Thread: Trig Equations

Solve the following equations for 0<x<2pi

4cosx(cosx-1)=-5cosx

i managed to do-

4cos^2(x) - 4cosx = -5cosx
4cos^2(x) + cosx = 0
4cosx + 1 = 0
cosx = -1/4

x = 104.5

I used the cos graph but the answers I was given were-

x= 90, -90, 104, -104

bit confused

Originally Posted by greghunter

i managed to do-

4cos^2(x) - 4cosx = -5cosx
4cos^2(x) + cosx = 0
4cosx + 1 = 0
cosx = -1/4

x = 104.5

I used the cos graph but the answers I was given were-

x= 90, -90, 104, -104

You have one of the answers, but you lost the other when you divided by in step 3.

From we can factor



Equating the two factors with zero gives two separate equations:

(solution on is )

and



(solution on is ).

There should not be any negative solutions, since it was stated that