SOLUTION: Solve the equation: cos 2ω + cos ω + 1 = 0 Find all solutions on [0,2π).

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the equation: cos 2ω + cos ω + 1 = 0 Find all solutions on [0,2π).      Log On


   

Question 929305: Solve the equation:
cos 2ω + cos ω + 1 = 0
Find all solutions on [0,2π).
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation:
cos 2ω + cos ω + 1 = 0
Find all solutions on [0,2π).
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cos%282x%29%2Bcosx%2B1=0
cos%5E2%28x%29-sin%5E2%28x%29%2Bcosx%2B1=0
cos%5E2%28x%29-%281-cos%5E2%28x%29%29%2Bcosx%2B1=0
cos%5E2%28x%29-1%2Bcos%5E2%28x%29%2Bcosx%2B1=0
2cos%5E2%28x%29%2Bcosx=0
cosx(2cosx+1)=0
cosx=0
x=π/2, 2π/3
or
2cosx+1=0
cosx=-1/2
x=2π/3, 4π/3 (In quadrants II and III where cos<0)