Question

Find all solutions in the interval [0, 2π).
cos^2x + 2 cos x + 1 = 0

A) x = 2π
B) x = π
C) x = pi/4, 7pi/4
D) x = pi/2, 3pi/2

Answer 1

Suppose cos x as y.

Rewrite:

y^2 + 2y + 1 =0

Solve the quadratic.

Answer 2

Y=-1

Answer 3

Now since y = -1

cos x = y

cos x = -1

Can you solve from here?

Answer 4

not really?

Answer 5

cos x = 1
x = cos^-1(1)

Calc should say pi/

Answer 6

pi/? It doesnt say anything but -1

Answer 7

\[\Large \cos^{-1} (-1)\]

Answer 8

Oh! Now I understand, thank you so much