Question

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

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

Answer 1

Could it be simplified to (cos(x) + 1)^2?

Answer 2

and i am totally confused how to do it after that

Answer 3

Answers are 2pi, pi, pi/4 and 7pi/4, or pi/2 and 3pi/2

Answer 4

your first step is correct, the next step is to take the square root of both sides

Answer 5

look at it like \(y^2+2y+1=0\)

Answer 6

so cos(x) = -1 ???

Answer 7

solve for y tell you found the values
then replace y by cosx
then solve

Answer 8

oh yes

Answer 9

yes! now find every x for which cos(x) = -1

Answer 10

Solve by putting y=cosx
At last check values of y only in range of cosx then you will get the answer.

Answer 11

pi?

Answer 12

yup, good job!

Answer 13

sorry my computer froze for a bit

Answer 14

ty for your help

Answer 15

what if we extended the domain to (0, 5pi)
what are the solutions ?

Answer 16

@starwars18

Answer 17

-1 + n2pi, n being a real integer from 0 to 2