Question 1045455: Please help. I would like the answer in radians. Thanks!
2cos^2x + sinx -1 =0 Found 3 solutions by josgarithmetic, ikleyn, advanced_Learner:Answer by josgarithmetic(39623) (Show Source):
You can put this solution on YOUR website! .
Please help. I would like the answer in radians. Thanks!
2cos^2x + sinx -1 =0
~~~~~~~~~~~~~~~~~~~~~~~~
First what we need to do is to reduce the given equation to the quadratic equation for sin(x).
For it, use the identity cos^2(x) = 1-sin^2(x) and replace cos^2(x) in the equation by this expression. You will get
2*(1-sin^2(x) + sin(x) - 1 = 0, or
2 - 2sin^2(x) + sin(x) - 1 = 0, or
2sin^2(x) - sin(x) - 1 = 0.
Factor left side:
(2sin(x) + 1)*(sin(x) - 1) = 0.
Now the equation deploys in two independent equations:
1. 2sin(x) + 1 = 0 ---> sin(x) = ---> x = and/or x = .
2. sin(x) - 1 = 0 ---> sin(x) = 1 ---> x = .
Answer. The solutions are x = , and .
(
