Find all solutions in the interval $\sf [0, 2\pi).$

$\sf cos^2x + 2 cos x + 1 = 0$

Question

Find all solutions in the interval $\sf [0, 2\pi).$

$\sf cos^2x + 2 cos x + 1 = 0$

sleepyjess · Answer

@amistre64

anonymous · Answer

$$\cos^2x+2\cos x+1=(\cos x+1)^2=0$$

sleepyjess · Answer

@sleepyhead314

sleepyjess · Answer

I just don't get it.......

sleepyhead314 · Answer

I agree with siths
imagine (random letter)  X = (cos(x))
then   X^2 +2X + 1 = 0
factor it, what do you get? :)

sleepyhead314 · Answer

x^2 + 2x + 1
factor, what do you get? ^_^
this is Algebra 1 style :P

sleepyjess · Answer

(x+1)(x+1)

sleepyhead314 · Answer

yes!
which is the same as   (x+1)^2
right? :)

sleepyjess · Answer

yes

sleepyhead314 · Answer

so before I said   let   X = cos(x)
now we will plug that back in :)
so   ( cos(x) + 1 )^2     <---- do you see where siths got that now? :)

sleepyjess · Answer

Yeah

sleepyhead314 · Answer

then if we squareroot both sides we will still get
cos(x) + 1 = 0
then subtract 1 from both sides

sleepyjess · Answer

cos(x)=-1

sleepyhead314 · Answer

now when does cos(x) = -1 ?|dw:1418693093268:dw|