Question

Find all solutions to the equation. cos2x + 2 cos x + 1 = 0

Answer 1

write cos(2x) in terms of cos^2(x) using an identity
then you would have a quadratic type equation

Answer 2

recall the double angle identity

Answer 3

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

Answer 4

cos(2x) doesn't equal cos^2(x)

Answer 5

use an identity for cos(2x)

Answer 6

no that's the original problem. the squared didn't show at first.

Answer 7

I took out a gcf of cosx and was left with cosx=0 and cosx=-3

Answer 8

do you know how to solve u^2+2u+1=0?

Answer 9

the gcf isn't cos(x) because cos(x) doesn't divide 1

Answer 10

no I don't , i got 3pi/2 ? but im not sure if its correct

Answer 11

do you know how to solve u^2+2u+1=0?

Answer 12

no

Answer 13

so you were never thought how to use the quadratic formula or how to factor?

Answer 14

taught*

Answer 15

yes i have been taught that. its just that we haven't done it in awhile so ts a little blurry

Answer 16

that is the way you are expected to solve this one

Answer 17

the coefficient of u^2 is 1
so all you need to answer is what two numbers multiply to be c and add up to be b
in other words
what two numbers multiply to be 1 and add up to be 2?

Answer 18

1 and 1

Answer 19

so u^2+2u+1
can be written as
(u+1)(u+1)
now back to solving u^2+2u+1=0
so we have (u+1)(u+1)=0
which means u has to be equal to?

Answer 20

-1

Answer 21

so if u=-1
and we solved u^2+2u+1=0
instead of cos^2(x)+2cos(x)+1=0
then that means u=cos(x)
which means cos(x)=-1

Answer 22

can you solve this equation for x
cos(x)=-1?

Answer 23

ohhh so it would be (pi)

Answer 24

i understand it now. thank you

Answer 25

pi is a solution between 0 and 2 pi
there are many more solutions outside that domain of numbers