SOLUTION: Solve for x on the interval [0,2pi]. cos^2(x)+3cos(x)+2=0 Someone please help, this assignment is due tomorrow and I cannot find how to do this anywhere.

Algebra ->  Trigonometry-basics -> SOLUTION: Solve for x on the interval [0,2pi]. cos^2(x)+3cos(x)+2=0 Someone please help, this assignment is due tomorrow and I cannot find how to do this anywhere.      Log On


   



Question 1043022: Solve for x on the interval [0,2pi].

cos^2(x)+3cos(x)+2=0

Someone please help, this assignment is due tomorrow and I cannot find how to do this anywhere.

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
cos%5E2%28x%29%2B3cos%28x%29%2B2 = 0


Factor left side

(cos(x) + 1)*(cos(x) + 2) = 0.


Then the original equation deploys in two separate independent equations

1.  cos(x) + 1 = 0  --->  cos(x) = -1  --->  x = 3pi%2F2,  and


2.  cos(x) + 2 = 0  --->  cos(x) = -2,  which has no solutions.

Answer.  x = 3pi%2F2.

See the lessons in this site
    - Solving simple problems on trigonometric equations
    - Solving more complicated problems on trigonometric equations
    - Solving advanced problems on trigonometric equations

They teach you by examples on how to solve similar and other trigonometric equations.