Question

Find all solutions in the interval [0, 2π).

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

Answer 1

Factorise:
\[\cos^2x+2\cos x+1=0\\
(\cos x+1)^2=0\]
So you have
\[\cos x=-1\]
Now, which value of \(x\) in \([0,2\pi)\) gives you \(\cos x=-1\)?

Answer 2

pi

Answer 3

Yep

Answer 4

so that it?

Answer 5

Yes, unless you can think of any other \(x\) that make \(\cos x=-1\) ?

Answer 6

alright thanks

Answer 7

you're welcome