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cos(x)/5=-1

cos(x)/5=-1 equation

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Numerical solution:

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The solution

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

The equation is transformed to
cos⁡(x)=−5\cos{\left(x \right)} = -5
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
0-80-60-40-2020406080-1001001-2
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -re(acos(-5)) + 2*pi - I*im(acos(-5))
x1=−re⁡(acos⁡(−5))+2π−iim⁡(acos⁡(−5))x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}
Simplify 
x2 = I*im(acos(-5)) + re(acos(-5))
x2=re⁡(acos⁡(−5))+iim⁡(acos⁡(−5))x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}
Simplify
Sum and product of roots [src] 
sum
0 + -re(acos(-5)) + 2*pi - I*im(acos(-5)) + I*im(acos(-5)) + re(acos(-5))
(re⁡(acos⁡(−5))+iim⁡(acos⁡(−5)))−(−2π+re⁡(acos⁡(−5))+iim⁡(acos⁡(−5)))\left(\operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) - \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) 
=
2*pi
2π2 \pi 
product
1*(-re(acos(-5)) + 2*pi - I*im(acos(-5)))*(I*im(acos(-5)) + re(acos(-5)))
(re⁡(acos⁡(−5))+iim⁡(acos⁡(−5)))1(−re⁡(acos⁡(−5))+2π−iim⁡(acos⁡(−5)))\left(\operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) 
=
-(I*im(acos(-5)) + re(acos(-5)))*(-2*pi + I*im(acos(-5)) + re(acos(-5)))
−(re⁡(acos⁡(−5))+iim⁡(acos⁡(−5)))(−2π+re⁡(acos⁡(−5))+iim⁡(acos⁡(−5)))- \left(\operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-5 \right)}\right)}\right) 
-(i*im(acos(-5)) + re(acos(-5)))*(-2*pi + i*im(acos(-5)) + re(acos(-5)))
Numerical answer [src] 
x1 = 3.14159265358979 + 2.29243166956118*i
x2 = 3.14159265358979 - 2.29243166956118*i
x2 = 3.14159265358979 - 2.29243166956118*i
The graph
cos(x)/5=-1 equation
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