation

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Numerical solution:

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The solution

You have entered [src] 
     /    pi\    
2*cos|x + --| = 5
     \    3 /
2cos⁡(x+π3)=52 \cos{\left(x + \frac{\pi}{3} \right)} = 5
Simplify
Detail solution
Given the equation
2cos⁡(x+π3)=52 \cos{\left(x + \frac{\pi}{3} \right)} = 5
- this is the simplest trigonometric equation
Divide both parts of the equation by 2

The equation is transformed to
cos⁡(x+π3)=52\cos{\left(x + \frac{\pi}{3} \right)} = \frac{5}{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
0-80-60-40-2020406080-100100-1010
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
       pi                                  
x1 = - -- + I*im(acos(5/2)) + re(acos(5/2))
       3
x1=−π3+re⁡(acos⁡(52))+iim⁡(acos⁡(52))x_{1} = - \frac{\pi}{3} + \operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} 
     5*pi                  
x2 = ---- - I*im(acos(5/2))
      3
x2=5π3−iim⁡(acos⁡(52))x_{2} = \frac{5 \pi}{3} - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} 
x2 = 5*pi/3 - i*im(acos(5/2))
Sum and product of roots [src] 
sum
  pi                                     5*pi                  
- -- + I*im(acos(5/2)) + re(acos(5/2)) + ---- - I*im(acos(5/2))
  3                                       3
(5π3−iim⁡(acos⁡(52)))+(−π3+re⁡(acos⁡(52))+iim⁡(acos⁡(52)))\left(\frac{5 \pi}{3} - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) + \left(- \frac{\pi}{3} + \operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) 
=
4*pi                
---- + re(acos(5/2))
 3
re⁡(acos⁡(52))+4π3\operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + \frac{4 \pi}{3} 
product
/  pi                                  \ /5*pi                  \
|- -- + I*im(acos(5/2)) + re(acos(5/2))|*|---- - I*im(acos(5/2))|
\  3                                   / \ 3                    /
(5π3−iim⁡(acos⁡(52)))(−π3+re⁡(acos⁡(52))+iim⁡(acos⁡(52)))\left(\frac{5 \pi}{3} - i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) \left(- \frac{\pi}{3} + \operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) 
=
(5*pi - 3*I*im(acos(5/2)))*(-pi + 3*re(acos(5/2)) + 3*I*im(acos(5/2)))
----------------------------------------------------------------------
                                  9
(5π−3iim⁡(acos⁡(52)))(−π+3re⁡(acos⁡(52))+3iim⁡(acos⁡(52)))9\frac{\left(5 \pi - 3 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) \left(- \pi + 3 \operatorname{re}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + 3 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right)}{9} 
(5*pi - 3*i*im(acos(5/2)))*(-pi + 3*re(acos(5/2)) + 3*i*im(acos(5/2)))/9
Numerical answer [src] 
x1 = -1.0471975511966 + 1.56679923697241*i
x2 = 5.23598775598299 - 1.56679923697241*i
x2 = 5.23598775598299 - 1.56679923697241*i
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