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cos(x)=-2

cos(x)=-2 equation

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Numerical solution:

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The solution

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cos(x) = -2
$$\cos{\left(x \right)} = -2$$
Detail solution
Given the equation
$$\cos{\left(x \right)} = -2$$
- 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
Rapid solution [src]
x1 = -re(acos(-2)) + 2*pi - I*im(acos(-2))
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}$$
x2 = I*im(acos(-2)) + re(acos(-2))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}$$
Sum and product of roots [src]
sum
0 + -re(acos(-2)) + 2*pi - I*im(acos(-2)) + I*im(acos(-2)) + re(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
$$2 \pi$$
product
1*(-re(acos(-2)) + 2*pi - I*im(acos(-2)))*(I*im(acos(-2)) + re(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)))
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right)$$
-(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