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cos(x)=-2

cos(x)=-2 equation

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Numerical solution:

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The solution

You have entered [src] 
cos(x) = -2
cos⁡(x)=−2\cos{\left(x \right)} = -2
Simplify
Detail solution
Given the equation
cos⁡(x)=−2\cos{\left(x \right)} = -2
- this is the simplest trigonometric equation
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
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = -re(acos(-2)) + 2*pi - I*im(acos(-2))
x1=−re⁡(acos⁡(−2))+2π−iim⁡(acos⁡(−2))x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}
Simplify 
x2 = I*im(acos(-2)) + re(acos(-2))
x2=re⁡(acos⁡(−2))+iim⁡(acos⁡(−2))x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}
Simplify
Sum and product of roots [src] 
sum
0 + -re(acos(-2)) + 2*pi - I*im(acos(-2)) + I*im(acos(-2)) + re(acos(-2))
(re⁡(acos⁡(−2))+iim⁡(acos⁡(−2)))−(−2π+re⁡(acos⁡(−2))+iim⁡(acos⁡(−2)))\left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) - \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) 
=
2*pi
2π2 \pi 
product
1*(-re(acos(-2)) + 2*pi - I*im(acos(-2)))*(I*im(acos(-2)) + re(acos(-2)))
(re⁡(acos⁡(−2))+iim⁡(acos⁡(−2)))1(−re⁡(acos⁡(−2))+2π−iim⁡(acos⁡(−2)))\left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) 
=
-(I*im(acos(-2)) + re(acos(-2)))*(-2*pi + I*im(acos(-2)) + re(acos(-2)))
−(re⁡(acos⁡(−2))+iim⁡(acos⁡(−2)))(−2π+re⁡(acos⁡(−2))+iim⁡(acos⁡(−2)))- \left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) 
-(i*im(acos(-2)) + re(acos(-2)))*(-2*pi + i*im(acos(-2)) + re(acos(-2)))
Numerical answer [src] 
x1 = 3.14159265358979 + 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i
The graph
cos(x)=-2 equation
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