Question

Help please?

Answer 1

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

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

Answer 2

I'm a visual learner so the book's not helping too much :s

Answer 3

a.) x = 2π

b.) x = π

c.) x = π/4, 7π/4

d.) x = π/2, 3π/2

Answer 4

does it help to know that \(z^2+2z+1=(z+1)^2\)

Answer 5

i.e.
\[\cos^2(x)+2\cos(x)+1=(\cos(x)+1)^2\]

Answer 6

so (cos(x) + 1)^2 = 0?

Answer 7

yes

Answer 8

making \(\cos(x)=-1\)