Question

Find all solutions to the equation.

cos2x + 2 cos x + 1 = 0

Answer 1

let cosx = x
then deal with it as quadratic equation \[\huge\rm x^2 +2x +1 =0\]

Answer 2

can you u factor it ?

Answer 3

So it is like (x+1)(x+)1.

Answer 4

the 1 should be on the parenthesis*

Answer 5

yes right set it equal to zero

Answer 6

It'll be -1.

Answer 7

x = -1 so now we can change x to cos x
cos x = -1

Answer 8

Is pi the only solution?

Answer 9

yep right or -1 has multiplicity of 2
bec cox = -1 , cosx =- 1 are solution

Answer 10

yes right cos x = -1 = pi

Answer 11

Uhm do I have to put pi+2 pi n as the solution or just pi?

Answer 12

pi +2 ?

Answer 13

just pi

Answer 14

\[\pi + 2 \cancel =\pi \]

Answer 15

I know that haha, but base on my textbook,

"Method for Solving Trigonometric Equations
Unless the equation is factorable, use substitution to get just one trigonometric function.

Solve the equation for the trigonometric function.

Solve for the variable in a general window of +2pin for sine and cosine and +pin for tangent.

Find the specific solutions in the given interval by replacing n with integers."

Answer 16

So I'm kinda confused.

Answer 17

It said to find all solutions. One solution is pi. Another solution is 3pi. Another solution is 5pi...
We write that like this:
\[x=\pi+2\pi n\]

Answer 18

@Mertsj That's what I'm talking about lol thank you for the help guys!

Answer 19

yw

Answer 20

cool i didn't know this x = pi + 2pi n thingy