Question

Find all solutions to the equation.

cos2x + 2 cos x + 1 = 0

Answer 1

i dont understand

Answer 2

Do you know a formula for cos2x?

Answer 3

Like cos2x = 2cos²x-1 ?

Answer 4

no but i know cosx= (1/secx)

Answer 5

If you replace cos2x with 2cos²x-1, you have a quadratic equation, with cosx as variable.

Answer 6

ok..

Answer 7

error, my bad. cos^(2)x + 2 cos x + 1 = 0

Answer 8

OK, so you already have a quadratic equation in cosx:
\[(\cos x)^2 + 2\cos x +1 = 0\]
If you like you could temporarily set p=cosx to get:\[p^2+2p+1=0\]Could you try to solve that one?

Answer 9

im stuck at p^(3)=-1/2

Answer 10

How do you get p^3 ?

Answer 11

@Lauren01 is it cos^2 x or cos 2x

Answer 12

This is the form you can use: (p+...)(p+...)=0.
You must have done that before, I guess.
Just look for the numbers on the dots: their sum is 2, their product is 1.
They are not difficult to find...

Answer 13

@Yahoo! It is cos²x, @Lauren01 already mentioned...

Answer 14

oh...Sorry ...Did nt See !

Answer 15

We're waiting for Lauren01 to make a move.. ;)

Answer 16

sorry i got distracted by the office. its pie. because x=-1 is on Pie. (unit circle)

Answer 17

(p+1)(p+1)=0
cosx+1=0
cosx=-1

using the unit cirle x=-1 is on Pie.

Answer 18

Well done!
BTW, aren't you supposed to give more answers, like x=pi+2k*pi, or do you have to solve only for x in [0,2pi]?

Answer 19

only one is fine

Answer 20

OK, next prob!

Answer 21

lol do you wanna do all my homework? lmao

Answer 22

Now you do your homework, then I'll only help you along...

Answer 23

lol goood choice