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.
trig - drwls, Thursday, March 18, 2010 at 11:13am
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.