Find all solutions to the equation.

cos^2x + 2 cos x + 1 = 0

Question

Find all solutions to the equation.

cos^2x + 2 cos x + 1 = 0

caozeyuan · Answer

you mean$$\cos ^{2}x+2\cos x+1=0 $$

anonymous · Answer

put Cos x = y and turn the equation into a quadratic in y.

caozeyuan · Answer

set cos x = A 
 thus  A^2+2A=1=0
so A+1)^2 =0
that is A+1=0
meaning A=-1
now substitute back to x giving cos x =-1
can you solve it now?
BTW is x is degree or radius and what's the range for value of x?

anonymous · Answer

it doesnt say if its in radians or degrees 
@caozeyuan

caozeyuan · Answer

well I would like to treat it as radius, but you can deal with it whichever way you want

caozeyuan · Answer

if cos x =-1 that means x=arccos(-1)=pi.
if the values are from -pi to pi then, -pi is another solution. 
if they are supposed to be in 0 to 2pi then there are no other solutions in range.

dumbcow · Answer

usually default parameters for these problems are :
answer in radians from 0 to 2pi