posted by Kayla on .
Hi I need to solve this question for x, where 0<x<2pi. The question is 2cos^2 x + cos x =1. Then it asks me to wrtie a general solution for it. I really don't understand how to do any of this. I just started this unit and I'm finding it so difficult. Any help would be so much appreciated.
Use algebra to solve for the variable cos x. The equation we are solving will look simler if give that cos x a new name, y.
2y^2 +y -1 = 0
That equation can be factored as follows:
(2y -1)(y+1) = 0
This means that y = 1/2 or y = -1. Both are solutions. The corresponding angles are:
60 degrees, 300 degrees and 180 degrees.