2 cos^2 θ + sin θ = 1 Find all solutions.

I tried to substitute sin theta for x and went to 2(1-x^2) +x =1 and then factor from there. Got to sintheta = -1, -1/2, but those answers aren't working. What's my problem?

Question

2 cos^2 θ + sin θ = 1 Find all solutions.

I tried to substitute sin theta for x and went to 2(1-x^2) +x =1 and then factor from there. Got to sintheta = -1, -1/2, but those answers aren't working. What's my problem?

dumbcow · Answer

your substitution is correct

dumbcow · Answer

you should get
2x^2 - x -1 = 0

(2x+1)(x-1) = 0

anonymous · Answer

Well, using that then, I get solutions of 3pi/2 +2pik, 11pi/6 +2pik, and 7pi/6 +2pik

anonymous · Answer

it's in terms of k, and we were taught to add 2*pi*k to the end of the answer

anonymous · Answer

because sin is negative in the third and fourth quadrants, i used the radians for the thirty angles in those quadrants

dumbcow · Answer

looks good except it should be pi/2 +2pik
Not 3pi/2 ...

sin theta = 1   not -1

anonymous · Answer

oh whoops. It's correct now, I feel like an idiot, thank you!

dumbcow · Answer

haha your welcome seems like you understood the concepts, just need to check the answer may i suggest using wolframalpha.com http://www.wolframalpha.com/input/?i=2cos%5E2+x+%2B+sin+x+%3D+1