## anonymous one year ago Find all solutions to the equation. cos2x + 2 cos x + 1 = 0

1. Nnesha

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

2. Nnesha

can you u factor it ?

3. anonymous

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

4. anonymous

the 1 should be on the parenthesis*

5. Nnesha

yes right set it equal to zero

6. anonymous

It'll be -1.

7. Nnesha

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

8. anonymous

Is pi the only solution?

9. Nnesha

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

10. Nnesha

yes right cos x = -1 = pi

11. anonymous

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

12. Nnesha

pi +2 ?

13. Nnesha

just pi

14. Nnesha

$\pi + 2 \cancel =\pi$

15. anonymous

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."

16. anonymous

So I'm kinda confused.

17. Mertsj

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

18. anonymous

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

19. Mertsj

yw

20. Nnesha

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