Question

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

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

Answer 1

@amistre64

Answer 2

\[\cos^2x+2\cos x+1=(\cos x+1)^2=0\]

Answer 3

@sleepyhead314

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

(x+1)(x+1)

Answer 8

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

Answer 9

yes

Answer 10

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? :)

Answer 11

Yeah

Answer 12

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

Answer 13

cos(x)=-1

Answer 14

now when does cos(x) = -1 ?