cos(x)=-2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
cos(x)=−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
x1 = -re(acos(-2)) + 2*pi - I*im(acos(-2))
x1=−re(acos(−2))+2π−iim(acos(−2))
x2 = I*im(acos(-2)) + re(acos(-2))
x2=re(acos(−2))+iim(acos(−2))
Sum and product of roots
[src]
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)))
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)))
-(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)))
-(i*im(acos(-2)) + re(acos(-2)))*(-2*pi + i*im(acos(-2)) + re(acos(-2)))
x1 = 3.14159265358979 + 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i